--- /dev/null
+LIBS = -lSDL2 -lSDL2_ttf -lm
+
+PROG = balls
+
+build: $(PROG).c
+ gcc -g -o $(PROG) $(PROG).c $(LIBS)
+
+clean:
+ rm -rf $(PROG)
+
+.PHONY: clean
--- /dev/null
+/*
+ * Copyright (C) 2024 Austin Larsen
+ *
+ * This program is free software; you can redistribute it and/or modify it under
+ * the terms of the GNU General Public License as published by the Free Software
+ * Foundation; either version 2 of the License, or (at your option) any later
+ * version.
+ *
+ * This program is distributed in the hope that it will be useful, but WITHOUT
+ * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+ * FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
+ * details.
+ *
+ * You should have received a copy of the GNU General Public License along with
+ * this program; if not, write to the Free Software Foundation, Inc., 51
+ * Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+#include <SDL2/SDL.h>
+#include <stdbool.h>
+#include <stdint.h>
+#include <math.h>
+
+#define SCREEN_WIDTH_PX 1600
+#define SCREEN_HEIGHT_PX 800
+#define ACC_GRAVITY_MPS 9.81f
+#define GROUND_HEIGHT_PX 750
+
+typedef struct _Mouse {
+ int x;
+ int y;
+ uint32_t button;
+} Mouse;
+
+enum /* color */ {COLOR_RED, COLOR_GREEN, COLOR_BLUE, COLOR_ORANGE, COLOR_GREY,
+ COLOR_WHITE, COLOR_BLACK, COLOR_SIZE};
+
+void getMouse(Mouse *mouse);
+void update(SDL_Renderer *renderer, uint64_t frame, float seconds,
+ SDL_KeyCode key, Mouse *mouse);
+void
+setColor(SDL_Renderer *renderer, uint8_t color);
+
+
+
+void
+drawBall(SDL_Renderer *renderer, int px, int py, uint8_t radius, uint8_t color)
+// (x - h)^2 + (y - k)^2 = r^2
+// Drawing a circle with the standard circle formula.
+// There may be a more performant way to do this...
+{
+ setColor(renderer, color);
+
+ // diameter is radius * 2
+ for (int x = 0; x < radius * 2; x++) {
+ for (int y = 0; y < radius * 2; y++) {
+ if ( ((x - radius) * (x - radius)) +
+ ((y - radius) * (y - radius)) <=
+ radius * radius) {
+ int tx = px - radius + x;
+ int ty = py - radius + y;
+
+ // TODO: wrap circle around screen
+ SDL_RenderDrawPoint(renderer, tx, ty);
+
+ }
+ }
+ }
+}
+
+int main(void)
+{
+ SDL_Window *window;
+ SDL_Renderer *renderer;
+
+ printf("\033[2J"); // clear entire screen escape sequence
+
+ { // SDL Initialization
+ if (SDL_Init(SDL_INIT_VIDEO) != 0)
+ fprintf(stderr, "could not init video\n%s", SDL_GetError());
+
+ window = SDL_CreateWindow("Projectile",
+ SDL_WINDOWPOS_UNDEFINED,
+ SDL_WINDOWPOS_UNDEFINED,
+ SCREEN_WIDTH_PX, SCREEN_HEIGHT_PX,
+ SDL_WINDOW_SHOWN);
+
+ renderer = SDL_CreateRenderer(window, 0, SDL_RENDERER_SOFTWARE);
+ } // SDL Initialization
+
+
+ { // game loop
+ bool quit = false;
+ const uint16_t fps = 60;
+ const float mspd = (1.0f / (float)fps) * 1000.0f;
+ uint64_t frame = 0;
+ float seconds = 0;
+
+ while (!quit) {
+ uint32_t loop_start = SDL_GetTicks();
+
+ SDL_Event event;
+ SDL_KeyCode key = 0;
+ Mouse mouse;
+ bool keydown = false;
+
+ getMouse(&mouse);
+
+ while (SDL_PollEvent(&event)) {
+ switch (event.type) {
+ case SDL_KEYDOWN: {
+ if (event.key.repeat == 0) {
+ key = event.key.keysym.sym;
+ keydown = true;
+ }
+ break;
+ }
+ case SDL_KEYUP: keydown = false; break;
+ case SDL_QUIT: quit = true; break;
+ }
+ }
+
+ setColor(renderer, COLOR_BLACK);
+ SDL_RenderClear(renderer);
+ update(renderer, frame, seconds, key, &mouse);
+ SDL_RenderPresent(renderer);
+ frame++;
+ seconds = ((float)frame / (float)fps);
+
+ uint32_t loop_end = SDL_GetTicks();
+ uint32_t elapsed_time = loop_end - loop_start;
+
+ uint32_t delay = ceilf(mspd - (float)elapsed_time);
+
+ if (delay > 0) {
+ SDL_Delay(delay);
+ }
+ }
+
+ } // game loop
+
+
+ { // quit
+ SDL_DestroyRenderer(renderer);
+ SDL_DestroyWindow(window);
+ SDL_Quit();
+ } // quit
+
+}
+
+void getMouse(Mouse * mouse)
+{
+ mouse->button = SDL_GetMouseState(&mouse->x, &mouse->y);
+}
+
+void drawPath(SDL_Renderer *renderer, SDL_Point *point, float velocity,
+ float angle, float seconds)
+ // velocity in meters per second
+{
+ // REMEMBER! negative is upward and positive is downward. That is why
+ // the initial velocity for y (vi_y) is negative and acceleration due to
+ // gravity (ACC_GRAVITY_MPS) is positive
+ float vi_y = -velocity * sinf(angle);
+ float vi_x = velocity * cosf(angle);
+ float delta_x = (float)vi_x * (float)seconds;
+ float delta_y = (float)vi_y * (float)seconds + (0.5f * ACC_GRAVITY_MPS
+ * (seconds * seconds));
+
+ // SDL_Rect rect = {
+ // .x = point->x + delta_x,
+ // .y = point->y + delta_y,
+ // .w = 10,
+ // .h = 10
+ // };
+ int tx = point->x + delta_x;
+ int ty = point->y + delta_y;
+
+ if (delta_y <= -1) {
+ printf("\033[H"); // clear and set to home position escape sequence
+ printf("seconds: %f\n", seconds);
+ printf("y displacement: %f\n", delta_y);
+ printf("x displacement: %f\n", delta_x);
+ printf("x: %d\n", tx);
+ printf("y: %d\n", ty);
+ // SDL_RenderFillRect(renderer, &rect);
+ drawBall(renderer, tx, ty, 20, COLOR_BLUE);
+ }
+
+}
+
+void update(SDL_Renderer *renderer, uint64_t frame, float seconds,
+ SDL_KeyCode key, Mouse *mouse)
+{
+ static float launch_start = 0;
+ static float launch_angle = 0;
+ static float launch_initial = 0;
+
+ SDL_Point point = {
+ .x = 10,
+ .y = GROUND_HEIGHT_PX
+ };
+
+ // 0 to 90 degrees (1/2 pi)
+ setColor(renderer, COLOR_BLUE);
+ SDL_RenderDrawLine(renderer, point.x, point.y, mouse->x, mouse->y);
+
+
+ int opposite = (mouse->y - point.y);
+ int adjacent = (mouse->x - point.x);
+ float angle = -atanf((float)opposite / (float)adjacent);
+
+ setColor(renderer, COLOR_RED);
+ SDL_RenderDrawLine(renderer, 0, GROUND_HEIGHT_PX, SCREEN_WIDTH_PX,
+ GROUND_HEIGHT_PX);
+
+ if (mouse->button == 1) {
+ launch_start = seconds;
+ launch_angle = angle;
+ // hypotenuse is velocity
+ launch_initial = sqrtf((opposite * opposite) + (adjacent * adjacent));
+ }
+
+ if (launch_start > 0) {
+ drawPath(renderer, &point, launch_initial, launch_angle, seconds -
+ launch_start);
+ }
+}
+
+void
+setColor(SDL_Renderer *renderer, uint8_t color)
+{
+ const SDL_Color colors[] = {
+ [COLOR_RED] = {.r = 217, .g = 100, .b = 89, .a = 255},
+ [COLOR_WHITE] = {.r = 255, .g = 255, .b = 255, .a = 255},
+ [COLOR_GREEN] = {.r = 88, .g = 140, .b = 126, .a = 255},
+ [COLOR_BLUE] = {.r = 146, .g = 161, .b = 185, .a = 255},
+ [COLOR_ORANGE] = {.r = 242, .g = 174, .b = 114, .a = 255},
+ [COLOR_GREY] = {.r = 89, .g = 89, .b = 89, .a = 89},
+ [COLOR_BLACK] = {.r = 0, .g = 0, .b = 0, .a = 0},
+ };
+
+ SDL_SetRenderDrawColor(renderer, colors[color].r, colors[color].g,
+ colors[color].b, colors[color].a);
+}
+
--- /dev/null
+:stem:
+:source-highlighter: pygments
+:pygments-style: monokai
+:wrap: normal
+
+= Formulas
+
+* Velocity of y
+ - stem:[\Deltay = V_{0}t + 1/2at^2]
+
+* Velocity of x
+ - stem:[\Deltax = V_{0}t]
+
+* Angle of trojectory
+ - stem:[\theta = \arctan(frac{opposite}{adjactent})]
+
+* Getting initial y velocity (going downward increases in value)
+ - stem:[y_{0} = -l_0 * \sin(\theta)]
+
+* Getting initial x velocity
+ - stem:[x_{0} = l_0 * \cos(\theta)]
+
+* Pathagorean Theorem
+ - stem:[a^2 + b^2 = c^2]
+
+NOTE: launch_initial is just an intial, almost arbitrary, value. It is just a
+ distance the launch pad is from the mouse and is used to control the
+ amount of velocity you want.
--- /dev/null
+<!DOCTYPE html>
+<html lang="en">
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+</head>
+<body class="article">
+<div id="header">
+<h1>Formulas</h1>
+</div>
+<div id="content">
+<div class="ulist">
+<ul>
+<li>
+<p>Velocity of y</p>
+<div class="ulist">
+<ul>
+<li>
+<p>\$\Deltay = V_{0}t + 1/2at^2\$</p>
+</li>
+</ul>
+</div>
+</li>
+<li>
+<p>Velocity of x</p>
+<div class="ulist">
+<ul>
+<li>
+<p>\$\Deltax = V_{0}t\$</p>
+</li>
+</ul>
+</div>
+</li>
+<li>
+<p>Angle of trojectory</p>
+<div class="ulist">
+<ul>
+<li>
+<p>\$\theta = \arctan(frac{opposite}{adjactent})\$</p>
+</li>
+</ul>
+</div>
+</li>
+<li>
+<p>Getting initial y velocity (going downward increases in value)</p>
+<div class="ulist">
+<ul>
+<li>
+<p>\$y_{0} = -l_0 * \sin(\theta)\$</p>
+</li>
+</ul>
+</div>
+</li>
+<li>
+<p>Getting initial x velocity</p>
+<div class="ulist">
+<ul>
+<li>
+<p>\$x_{0} = l_0 * \cos(\theta)\$</p>
+</li>
+</ul>
+</div>
+</li>
+<li>
+<p>Pathagorean Theorem</p>
+<div class="ulist">
+<ul>
+<li>
+<p>\$a^2 + b^2 = c^2\$</p>
+</li>
+</ul>
+</div>
+</li>
+</ul>
+</div>
+<div class="admonitionblock note">
+<table>
+<tr>
+<td class="icon">
+<div class="title">Note</div>
+</td>
+<td class="content">
+launch_initial is just an intial, almost arbitrary, value. It is just a
+ distance the launch pad is from the mouse and is used to control the
+ amount of velocity you want.
+</td>
+</tr>
+</table>
+</div>
+</div>
+<div id="footer">
+<div id="footer-text">
+Last updated 2025-12-23 12:07:18 -0500
+</div>
+</div>
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+ data.math.root.display = "block"
+ }
+ return data
+ })
+})
+</script>
+<script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.9/MathJax.js?config=TeX-MML-AM_HTMLorMML"></script>
+</body>
+</html>
\ No newline at end of file
--- /dev/null
+ GNU GENERAL PUBLIC LICENSE
+ Version 2, June 1991
+
+ Copyright (C) 1989, 1991 Free Software Foundation, Inc.,
+ 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
+ Everyone is permitted to copy and distribute verbatim copies
+ of this license document, but changing it is not allowed.
+
+ Preamble
+
+ The licenses for most software are designed to take away your
+freedom to share and change it. By contrast, the GNU General Public
+License is intended to guarantee your freedom to share and change free
+software--to make sure the software is free for all its users. This
+General Public License applies to most of the Free Software
+Foundation's software and to any other program whose authors commit to
+using it. (Some other Free Software Foundation software is covered by
+the GNU Lesser General Public License instead.) You can apply it to
+your programs, too.
+
+ When we speak of free software, we are referring to freedom, not
+price. Our General Public Licenses are designed to make sure that you
+have the freedom to distribute copies of free software (and charge for
+this service if you wish), that you receive source code or can get it
+if you want it, that you can change the software or use pieces of it
+in new free programs; and that you know you can do these things.
+
+ To protect your rights, we need to make restrictions that forbid
+anyone to deny you these rights or to ask you to surrender the rights.
+These restrictions translate to certain responsibilities for you if you
+distribute copies of the software, or if you modify it.
+
+ For example, if you distribute copies of such a program, whether
+gratis or for a fee, you must give the recipients all the rights that
+you have. You must make sure that they, too, receive or can get the
+source code. And you must show them these terms so they know their
+rights.
+
+ We protect your rights with two steps: (1) copyright the software, and
+(2) offer you this license which gives you legal permission to copy,
+distribute and/or modify the software.
+
+ Also, for each author's protection and ours, we want to make certain
+that everyone understands that there is no warranty for this free
+software. If the software is modified by someone else and passed on, we
+want its recipients to know that what they have is not the original, so
+that any problems introduced by others will not reflect on the original
+authors' reputations.
+
+ Finally, any free program is threatened constantly by software
+patents. We wish to avoid the danger that redistributors of a free
+program will individually obtain patent licenses, in effect making the
+program proprietary. To prevent this, we have made it clear that any
+patent must be licensed for everyone's free use or not licensed at all.
+
+ The precise terms and conditions for copying, distribution and
+modification follow.
+
+ GNU GENERAL PUBLIC LICENSE
+ TERMS AND CONDITIONS FOR COPYING, DISTRIBUTION AND MODIFICATION
+
+ 0. This License applies to any program or other work which contains
+a notice placed by the copyright holder saying it may be distributed
+under the terms of this General Public License. The "Program", below,
+refers to any such program or work, and a "work based on the Program"
+means either the Program or any derivative work under copyright law:
+that is to say, a work containing the Program or a portion of it,
+either verbatim or with modifications and/or translated into another
+language. (Hereinafter, translation is included without limitation in
+the term "modification".) Each licensee is addressed as "you".
+
+Activities other than copying, distribution and modification are not
+covered by this License; they are outside its scope. The act of
+running the Program is not restricted, and the output from the Program
+is covered only if its contents constitute a work based on the
+Program (independent of having been made by running the Program).
+Whether that is true depends on what the Program does.
+
+ 1. You may copy and distribute verbatim copies of the Program's
+source code as you receive it, in any medium, provided that you
+conspicuously and appropriately publish on each copy an appropriate
+copyright notice and disclaimer of warranty; keep intact all the
+notices that refer to this License and to the absence of any warranty;
+and give any other recipients of the Program a copy of this License
+along with the Program.
+
+You may charge a fee for the physical act of transferring a copy, and
+you may at your option offer warranty protection in exchange for a fee.
+
+ 2. You may modify your copy or copies of the Program or any portion
+of it, thus forming a work based on the Program, and copy and
+distribute such modifications or work under the terms of Section 1
+above, provided that you also meet all of these conditions:
+
+ a) You must cause the modified files to carry prominent notices
+ stating that you changed the files and the date of any change.
+
+ b) You must cause any work that you distribute or publish, that in
+ whole or in part contains or is derived from the Program or any
+ part thereof, to be licensed as a whole at no charge to all third
+ parties under the terms of this License.
+
+ c) If the modified program normally reads commands interactively
+ when run, you must cause it, when started running for such
+ interactive use in the most ordinary way, to print or display an
+ announcement including an appropriate copyright notice and a
+ notice that there is no warranty (or else, saying that you provide
+ a warranty) and that users may redistribute the program under
+ these conditions, and telling the user how to view a copy of this
+ License. (Exception: if the Program itself is interactive but
+ does not normally print such an announcement, your work based on
+ the Program is not required to print an announcement.)
+
+These requirements apply to the modified work as a whole. If
+identifiable sections of that work are not derived from the Program,
+and can be reasonably considered independent and separate works in
+themselves, then this License, and its terms, do not apply to those
+sections when you distribute them as separate works. But when you
+distribute the same sections as part of a whole which is a work based
+on the Program, the distribution of the whole must be on the terms of
+this License, whose permissions for other licensees extend to the
+entire whole, and thus to each and every part regardless of who wrote it.
+
+Thus, it is not the intent of this section to claim rights or contest
+your rights to work written entirely by you; rather, the intent is to
+exercise the right to control the distribution of derivative or
+collective works based on the Program.
+
+In addition, mere aggregation of another work not based on the Program
+with the Program (or with a work based on the Program) on a volume of
+a storage or distribution medium does not bring the other work under
+the scope of this License.
+
+ 3. You may copy and distribute the Program (or a work based on it,
+under Section 2) in object code or executable form under the terms of
+Sections 1 and 2 above provided that you also do one of the following:
+
+ a) Accompany it with the complete corresponding machine-readable
+ source code, which must be distributed under the terms of Sections
+ 1 and 2 above on a medium customarily used for software interchange; or,
+
+ b) Accompany it with a written offer, valid for at least three
+ years, to give any third party, for a charge no more than your
+ cost of physically performing source distribution, a complete
+ machine-readable copy of the corresponding source code, to be
+ distributed under the terms of Sections 1 and 2 above on a medium
+ customarily used for software interchange; or,
+
+ c) Accompany it with the information you received as to the offer
+ to distribute corresponding source code. (This alternative is
+ allowed only for noncommercial distribution and only if you
+ received the program in object code or executable form with such
+ an offer, in accord with Subsection b above.)
+
+The source code for a work means the preferred form of the work for
+making modifications to it. For an executable work, complete source
+code means all the source code for all modules it contains, plus any
+associated interface definition files, plus the scripts used to
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+anything that is normally distributed (in either source or binary
+form) with the major components (compiler, kernel, and so on) of the
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+
+If distribution of executable or object code is made by offering
+access to copy from a designated place, then offering equivalent
+access to copy the source code from the same place counts as
+distribution of the source code, even though third parties are not
+compelled to copy the source along with the object code.
+
+ 4. You may not copy, modify, sublicense, or distribute the Program
+except as expressly provided under this License. Any attempt
+otherwise to copy, modify, sublicense or distribute the Program is
+void, and will automatically terminate your rights under this License.
+However, parties who have received copies, or rights, from you under
+this License will not have their licenses terminated so long as such
+parties remain in full compliance.
+
+ 5. You are not required to accept this License, since you have not
+signed it. However, nothing else grants you permission to modify or
+distribute the Program or its derivative works. These actions are
+prohibited by law if you do not accept this License. Therefore, by
+modifying or distributing the Program (or any work based on the
+Program), you indicate your acceptance of this License to do so, and
+all its terms and conditions for copying, distributing or modifying
+the Program or works based on it.
+
+ 6. Each time you redistribute the Program (or any work based on the
+Program), the recipient automatically receives a license from the
+original licensor to copy, distribute or modify the Program subject to
+these terms and conditions. You may not impose any further
+restrictions on the recipients' exercise of the rights granted herein.
+You are not responsible for enforcing compliance by third parties to
+this License.
+
+ 7. If, as a consequence of a court judgment or allegation of patent
+infringement or for any other reason (not limited to patent issues),
+conditions are imposed on you (whether by court order, agreement or
+otherwise) that contradict the conditions of this License, they do not
+excuse you from the conditions of this License. If you cannot
+distribute so as to satisfy simultaneously your obligations under this
+License and any other pertinent obligations, then as a consequence you
+may not distribute the Program at all. For example, if a patent
+license would not permit royalty-free redistribution of the Program by
+all those who receive copies directly or indirectly through you, then
+the only way you could satisfy both it and this License would be to
+refrain entirely from distribution of the Program.
+
+If any portion of this section is held invalid or unenforceable under
+any particular circumstance, the balance of the section is intended to
+apply and the section as a whole is intended to apply in other
+circumstances.
+
+It is not the purpose of this section to induce you to infringe any
+patents or other property right claims or to contest validity of any
+such claims; this section has the sole purpose of protecting the
+integrity of the free software distribution system, which is
+implemented by public license practices. Many people have made
+generous contributions to the wide range of software distributed
+through that system in reliance on consistent application of that
+system; it is up to the author/donor to decide if he or she is willing
+to distribute software through any other system and a licensee cannot
+impose that choice.
+
+This section is intended to make thoroughly clear what is believed to
+be a consequence of the rest of this License.
+
+ 8. If the distribution and/or use of the Program is restricted in
+certain countries either by patents or by copyrighted interfaces, the
+original copyright holder who places the Program under this License
+may add an explicit geographical distribution limitation excluding
+those countries, so that distribution is permitted only in or among
+countries not thus excluded. In such case, this License incorporates
+the limitation as if written in the body of this License.
+
+ 9. The Free Software Foundation may publish revised and/or new versions
+of the General Public License from time to time. Such new versions will
+be similar in spirit to the present version, but may differ in detail to
+address new problems or concerns.
+
+Each version is given a distinguishing version number. If the Program
+specifies a version number of this License which applies to it and "any
+later version", you have the option of following the terms and conditions
+either of that version or of any later version published by the Free
+Software Foundation. If the Program does not specify a version number of
+this License, you may choose any version ever published by the Free Software
+Foundation.
+
+ 10. If you wish to incorporate parts of the Program into other free
+programs whose distribution conditions are different, write to the author
+to ask for permission. For software which is copyrighted by the Free
+Software Foundation, write to the Free Software Foundation; we sometimes
+make exceptions for this. Our decision will be guided by the two goals
+of preserving the free status of all derivatives of our free software and
+of promoting the sharing and reuse of software generally.
+
+ NO WARRANTY
+
+ 11. BECAUSE THE PROGRAM IS LICENSED FREE OF CHARGE, THERE IS NO WARRANTY
+FOR THE PROGRAM, TO THE EXTENT PERMITTED BY APPLICABLE LAW. EXCEPT WHEN
+OTHERWISE STATED IN WRITING THE COPYRIGHT HOLDERS AND/OR OTHER PARTIES
+PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESSED
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+TO THE QUALITY AND PERFORMANCE OF THE PROGRAM IS WITH YOU. SHOULD THE
+PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF ALL NECESSARY SERVICING,
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+
+ 12. IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING
+WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MAY MODIFY AND/OR
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+OUT OF THE USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED
+TO LOSS OF DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY
+YOU OR THIRD PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER
+PROGRAMS), EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE
+POSSIBILITY OF SUCH DAMAGES.
+
+ END OF TERMS AND CONDITIONS
+
+ How to Apply These Terms to Your New Programs
+
+ If you develop a new program, and you want it to be of the greatest
+possible use to the public, the best way to achieve this is to make it
+free software which everyone can redistribute and change under these terms.
+
+ To do so, attach the following notices to the program. It is safest
+to attach them to the start of each source file to most effectively
+convey the exclusion of warranty; and each file should have at least
+the "copyright" line and a pointer to where the full notice is found.
+
+ <one line to give the program's name and a brief idea of what it does.>
+ Copyright (C) <year> <name of author>
+
+ This program is free software; you can redistribute it and/or modify
+ it under the terms of the GNU General Public License as published by
+ the Free Software Foundation; either version 2 of the License, or
+ (at your option) any later version.
+
+ This program is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+ GNU General Public License for more details.
+
+ You should have received a copy of the GNU General Public License along
+ with this program; if not, write to the Free Software Foundation, Inc.,
+ 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+Also add information on how to contact you by electronic and paper mail.
+
+If the program is interactive, make it output a short notice like this
+when it starts in an interactive mode:
+
+ Gnomovision version 69, Copyright (C) year name of author
+ Gnomovision comes with ABSOLUTELY NO WARRANTY; for details type `show w'.
+ This is free software, and you are welcome to redistribute it
+ under certain conditions; type `show c' for details.
+
+The hypothetical commands `show w' and `show c' should show the appropriate
+parts of the General Public License. Of course, the commands you use may
+be called something other than `show w' and `show c'; they could even be
+mouse-clicks or menu items--whatever suits your program.
+
+You should also get your employer (if you work as a programmer) or your
+school, if any, to sign a "copyright disclaimer" for the program, if
+necessary. Here is a sample; alter the names:
+
+ Yoyodyne, Inc., hereby disclaims all copyright interest in the program
+ `Gnomovision' (which makes passes at compilers) written by James Hacker.
+
+ <signature of Ty Coon>, 1 April 1989
+ Ty Coon, President of Vice
+
+This General Public License does not permit incorporating your program into
+proprietary programs. If your program is a subroutine library, you may
+consider it more useful to permit linking proprietary applications with the
+library. If this is what you want to do, use the GNU Lesser General
+Public License instead of this License.
--- /dev/null
+#!/usr/bin/env bash
+. docinfo.conf
+
+clean () {
+rm -rf diag*.png
+rm -rf $(find . \
+ -type f \
+ -regex '.*\.html' \
+ -not -name "rendered.html" \
+ | grep -v docinfo)
+}
+
+build () {
+FILENAME="$(find . -type f -name "*.adoc" -not -name "README.adoc" -not -name "notes.adoc")"
+asciidoctor -b html5 $FILENAME
+}
+
+make () {
+ clean
+ build
+}
+
+# use this to call one of the above functions
+$@
--- /dev/null
+= Balls
+
+This repository has physics examples using balls. Each folder has a different
+example, with a link to the formulas used in the readme's.
+
+== 2D Projectile Motion
+checkout this link
+https://nyquistdev.net/git/?p=balls.git;a=blob_plain;f=2d-projectile-motion/docs/formulas.html;hb=HEAD[formulas].
+for a list of forumlas used.
+
+[%header,cols="1,1"]
+|===
+| control | action
+| right-click and drag | determine direction and velocity of ball
+| right-click release | launch ball
+|===
+
+== Bouncing
+check out this link
+https://nyquistdev.net/git/?p=balls.git;a=blob_plain;f=bounce/docs/formulas.html;hb=HEAD[formulas].
+for the formulas used.
+
+== Collisions
+Creates random balls. These balls will resolve any collision issues. Launching a
+ball will show you an example of elastic collision.
+
+checkout this link
+https://nyquistdev.net/git/?p=balls.git;a=blob_plain;f=collisions/docs/formulas.html;hb=HEAD[formulas].
+for a list of forumlas used.
+
+[%header,cols="1,1"]
+|===
+| control | action
+| right-click | select ball
+| right-click and left-click and drag | flings ball on release, the distance
+ away from the ball determines the amount
+ of velocity to launch the ball at
+|===
+
+== Building html from formula _.adoc_ files
+
+----
+./Makehtml make
+----
+
+== Links
+* https://www.studyplan.dev/sdl2/sdl2-relative-mode[sdl2-relative-mouse-mode]
+* https://www.youtube.com/watch?v=XJnIdRXUi7A&t=315s[permutations and combinations]
+* https://www.youtube.com/watch?v=CFbo_nBdBco[OCT | Elastic Collisions]
+* https://www.wikihow.com/Normalize-a-Vector[Normalizing a Vector]
+* https://www.youtube.com/watch?v=Fp7D5D8Bqjc[conservation of Momentum]
+
--- /dev/null
+LIBS = -lSDL2 -lSDL2_ttf -lm
+
+PROG = balls
+
+build: $(PROG).c
+ gcc -g -o $(PROG) $(PROG).c $(LIBS)
+
+clean:
+ rm -rf $(PROG)
+
+.PHONY: clean
--- /dev/null
+#include <stdio.h>
+#include <SDL2/SDL.h>
+#include <stdbool.h>
+#include <SDL2/SDL_ttf.h>
+#include <assert.h>
+#include <stdint.h>
+#include <math.h>
+#include <SDL2/SDL_rect.h>
+
+// NOTE:
+// This is a less accurate depiction of gravity. I am using a different number
+// as the mesurement in meters per second because you cannot have fractions of a
+// pixel. In order to depict this more accurately I would need an approximate
+// size of a pixel, and not every pixel is the same size. I have decided not to
+// be THAT accurate.
+#define METER_AS_PIXELS 3779U
+// #define GRAVITY 0.5f
+
+#define END(check, str1, str2) \
+ if (check) { \
+ assert(check); \
+ fprintf(stderr, "%s\n%s", str1, str2); \
+ exit(1); \
+ } \
+
+#define SDL_main main
+
+
+typedef struct _Game {
+ SDL_Renderer *renderer;
+ SDL_Window *window;
+ bool out_of_bounds;
+ uint16_t fps;
+ float gravity;
+ float terminal_velocity;
+ SDL_Rect screen_rect;
+} Game;
+
+typedef struct _Ball {
+ SDL_Point center;
+ SDL_Point velocities;
+ uint16_t radius;
+ bool down; // check if the ball is
+ // these two varaibles reset with each fall
+ float time_falling; // time it takes to fall from peak
+ float height_falling; // max height for each fall
+ float e; // restition value
+} Ball;
+
+typedef uint8_t (*Update_callback) (Game *game,
+ float seconds,
+ uint64_t frame,
+ SDL_KeyCode key,
+ bool keydown);
+
+enum {UPDATE_MAIN, UPDATE_NOTHING};
+
+enum {COLOR_RED, COLOR_GREEN, COLOR_BLUE, COLOR_ORANGE, COLOR_GREY,
+ COLOR_BLACK, COLOR_SIZE};
+
+void
+setColor(SDL_Renderer *renderer,
+ uint8_t color)
+{
+ const SDL_Color colors[] = {
+ [COLOR_RED] = {.r = 217, .g = 100, .b = 89, .a = 255},
+ [COLOR_GREEN] = {.r = 88, .g = 140, .b = 126, .a = 255},
+ [COLOR_BLUE] = {.r = 146, .g = 161, .b = 185, .a = 255},
+ [COLOR_ORANGE] = {.r = 242, .g = 174, .b = 114, .a = 255},
+ [COLOR_GREY] = {.r = 89, .g = 89, .b = 89, .a = 89},
+ [COLOR_BLACK] = {.r = 0, .g = 0, .b = 0, .a = 0},
+ };
+
+ SDL_SetRenderDrawColor(renderer, colors[color].r, colors[color].g,
+ colors[color].b, colors[color].a);
+}
+
+void
+drawCircle(SDL_Renderer *renderer,
+ int radius,
+ SDL_Point center,
+ uint8_t color)
+// (x - h)^2 + (y - k)^2 = r^2
+// Drawing a circle with the standard circle formula.
+// There may be a more performant way to do this...
+{
+ int size = radius;
+ setColor(renderer, color);
+
+ // diameter is radius * 2
+ for (int x = 0; x < radius * 2; x++) {
+ for (int y = 0; y < radius * 2; y++) {
+ if (((x - size)*(x - size)) + ((y - size)*(y - size)) <= radius
+ * radius)
+ SDL_RenderDrawPoint(renderer, center.x - radius + x, center.y - radius + y);
+ }
+ }
+}
+
+float clamp(float v, float min, float max) {
+ if (v < min) return min;
+ if (v > max) return max;
+ return v;
+}
+
+bool circleRectCollide(SDL_Point circle,
+ float r,
+ SDL_Rect rect)
+{
+ float closestX = clamp(circle.x, rect.x, rect.x + rect.w);
+ float closestY = clamp(circle.y, rect.y, rect.y + rect.h);
+
+ // this gets the distance form the center of the circle to a side of a
+ // rectangle. It could be negative or positive. Because we are squaring them
+ // it doesn't matter.
+ float dx = circle.x - closestX;
+ float dy = circle.y - closestY;
+
+ // use the dot product to determine collision
+ return (dx*dx + dy*dy) <= (r*r);
+}
+
+static uint8_t
+updateNothing(Game *game,
+ float seconds,
+ uint64_t frame,
+ SDL_KeyCode key,
+ bool keydown)
+{
+ return UPDATE_NOTHING;
+}
+
+void
+worldBoundry(Game *game, Ball *ball)
+{
+ int padding = 1;
+
+ if (ball->center.x - ball->radius <= 0) {
+ ball->center.x = ball->radius + padding;
+ }
+
+ if (ball->center.y - ball->radius <= 0) {
+ ball->center.y = ball->radius + padding;
+ }
+
+ if (ball->center.x + ball->radius >= game->screen_rect.w) {
+ ball->center.x = game->screen_rect.w - ball->radius - padding;
+ }
+
+ if (ball->center.y + ball->radius >= game->screen_rect.h) {
+ ball->center.y = game->screen_rect.h - ball->radius - padding;
+ }
+}
+
+static uint8_t
+updateMain(Game *game,
+ float seconds,
+ uint64_t frame,
+ SDL_KeyCode key,
+ bool keydown)
+{
+ // as long as gravity and time are using the same units the fomrulas will
+ // work. in this case we will do frames as out unit
+ // * Rubber ball: (e \approx 0.8 - 0.9)
+ // * Basketball: (e \approx 0.75)
+ // * Tennis ball: (e \approx 0.6)
+ static Ball ball = {
+ .center = {.x = 400, .y = 400},
+ .radius = 30,
+ .down = true,
+ .e = 0.9f
+ };
+
+ static float initial_y = 400;
+ static float y = 400;
+ static float restitution = 1;
+ static float f = 0;
+ static float acceleration = 0;
+
+
+ if (ball.down) // falling downward
+ acceleration += (game->gravity * f);
+ else
+ acceleration -= restitution - (game->gravity * f);
+
+ // clip this to world border
+ ball.center.y = y + acceleration;
+
+ // ball.height_falling = initial_y + (0.5f * game->gravity) * (f * f);
+
+ // ball.time_falling = sqrt(2 * (initial_y - ball.radius) / game->gravity);
+ //
+ // This if statement cannot be used because
+ // if (f > time && ball.down) {
+ if ((ball.center.y + ball.radius >= game->screen_rect.h) &&
+ restitution >= 0) {
+ f = 0;
+ ball.down = false;
+ restitution *= ball.e;
+ }
+
+ worldBoundry(game, &ball);
+
+ // Should not go out of bounds. but check if it does
+ game->out_of_bounds =
+ !circleRectCollide(ball.center, ball.radius, game->screen_rect);
+
+ drawCircle(game->renderer, ball.radius, ball.center, COLOR_RED);
+ f++;
+
+ return UPDATE_MAIN;
+}
+
+void
+Game_Update(Game *game)
+// The main game loop. Sets up which callback will be used in the function loop.
+// Each update callback determines what update callback will be called next by
+// returning the appropriate enum value
+{
+ uint64_t frame = 0;
+ bool quit = false;
+ bool keydown = false;
+ uint8_t update_id = 0;
+ Update_callback update;
+ float mspd = (1.0f / (float)game->fps) * 1000.0f;
+ float seconds = 0;
+ SDL_Event event;
+ SDL_KeyCode key = 0;
+ uint32_t end = 0;
+ uint32_t elapsed_time = 0;
+ uint8_t color = COLOR_BLACK;
+
+ while (!quit) {
+ uint32_t start = SDL_GetTicks();
+ // clear screen
+ if (game->out_of_bounds) color = COLOR_GREEN;
+ setColor(game->renderer, color);
+ SDL_RenderClear(game->renderer);
+ // TODO:
+ // find milliseconds so you can update gravity more acurately
+ // (1 / frame)
+ seconds = ((float)frame / (float)game->fps);
+ // printf("%lu: %f\n", frame, seconds);
+
+
+ // Place update functions here
+ switch (update_id) {
+ case UPDATE_MAIN: update = updateMain; break;
+ case UPDATE_NOTHING: update = updateNothing; break;
+ // case UPDATE_LOSE: update = updateLose; break;
+ }
+
+
+
+ while (SDL_PollEvent(&event)) {
+ switch (event.type) {
+ case SDL_KEYDOWN: {
+ if (event.key.repeat == 0) {
+ key = event.key.keysym.sym;
+ keydown = true;
+ }
+
+ break;
+ }
+
+ case SDL_KEYUP: keydown = false; break;
+ case SDL_QUIT: quit = true; break;
+ }
+ }
+
+ update_id = update(game, seconds, frame, key, keydown);
+
+ end = SDL_GetTicks();
+ elapsed_time = end - start;
+
+ if (elapsed_time < mspd) {
+ elapsed_time = mspd - elapsed_time;
+ SDL_Delay(elapsed_time);
+ }
+
+ SDL_RenderPresent(game->renderer);
+ frame++;
+ }
+}
+
+void
+Game_Init(Game *game)
+// All the variable and data initialization needed for SDL and perhaps game
+// variables
+{
+ memset(game, 0, sizeof(Game));
+ game->screen_rect.x = 0;
+ game->screen_rect.y = 0;
+ game->screen_rect.w = 800;
+ game->screen_rect.h = 800;
+
+ END(SDL_Init(SDL_INIT_VIDEO) != 0, "Could not create texture",
+ SDL_GetError());
+
+ END(TTF_Init() != 0, "Could not initialize TTF", TTF_GetError());
+
+
+
+ game->window = SDL_CreateWindow("balls", SDL_WINDOWPOS_UNDEFINED,
+ SDL_WINDOWPOS_UNDEFINED, game->screen_rect.w,
+ game->screen_rect.h, SDL_WINDOW_SHOWN);
+
+ END(game->window == NULL, "Could not create window", SDL_GetError());
+
+ game->renderer = SDL_CreateRenderer(game->window, 0,
+ SDL_RENDERER_SOFTWARE);
+
+ END(game->renderer == NULL, "Could not create renderer", SDL_GetError());
+ game->fps = 400;
+ // game->terminal_velocity =
+ game->gravity = 0.004f;
+}
+
+void
+Game_Quit(Game *game)
+{
+ SDL_DestroyWindow(game->window);
+ SDL_DestroyRenderer(game->renderer);
+ TTF_Quit();
+ SDL_Quit();
+}
+
+int
+main(void)
+{
+ Game game;
+ Game_Init(&game);
+ Game_Update(&game);
+ Game_Quit(&game);
+ return 0;
+}
--- /dev/null
+Below is a clear explanation of **circle–circle collision detection**, including the **math formulas** and **C code examples**.
+
+---
+
+# ✅ **Math Behind Circle Collision**
+
+Two circles collide (intersect or touch) when the **distance between their centers** is **less than or equal to** the **sum of their radii**.
+
+Let:
+
+* Circle 1 center: ((x_1, y_1)), radius (r_1)
+* Circle 2 center: ((x_2, y_2)), radius (r_2)
+
+### **1. Compute distance between centers**
+
+[
+d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
+]
+
+### **2. Collision condition**
+
+[
+d \le r_1 + r_2
+]
+
+A common optimization is to avoid the expensive `sqrt()`:
+
+### **Squared distance method (no sqrt)**
+
+[
+(x_2 - x_1)^2 + (y_2 - y_1)^2 \le (r_1 + r_2)^2
+]
+
+This is identical mathematically, but faster.
+
+---
+
+# ✅ **C Example: Basic Circle Collision Check**
+
+```c
+#include <stdio.h>
+#include <math.h>
+#include <stdbool.h>
+
+typedef struct {
+ float x;
+ float y;
+ float r;
+} Circle;
+
+bool circlesCollide(Circle a, Circle b) {
+ float dx = b.x - a.x;
+ float dy = b.y - a.y;
+ float distance = sqrtf(dx * dx + dy * dy);
+
+ return distance <= (a.r + b.r);
+}
+
+int main() {
+ Circle c1 = {0.0f, 0.0f, 5.0f};
+ Circle c2 = {6.0f, 0.0f, 5.0f};
+
+ if (circlesCollide(c1, c2)) {
+ printf("Circles collide!\n");
+ } else {
+ printf("No collision.\n");
+ }
+
+ return 0;
+}
+```
+
+---
+
+# ✅ **C Example: Optimized (No sqrt)**
+
+```c
+#include <stdio.h>
+#include <stdbool.h>
+
+typedef struct {
+ float x;
+ float y;
+ float r;
+} Circle;
+
+bool circlesCollideFast(Circle a, Circle b) {
+ float dx = b.x - a.x;
+ float dy = b.y - a.y;
+
+ float distanceSquared = dx * dx + dy * dy;
+ float radiusSum = a.r + b.r;
+
+ return distanceSquared <= radiusSum * radiusSum;
+}
+
+int main() {
+ Circle c1 = {0.0f, 0.0f, 5.0f};
+ Circle c2 = {6.0f, 0.0f, 5.0f};
+
+ if (circlesCollideFast(c1, c2)) {
+ printf("Circles collide!\n");
+ } else {
+ printf("No collision.\n");
+ }
+
+ return 0;
+}
+```
+
+---
+
+# 🚀 **Example Output**
+
+For the sample circles, they collide because distance = 6 and r1 + r2 = 10.
+
+```
+Circles collide!
+```
+
+---
+
+# 🧠 Optional: Collision Penetration Depth (Extra Useful)
+
+Sometimes you want *how much* they overlap:
+
+[
+\text{penetration} = (r_1 + r_2) - d
+]
+
+C example:
+
+```c
+float penetrationDepth(Circle a, Circle b) {
+ float dx = b.x - a.x;
+ float dy = b.y - a.y;
+ float d = sqrtf(dx * dx + dy * dy);
+ return (a.r + b.r) - d;
+}
+```
+
+---
+
+If you'd like, I can also show:
+
+✅ Circle vs Rectangle collision
+✅ Circle movement simulation
+✅ Game-loop example using SDL2
+✅ Visual ASCII output
+
+Just tell me!
--- /dev/null
+```c
+#include <SDL2/SDL.h>
+#include <stdbool.h>
+#include <math.h>
+
+// -----------------------------------------
+// Utility functions
+// -----------------------------------------
+float clamp(float v, float min, float max) {
+ if (v < min) return min;
+ if (v > max) return max;
+ return v;
+}
+
+bool circleRectCollide(float cx, float cy, float r,
+ float rx, float ry, float rw, float rh)
+{
+ float closestX = clamp(cx, rx, rx + rw);
+ float closestY = clamp(cy, ry, ry + rh);
+
+ float dx = cx - closestX;
+ float dy = cy - closestY;
+
+ return (dx*dx + dy*dy) <= (r*r);
+}
+
+// -----------------------------------------
+// Main SDL demo
+// -----------------------------------------
+int main() {
+ SDL_Init(SDL_INIT_VIDEO);
+
+ SDL_Window* window = SDL_CreateWindow(
+ "Circle vs Rectangle Collision - SDL2",
+ SDL_WINDOWPOS_CENTERED, SDL_WINDOWPOS_CENTERED,
+ 800, 600,
+ SDL_WINDOW_SHOWN
+ );
+
+ SDL_Renderer* renderer = SDL_CreateRenderer(window, -1, SDL_RENDERER_ACCELERATED);
+
+ // Circle properties
+ float cx = 100.0f;
+ float cy = 100.0f;
+ float cr = 25.0f;
+ float speed = 200.0f; // pixels per second
+
+ // Rectangle properties
+ float rx = 400.0f;
+ float ry = 250.0f;
+ float rw = 150.0f;
+ float rh = 100.0f;
+
+ Uint32 last = SDL_GetTicks();
+ bool running = true;
+
+ while (running) {
+ Uint32 now = SDL_GetTicks();
+ float dt = (now - last) / 1000.0f;
+ last = now;
+
+ // ------------------
+ // Input
+ // ------------------
+ SDL_Event e;
+ while (SDL_PollEvent(&e)) {
+ if (e.type == SDL_QUIT) running = false;
+ }
+
+ const Uint8* keys = SDL_GetKeyboardState(NULL);
+ if (keys[SDL_SCANCODE_ESCAPE]) running = false;
+
+ // Move circle
+ if (keys[SDL_SCANCODE_W]) cy -= speed * dt;
+ if (keys[SDL_SCANCODE_S]) cy += speed * dt;
+ if (keys[SDL_SCANCODE_A]) cx -= speed * dt;
+ if (keys[SDL_SCANCODE_D]) cx += speed * dt;
+
+ // ------------------
+ // Collision check
+ // ------------------
+ bool hit = circleRectCollide(cx, cy, cr, rx, ry, rw, rh);
+
+ // ------------------
+ // Render
+ // ------------------
+ SDL_SetRenderDrawColor(renderer, 20, 20, 20, 255);
+ SDL_RenderClear(renderer);
+
+ // Rectangle (turn red when hit)
+ if (hit)
+ SDL_SetRenderDrawColor(renderer, 255, 50, 50, 255);
+ else
+ SDL_SetRenderDrawColor(renderer, 100, 100, 255, 255);
+
+ SDL_Rect rect = { (int)rx, (int)ry, (int)rw, (int)rh };
+ SDL_RenderFillRect(renderer, &rect);
+
+ // Draw circle (simple filled circle)
+ SDL_SetRenderDrawColor(renderer, 200, 200, 200, 255);
+ for (int w = 0; w < cr * 2; w++) {
+ for (int h = 0; h < cr * 2; h++) {
+ int dx = cr - w;
+ int dy = cr - h;
+ if ((dx*dx + dy*dy) <= (cr * cr)) {
+ SDL_RenderDrawPoint(renderer, cx + dx, cy + dy);
+ }
+ }
+ }
+
+ SDL_RenderPresent(renderer);
+ }
+
+ SDL_DestroyRenderer(renderer);
+ SDL_DestroyWindow(window);
+ SDL_Quit();
+ return 0;
+}
+```
--- /dev/null
+Below is a clear explanation of **Circle vs Rectangle collision detection**, including **math formulas**, **edge-case handling**, and **C programming examples**.
+
+---
+
+# 🟢 **Circle vs Axis-Aligned Rectangle Collision**
+
+We assume the rectangle is **axis-aligned (AABB)** and defined by:
+
+* Rectangle min corner: ((rx, ry))
+* Width (w), height (h)
+* So max corner is ((rx+w,; ry+h))
+
+Circle:
+
+* Center: ((cx, cy))
+* Radius (r)
+
+---
+
+# ✅ **Math Formula (Shortest Distance Method)**
+
+The basic idea:
+
+1. **Clamp** the circle center to the edges of the rectangle
+2. Compute the closest point **inside the rectangle**
+3. Compute distance from the circle center to that point
+4. If distance ≤ radius → collision
+
+### 1. Clamp function
+
+[
+\text{clamp}(v, min, max) = \max(min,;\min(v, max))
+]
+
+### 2. Closest point on rectangle to circle
+
+[
+\text{closestX} = \text{clamp}(cx,; rx,; rx+w)
+]
+[
+\text{closestY} = \text{clamp}(cy,; ry,; ry+h)
+]
+
+### 3. Distance from circle to closest point
+
+[
+dx = cx - \text{closestX}
+]
+[
+dy = cy - \text{closestY}
+]
+
+### 4. Collision rule
+
+[
+dx^2 + dy^2 \le r^2
+]
+
+No square root needed → fast.
+
+---
+
+# 🟦 **C Code Example: Circle vs Rectangle Collision**
+
+```c
+#include <stdio.h>
+#include <stdbool.h>
+
+float clamp(float value, float min, float max) {
+ if (value < min) return min;
+ if (value > max) return max;
+ return value;
+}
+
+typedef struct {
+ float x, y; // top-left corner
+ float w, h;
+} Rect;
+
+typedef struct {
+ float x, y; // center
+ float r;
+} Circle;
+
+bool circleRectCollide(Circle c, Rect r) {
+ // Find the closest point on the rectangle to the circle
+ float closestX = clamp(c.x, r.x, r.x + r.w);
+ float closestY = clamp(c.y, r.y, r.y + r.h);
+
+ // Compute distance from circle center to that point
+ float dx = c.x - closestX;
+ float dy = c.y - closestY;
+
+ // If within radius, collision
+ return (dx * dx + dy * dy) <= (c.r * c.r);
+}
+
+int main() {
+ Circle c = { 5.0f, 5.0f, 3.0f };
+ Rect r = { 7.0f, 4.0f, 6.0f, 4.0f };
+
+ if (circleRectCollide(c, r)) {
+ printf("Collision!\n");
+ } else {
+ printf("No collision.\n");
+ }
+}
+```
+
+---
+
+# 🧪 **Explanation of the above example**
+
+Circle at (5,5), radius 3
+Rectangle at (7,4), size 6×4
+
+The closest point on the rect to the circle is (7,5).
+Distance = 2 → less than radius 3 → collision.
+
+---
+
+# 🧠 Extra: Detecting Penetration Vector / Push-out Direction
+
+If you're making a game, you often need to **push the circle out** of the rectangle.
+
+Short version:
+
+1. Compute closest point
+2. Compute distance
+3. Compute penetration vector
+
+Example:
+
+```c
+#include <math.h>
+
+void circleRectPenetration(Circle c, Rect r, float *outX, float *outY) {
+ float closestX = clamp(c.x, r.x, r.x + r.w);
+ float closestY = clamp(c.y, r.y, r.y + r.h);
+
+ float dx = c.x - closestX;
+ float dy = c.y - closestY;
+
+ float distSq = dx*dx + dy*dy;
+ float dist = sqrtf(distSq);
+
+ float penetration = c.r - dist;
+
+ if (penetration > 0) {
+ *outX = (dx / dist) * penetration;
+ *outY = (dy / dist) * penetration;
+ } else {
+ *outX = *outY = 0.0f;
+ }
+}
+```
+
+This gives the shortest vector needed to push the circle out of the rectangle.
+
+---
+
+# Want more?
+
+I can also show:
+
+✔ **Circle vs rotated rectangle (OBB)**
+✔ **Collision response (velocity reflection)**
+✔ **Graphical ASCII demo**
+✔ **SDL2 example with moving circle and rectangle**
+
+Just tell me!
--- /dev/null
+Below is a **clear physics explanation**, the **math**, and **C programming examples** showing how to simulate a bouncing ball.
+
+---
+
+# 🌟 **Physics of a Bouncing Ball**
+
+A bouncing ball is controlled by three main ideas:
+
+---
+
+# 1️⃣ **Gravity Accelerates the Ball Downward**
+
+The ball’s vertical motion follows:
+
+[
+h(t) = h_0 - \tfrac{1}{2} g t^2
+]
+
+Velocity increases downward as:
+
+[
+v(t) = -gt
+]
+
+Where:
+
+* (h) = height
+* (g = 9.8\ \text{m/s}^2)
+* (v) = velocity
+* Downward is negative
+
+---
+
+# 2️⃣ **Impact With the Ground**
+
+When the ball hits the ground, it changes direction.
+
+A real ball **does NOT return to full height**; some energy is lost.
+
+This is described using the **coefficient of restitution**, (e):
+
+[
+e = \frac{v_{\text{after}}}{v_{\text{before}}}
+]
+
+Typical values:
+
+* Rubber ball: (e \approx 0.8 - 0.9)
+* Basketball: (e \approx 0.75)
+* Tennis ball: (e \approx 0.6)
+
+Meaning:
+
+* If velocity before impact is (-10\ \text{m/s})
+* With (e = 0.8), after impact:
+ [
+ v_{\text{after}} = -e \cdot v_{\text{before}} = 8\ \text{m/s}
+ ]
+
+(The sign flips because the direction reverses.)
+
+---
+
+# 3️⃣ **Each Bounce Gets Shorter**
+
+Because energy is lost each bounce, the maximum height shrinks:
+
+[
+h_{\text{after}} = e^2 \cdot h_{\text{before}}
+]
+
+---
+
+# ⭐ **MATHEMATICAL MODEL**
+
+Let:
+
+* (h) = current height
+* (v) = velocity
+* (dt) = time step
+
+Update each frame:
+
+### Gravity:
+
+[
+v = v - g \cdot dt
+]
+
+### Position:
+
+[
+h = h + v \cdot dt
+]
+
+### Bounce:
+
+If (h < 0):
+[
+h = 0
+]
+[
+v = -e \cdot v
+]
+
+---
+
+# 🖥️ **C Programming Example — Simple Bounce Simulation**
+
+This uses a time-step loop to simulate the ball in text mode.
+
+```c
+#include <stdio.h>
+
+int main() {
+ double h = 10.0; // initial height in meters
+ double v = 0.0; // initial velocity
+ double g = 9.8; // gravity
+ double e = 0.8; // coefficient of restitution
+ double dt = 0.01; // time step (seconds)
+
+ for (int i = 0; i < 5000; i++) {
+ // apply gravity
+ v = v - g * dt;
+
+ // update position
+ h = h + v * dt;
+
+ // bounce
+ if (h < 0) {
+ h = 0;
+ v = -v * e;
+ }
+
+ printf("time = %.2f s, height = %.3f m, velocity = %.3f m/s\n",
+ i * dt, h, v);
+ }
+
+ return 0;
+}
+```
+
+This produces output like:
+
+```
+time = 0.00 s, height = 9.999 m, velocity = -0.098 m/s
+time = 0.01 s, height = 9.997 m, velocity = -0.196 m/s
+...
+Bounce!
+...
+```
+
+A very realistic-looking bounce.
+
+---
+
+# 🖥️ **C Example — Detecting Ground Collision Inside a Loop**
+
+```c
+if (h <= 0) {
+ h = 0;
+ v = -v * e; // reverse and reduce velocity
+}
+```
+
+This is the typical “bounce line” used in game loops.
+
+---
+
+# 🖥️ **C Example — Continuous Simulation with ASCII Display**
+
+```c
+#include <stdio.h>
+#include <unistd.h>
+
+int main() {
+ double h = 20.0;
+ double v = 0.0;
+ double g = 9.8;
+ double e = 0.85;
+ double dt = 0.02;
+
+ while (1) {
+ v = v - g * dt;
+ h = h + v * dt;
+
+ if (h < 0) {
+ h = 0;
+ v = -v * e;
+ }
+
+ int screen_height = 25;
+ int pos = (int)(screen_height - h);
+
+ printf("\033[2J\033[1;1H"); // clear screen
+ for (int i = 0; i < pos; i++) printf("\n");
+ printf(" o\n"); // the ball
+ fflush(stdout);
+
+ usleep(20000);
+ }
+}
+```
+
+This animates the bouncing ball in your terminal.
+
+---
+
+# 🎯 Summary
+
+| Concept | Equation |
+| --------------------------- | ------------------------------------------ |
+| Gravity acceleration | (v = v - g \cdot dt) |
+| Position update | (h = h + v \cdot dt) |
+| Bounce | (v = -e v) |
+| New max height after bounce | (h_{\text{after}} = e^2 h_{\text{before}}) |
+
+This combination gives a physically accurate bouncing ball.
+
+---
+
+If you want, I can also show:
+
+* horizontal + vertical motion (parabolic bounce)
+* collisions with walls
+* 2D physics with vectors
+* full game loop frameworks for SDL, Raylib, or OpenGL
--- /dev/null
+:stem: latexmath
+:source-highlighter: pygments
+:pygments-style: monokai
+:wrap: normal
+
+= Formulas
+
+* velocity downward
+ - stem:[v = g t]
+
+* height
+ - stem:[h = h_0 - \frac{1}{2}t^2]
+
+* how long any object takes to fall from a given height
+ - stem:[t = \sqrt{\frac{2h}{g}}]
+
+* restitution
+ - stem:[v_1 = e * v_0]
+
+* rising
+ - stem:[ v = e * v - g t ]
+
+* falling
+ - stem:[ v = g t ]
+
+NOTE: the coefficent of restitution (e) represents energy loss.
+
+Typical values for restitution:
+
+* Rubber ball: stem:[e \approx 0.8 - 0.9]
+* Basketball: stem:[e \approx 0.75]
+* Tennis ball: stem:[e \approx 0.6]
--- /dev/null
+<!DOCTYPE html>
+<html lang="en">
+<head>
+<meta charset="UTF-8">
+<meta http-equiv="X-UA-Compatible" content="IE=edge">
+<meta name="viewport" content="width=device-width, initial-scale=1.0">
+<meta name="generator" content="Asciidoctor 2.0.20">
+<title>Formulas</title>
+<link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Open+Sans:300,300italic,400,400italic,600,600italic%7CNoto+Serif:400,400italic,700,700italic%7CDroid+Sans+Mono:400,700">
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+table{border-collapse:collapse;border-spacing:0}
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+pre .conum[data-value]{position:relative;top:-.125em}
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+.exampleblock>.content{background:#fffef7;border-color:#e0e0dc;box-shadow:0 1px 4px #e0e0dc}
+.print-only{display:none!important}
+@page{margin:1.25cm .75cm}
+@media print{*{box-shadow:none!important;text-shadow:none!important}
+html{font-size:80%}
+a{color:inherit!important;text-decoration:underline!important}
+a.bare,a[href^="#"],a[href^="mailto:"]{text-decoration:none!important}
+a[href^="http:"]:not(.bare)::after,a[href^="https:"]:not(.bare)::after{content:"(" attr(href) ")";display:inline-block;font-size:.875em;padding-left:.25em}
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+h2,h3,#toctitle,.sidebarblock>.content>.title{page-break-after:avoid}
+#header,#content,#footnotes,#footer{max-width:none}
+#toc,.sidebarblock,.exampleblock>.content{background:none!important}
+#toc{border-bottom:1px solid #dddddf!important;padding-bottom:0!important}
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+body.book #header .details{border:0!important;display:block;padding:0!important}
+body.book #header .details span:first-child{margin-left:0!important}
+body.book #header .details br{display:block}
+body.book #header .details br+span::before{content:none!important}
+body.book #toc{border:0!important;text-align:left!important;padding:0!important;margin:0!important}
+body.book #toc,body.book #preamble,body.book h1.sect0,body.book .sect1>h2{page-break-before:always}
+.listingblock code[data-lang]::before{display:block}
+#footer{padding:0 .9375em}
+.hide-on-print{display:none!important}
+.print-only{display:block!important}
+.hide-for-print{display:none!important}
+.show-for-print{display:inherit!important}}
+@media amzn-kf8,print{#header>h1:first-child{margin-top:1.25rem}
+.sect1{padding:0!important}
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+#footer{background:none}
+#footer-text{color:rgba(0,0,0,.6);font-size:.9em}}
+@media amzn-kf8{#header,#content,#footnotes,#footer{padding:0}}
+</style>
+</head>
+<body class="article">
+<div id="header">
+<h1>Formulas</h1>
+</div>
+<div id="content">
+<div class="ulist">
+<ul>
+<li>
+<p>velocity downward</p>
+<div class="ulist">
+<ul>
+<li>
+<p>\(v = g t\)</p>
+</li>
+</ul>
+</div>
+</li>
+<li>
+<p>height</p>
+<div class="ulist">
+<ul>
+<li>
+<p>\(h = h_0 - \frac{1}{2}t^2\)</p>
+</li>
+</ul>
+</div>
+</li>
+<li>
+<p>how long any object takes to fall from a given height</p>
+<div class="ulist">
+<ul>
+<li>
+<p>\(t = \sqrt{\frac{2h}{g}}\)</p>
+</li>
+</ul>
+</div>
+</li>
+<li>
+<p>restitution</p>
+<div class="ulist">
+<ul>
+<li>
+<p>\(v_1 = e * v_0\)</p>
+</li>
+</ul>
+</div>
+</li>
+<li>
+<p>rising</p>
+<div class="ulist">
+<ul>
+<li>
+<p>\( v = e * v - g t \)</p>
+</li>
+</ul>
+</div>
+</li>
+<li>
+<p>falling</p>
+<div class="ulist">
+<ul>
+<li>
+<p>\( v = g t \)</p>
+</li>
+</ul>
+</div>
+</li>
+</ul>
+</div>
+<div class="admonitionblock note">
+<table>
+<tr>
+<td class="icon">
+<div class="title">Note</div>
+</td>
+<td class="content">
+the coefficent of restitution (e) represents energy loss.
+</td>
+</tr>
+</table>
+</div>
+<div class="paragraph">
+<p>Typical values for restitution:</p>
+</div>
+<div class="ulist">
+<ul>
+<li>
+<p>Rubber ball: \(e \approx 0.8 - 0.9\)</p>
+</li>
+<li>
+<p>Basketball: \(e \approx 0.75\)</p>
+</li>
+<li>
+<p>Tennis ball: \(e \approx 0.6\)</p>
+</li>
+</ul>
+</div>
+</div>
+<div id="footer">
+<div id="footer-text">
+Last updated 2025-12-23 12:07:18 -0500
+</div>
+</div>
+<script type="text/x-mathjax-config">
+MathJax.Hub.Config({
+ messageStyle: "none",
+ tex2jax: {
+ inlineMath: [["\\(", "\\)"]],
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+ ignoreClass: "nostem|noasciimath"
+ },
+ TeX: { equationNumbers: { autoNumber: "none" } }
+})
+MathJax.Hub.Register.StartupHook("AsciiMath Jax Ready", function () {
+ MathJax.InputJax.AsciiMath.postfilterHooks.Add(function (data, node) {
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+ data.math.root.display = "block"
+ }
+ return data
+ })
+})
+</script>
+<script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.9/MathJax.js?config=TeX-MML-AM_HTMLorMML"></script>
+</body>
+</html>
\ No newline at end of file
--- /dev/null
+LIBS = -lSDL2 -lSDL2_ttf -lm
+
+PROG = balls
+
+build: $(PROG).c
+ gcc -g -o $(PROG) $(PROG).c $(LIBS)
+
+clean:
+ rm -rf $(PROG)
+
+.PHONY: clean
--- /dev/null
+#include <stdio.h>
+#include <stdbool.h>
+#include <assert.h>
+#include <stdint.h>
+#include <math.h>
+#include <stdlib.h>
+#include <time.h>
+
+#include <SDL2/SDL_rect.h>
+#include <SDL2/SDL_ttf.h>
+#include <SDL2/SDL.h>
+
+#define METER_AS_PIXELS 3779U
+#define BALL_COUNT 30
+
+// (BALL_COUNT * (BALL_COUNT - 1)) / 2
+// #define BALL_DISTINCT_UNORDERED_PAIRS 435
+
+#define END(check, str1, str2) \
+ if (check) { \
+ assert(check); \
+ fprintf(stderr, "%s\n%s", str1, str2); \
+ exit(1); \
+ } \
+
+#define SDL_main main
+
+typedef struct _Ball {
+ float px, py, vx, vy, ax, ay;
+ float radius;
+ uint8_t color;
+ float mass;
+} Ball;
+
+typedef struct _Mouse {
+ SDL_Point p;
+ bool down;
+ uint8_t button;
+} Mouse;
+
+typedef struct _Game {
+ SDL_Renderer *renderer;
+ SDL_Surface *backbuffer;
+ SDL_Window *window;
+ const SDL_Rect screen_rect;
+ Ball balls[BALL_COUNT];
+ uint32_t fps;
+ float terminal_velocity;
+ uint8_t ball_size_min;
+ uint8_t ball_size_max;
+ Ball **balls_colliding;
+ uint8_t collision_count;
+} Game;
+
+
+typedef uint8_t (*Update_callback) (Game *game,
+ float seconds,
+ uint32_t milliseconds,
+ SDL_KeyCode key,
+ Mouse mouse,
+ bool keydown);
+
+enum {UPDATE_MAIN, UPDATE_NOTHING};
+
+// Make sure last color is always black
+enum {COLOR_RED, COLOR_GREEN, COLOR_BLUE, COLOR_ORANGE, COLOR_GREY,
+ COLOR_PURPLE, COLOR_NEON_GREEN, COLOR_PINK, COLOR_YELLOW, COLOR_WHITE,
+ COLOR_BLACK, COLOR_SIZE};
+
+const SDL_Color colors[] = {
+ [COLOR_RED] = {.r = 217, .g = 100, .b = 89, .a = 255},
+ [COLOR_GREEN] = {.r = 88, .g = 140, .b = 126, .a = 255},
+ [COLOR_BLUE] = {.r = 39, .g = 211, .b = 245, .a = 255},
+ [COLOR_ORANGE] = {.r = 242, .g = 174, .b = 114, .a = 255},
+ [COLOR_GREY] = {.r = 89, .g = 89, .b = 89, .a = 89},
+ [COLOR_YELLOW] = {.r = 230, .g = 240, .b = 0, .a = 255},
+ [COLOR_PINK] = {.r = 245, .g = 39, .b = 108, .a = 255},
+ [COLOR_NEON_GREEN] = {.r = 39, .g = 245, .b = 176, .a = 255},
+ [COLOR_PURPLE] = {.r = 176, .g = 39, .b = 245, .a = 255},
+ [COLOR_WHITE] = {.r = 255, .g = 255, .b = 255, .a = 255},
+ [COLOR_BLACK] = {.r = 0, .g = 0, .b = 0, .a = 0},
+};
+
+void
+setColor(SDL_Renderer *renderer,
+ uint8_t color)
+{
+
+ SDL_SetRenderDrawColor(renderer, colors[color].r, colors[color].g,
+ colors[color].b, colors[color].a);
+}
+
+float getHyp(float x1, float y1, float x2, float y2) {
+ return sqrtf((x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2));
+}
+
+bool ballCollide(Ball b1,
+ Ball b2)
+{
+ return fabs((b1.px - b2.px) * (b1.px - b2.px) +
+ (b1.py - b2.py) * (b1.py - b2.py)) <=
+ (b1.radius + b2.radius) * (b1.radius + b2.radius);
+}
+
+bool pointInBall(Ball b,
+ SDL_Point p)
+{
+ return fabs((b.px - p.x) * (b.px - p.x) + (b.py - p.y) * (b.py - p.y))
+ <= (b.radius * b.radius);
+}
+
+void
+drawCircle(SDL_Renderer *renderer,
+ SDL_Rect border,
+ float radius,
+ int px,
+ int py,
+ int w,
+ uint8_t color)
+{
+
+ float x = 0;
+ float y = 0;
+ for(float i = 0; i < 2 * M_PI; i += 0.001f)
+ {
+ x = cosf(i);
+ y = sinf(i);
+ int rx = (x * radius);
+ int ry = (y * radius);
+ int tx = rx + px;
+ int ty = ry + py;
+ // wraping
+ // This works except in case where a ball is in the corner. Than the
+ // ball will apear in all four courners
+ // SDL_Rect point = {
+ // .x = (tx > border.w) ? tx -= border.w : (tx < 0) ? tx += border.w : tx,
+ // .y = (ty > border.h) ? ty -= border.h : (ty < 0) ? ty += border.h : ty,
+ // w,
+ // w
+ // };
+ SDL_Rect point = {
+ .x = tx,
+ .y = ty,
+ w,
+ w
+ };
+ setColor(renderer, color);
+ SDL_RenderFillRect(renderer, &point);
+ }
+}
+
+void
+drawBall(SDL_Renderer *renderer,
+ Ball ball)
+// (x - h)^2 + (y - k)^2 = r^2
+// Drawing a circle with the standard circle formula.
+// There may be a more performant way to do this...
+{
+ setColor(renderer, ball.color);
+
+ // diameter is radius * 2
+ for (int x = 0; x < ball.radius * 2; x++) {
+ for (int y = 0; y < ball.radius * 2; y++) {
+ if ( ((x - ball.radius) * (x - ball.radius)) +
+ ((y - ball.radius) * (y - ball.radius)) <=
+ ball.radius * ball.radius) {
+ int px = ball.px - ball.radius + x;
+ int py = ball.py - ball.radius + y;
+
+ // TODO: wrap circle around screen
+ SDL_RenderDrawPoint(renderer, px, py);
+
+ }
+ }
+ }
+}
+
+void
+drawBall2(SDL_Surface *surface,
+ Ball ball)
+// (x - h)^2 + (y - k)^2 = r^2
+// Drawing a circle with the standard circle formula.
+// There may be a more performant way to do this...
+{
+ // setColor(renderer, ball.color);
+
+ // diameter is radius * 2
+ for (int x = 0; x < ball.radius * 2; x++) {
+ for (int y = 0; y < ball.radius * 2; y++) {
+ if ( ((x - ball.radius) * (x - ball.radius)) +
+ ((y - ball.radius) * (y - ball.radius)) <=
+ ball.radius * ball.radius) {
+ int px = ball.px - ball.radius + x;
+ int py = ball.py - ball.radius + y;
+
+ // TODO: wrap circle around screen
+ // SDL_RenderDrawPoint(renderer, px, py);
+ SDL_Rect r = {.x = px, .y = py, .w = 1, .h = 1};
+ uint32_t color =
+ ((colors[ball.color].r << 24) | (colors[ball.color].g << 16) |
+ (colors[ball.color].b << 8) | colors[ball.color].a);
+ SDL_FillRect(surface, &r, color);
+
+ }
+ }
+ }
+}
+
+float clamp(float v,
+ float min,
+ float max) {
+ if (v < min) return min;
+ if (v > max) return max;
+ return v;
+}
+
+bool circleRectCollide(SDL_Point circle,
+ float r,
+ SDL_Rect rect)
+{
+ float closestX = clamp(circle.x, rect.x, rect.x + rect.w);
+ float closestY = clamp(circle.y, rect.y, rect.y + rect.h);
+
+ // this gets the distance form the center of the circle to a side of a
+ // rectangle. It could be negative or positive. Because we are squaring them
+ // it doesn't matter.
+ float dx = circle.x - closestX;
+ float dy = circle.y - closestY;
+
+ // use the dot product to determine collision
+ return (dx*dx + dy*dy) <= (r*r);
+}
+
+
+static uint8_t
+updateNothing(Game *game,
+ float seconds,
+ uint32_t milliseconds,
+ SDL_KeyCode key,
+ Mouse mouse,
+ bool keydown)
+{
+ return UPDATE_NOTHING;
+}
+
+void
+worldBoundry(Game *game, Ball *ball)
+{
+ int padding = 1;
+
+ if (ball->px - ball->radius <= 0) {
+ ball->px = ball->radius + padding;
+ }
+
+ if (ball->py - ball->radius <= 0) {
+ ball->py = ball->radius + padding;
+ }
+
+ if (ball->px + ball->radius >= game->screen_rect.w) {
+ ball->px = game->screen_rect.w - ball->radius - padding;
+ }
+
+ if (ball->py + ball->radius >= game->screen_rect.h) {
+ ball->py = game->screen_rect.h - ball->radius - padding;
+ }
+}
+
+void
+drawCursor(SDL_Renderer *renderer, SDL_Point p) {
+ SDL_Rect r = {
+ .x = p.x - 5,
+ .y = p.y - 5,
+ .w = 15,
+ .h = 15
+ };
+ setColor(renderer, COLOR_WHITE);
+ SDL_RenderFillRect(renderer, &r);
+}
+
+static uint8_t
+updateMain(Game *game,
+ float seconds,
+ uint32_t milliseconds,
+ SDL_KeyCode key,
+ Mouse mouse,
+ bool keydown)
+{
+ static float elapsedTime = 0;
+ static int selected = -1;
+
+ // Ball *colliding[BALL_DISTINCT_UNORDERED_PAIRS] = {0};
+ game->balls_colliding = NULL;
+ game->collision_count = 0;
+
+
+ // game->ball_distinct_unordered_pairs is the total number of possible
+ // collisions, it is multiplied was two because there needed to be two values
+ // for each collision, a ball at the target ball
+
+ // TODO
+ // Add a middle click feature that lets you look around. Then you could see
+ // balls that went off screen
+
+ // NOTE:
+ // issues arise when mouse movement is too fast
+ // don't check mouse click more than needed
+ if(mouse.button == SDL_BUTTON_LEFT && (selected < 0)) {
+ for (int i = 0; i < BALL_COUNT; ++i) {
+ Ball *b = &game->balls[i];
+ if (pointInBall(*b, mouse.p)) selected = i;
+ }
+ }
+
+ if((!mouse.down) && (mouse.button == SDL_BUTTON_RIGHT) && (selected >= 0)) {
+ Ball *b = &game->balls[selected];
+ b->vx = 5.0f * (b->px - (float)mouse.p.x);
+ b->vy = 5.0f * (b->py - (float)mouse.p.y);
+ }
+
+ if (!mouse.down) selected = -1;
+
+ if(selected >= 0 && mouse.button != SDL_BUTTON_RIGHT) {
+ elapsedTime = 0;
+ Ball *b = &game->balls[selected];
+ b->px = mouse.p.x;
+ b->py = mouse.p.y;
+ }
+
+ for (int i = 0; i < BALL_COUNT; ++i) {
+ Ball *b1 = &game->balls[i];
+ // drag
+ b1->ax = -b1->vx * 0.8f;
+ b1->ay = -b1->vy * 0.8f;
+
+ b1->vx += b1->ax * elapsedTime;
+ b1->vy += b1->ay * elapsedTime;
+ b1->px += b1->vx * elapsedTime;
+ b1->py += b1->vy * elapsedTime;
+
+ // wrap around screen
+ // Looks really bad, I'm removing this
+ // if (b1->px < 0) b1->px += (float)game->screen_rect.w;
+ // if (b1->px >= game->screen_rect.w) b1->px -= (float)game->screen_rect.w;
+ // if (b1->py < 0) b1->py += (float)game->screen_rect.h;
+ // if (b1->py >= game->screen_rect.h) b1->py -= (float)game->screen_rect.h;
+
+ if (fabs(b1->vx * b1->vx + b1->vy * b1->vy) < 0.01f) {
+ b1->vx = 0;
+ b1->vy = 0;
+ }
+
+ }
+
+ setColor(game->renderer, COLOR_BLACK);
+ SDL_RenderClear(game->renderer);
+
+ for (int i = 0; i < BALL_COUNT; ++i) {
+ Ball *b1 = &game->balls[i];
+ if (i == selected) drawBall(game->renderer, *b1);
+ else drawCircle(game->renderer, game->screen_rect, b1->radius, b1->px,
+ b1->py, 2, b1->color);
+
+ }
+
+ // TODO
+ // set up a list of values that will not conflict for i and j in gameInit
+
+ // TODO
+ // there is an error were the collision_count varaible will not reset to
+ // zero
+ for (int i = 0; i < BALL_COUNT; ++i) {
+ Ball *b1 = &game->balls[i];
+
+ for (int j = i + 1; j < BALL_COUNT; ++j) {
+ Ball *b2 = &game->balls[j];
+
+ if (!ballCollide(*b1, *b2)) continue;
+ game->balls_colliding = calloc(sizeof(Ball *),
+ (game->collision_count + 2));
+ END((!game->balls_colliding), "calloc()", "could not allocate game->balls_colliding()" );
+ game->balls_colliding[game->collision_count++] = b1;
+ game->balls_colliding[game->collision_count++] = b2;
+ float distance = fabs(getHyp(b1->px, b1->py, b2->px, b2->py));
+
+ float overlap = (distance - b1->radius - b2->radius);
+
+ if (distance == 0) continue;
+
+ b1->px -= overlap * (b1->px - b2->px) / distance;
+ b1->py -= overlap * (b1->py - b2->py) / distance;
+ b2->px += overlap * (b1->px - b2->px) / distance;
+ b2->py += overlap * (b1->py - b2->py) / distance;
+ // }
+ }
+ }
+ // printf("collision count: %d\n", game->collision_count);
+ for (int i = 0; i < game->collision_count; ++i) {
+ Ball *b1 = game->balls_colliding[i];
+ Ball *b2 = game->balls_colliding[i + 1];
+ if (!b1 || !b2) continue;
+ float distance = getHyp(b1->px, b1->py, b2->px, b2->py);
+
+ // normal
+ float nx = (b2->px - b1->px) / distance;
+ float ny = (b2->py - b1->py) / distance;
+
+ // tangent
+ float tx = -ny;
+ float ty = nx;
+
+ float dpTan1 = b1->vx * tx + b1->vy * ty;
+ float dpTan2 = b2->vx * tx + b2->vy * ty;
+
+ float dpNorm1 = b1->vx * nx + b1->vy * ny;
+ float dpNorm2 = b2->vx * nx + b2->vy * ny;
+
+ float m1 =
+ (dpNorm1 * (b1->mass - b2->mass) + 2.0f * b2->mass * dpNorm2)
+ / (b1->mass + b2->mass);
+
+ float m2 =
+ (dpNorm2 * (b2->mass - b1->mass) + 2.0f * b1->mass * dpNorm1)
+ / (b1->mass + b2->mass);
+
+ b1->vx = tx * dpTan1 + nx * m1;
+ b1->vy = ty * dpTan1 + ny * m1;
+ b2->vx = tx * dpTan2 + nx * m2;
+ b2->vy = ty * dpTan2 + ny * m2;
+
+ }
+
+ if((mouse.down) && (mouse.button == SDL_BUTTON_RIGHT) && (selected >= 0)) {
+ Ball *b = &game->balls[selected];
+ setColor(game->renderer, COLOR_WHITE);
+ SDL_RenderDrawLine(game->renderer, b->px, b->py, mouse.p.x, mouse.p.y);
+ }
+ if (selected < 0) drawCursor(game->renderer, mouse.p);
+
+ if (game->collision_count > 0) {
+ // I do not have free each individual ball in ball colliding because
+ // they are all on the stack
+ free(game->balls_colliding);
+ game->balls_colliding = NULL;
+ }
+
+ elapsedTime += 0.0008f;
+
+ return UPDATE_MAIN;
+}
+
+void
+Game_Update(Game *game)
+// The main game loop. Sets up which callback will be used in the function loop.
+// Each update callback determines what update callback will be called next by
+// returning the appropriate enum value
+{
+ uint8_t update_id = 0;
+ uint64_t frame = 0;
+ bool quit = false;
+ bool keydown = false;
+ float mspf = (1.0f / (float)game->fps) * 1000.0f;
+ SDL_Event event;
+ SDL_KeyCode key = 0;
+ Update_callback update;
+ uint32_t ticks_start = SDL_GetTicks();
+ Mouse mouse;
+
+ // TODO
+ // add backbuffer
+
+ while (!quit) {
+
+ // Place update functions here
+ switch (update_id) {
+ case UPDATE_MAIN: update = updateMain; break;
+ case UPDATE_NOTHING: update = updateNothing; break;
+ }
+
+ while (SDL_PollEvent(&event)) {
+
+ switch (event.type) {
+ case SDL_KEYDOWN: {
+ if (event.key.repeat == 0) {
+ key = event.key.keysym.sym;
+ keydown = true;
+ }
+
+ break;
+ }
+ case SDL_MOUSEBUTTONDOWN: {
+ mouse.button = event.button.button;
+ mouse.down = true;
+ break;
+ }
+ case SDL_MOUSEBUTTONUP: {
+ mouse.button = event.button.button;
+ mouse.down = false;
+ break;
+ }
+ case SDL_MOUSEMOTION: {
+ mouse.p.x = event.motion.x;
+ mouse.p.y = event.motion.y;
+ break;
+ }
+
+ case SDL_KEYUP: keydown = false; break;
+ case SDL_QUIT: quit = true; break;
+ }
+ }
+
+ update_id = update(game, SDL_GetTicks(), frame, key, mouse,keydown);
+
+ if ((SDL_GetTicks() - ticks_start) >= mspf) {
+ ticks_start = SDL_GetTicks();
+ // SDL_SetRenderDrawBlendMode(game->renderer, SDL_BLENDMODE_NONE);
+ // SDL_Texture *texture =
+ // SDL_CreateTextureFromSurface(game->renderer, game->backbuffer);
+ // SDL_RenderCopyEx(game->renderer, texture, NULL, &game->screen_rect,
+ // 0, NULL, SDL_FLIP_NONE);
+ SDL_RenderPresent(game->renderer);
+ // SDL_DestroyTexture(texture);
+ }
+
+ frame++;
+ }
+}
+
+void createBalls(Game *game) {
+ for (int i = 0; i < BALL_COUNT; ++i) {
+ Ball *b = &game->balls[i];
+ b->vx = 0;
+ b->vy = 0;
+ b->ax = 0;
+ b->ay = 0;
+ b->radius = ((rand() / (float)RAND_MAX) * (game->ball_size_max -
+ game->ball_size_min)) + game->ball_size_min;
+
+ b->px = (rand() / (float)RAND_MAX) * (float)game->screen_rect.w;
+
+ b->py = (rand() / (float)RAND_MAX) * (float)game->screen_rect.h;
+
+ b->color = (rand() / (float)RAND_MAX) * ((float)COLOR_SIZE - 2);
+
+ b->mass = b->radius * 10;
+ }
+
+}
+
+Game *
+Game_Init()
+// All the variable and data initialization needed for SDL and perhaps game
+// variables
+{
+ static Game game = {
+ .screen_rect = {.x = 0, .y = 0, .w = 800, .h = 800},
+ .fps = 60,
+ .ball_size_min = 15,
+ .ball_size_max = 50,
+ .backbuffer = NULL,
+ };
+
+ END(SDL_Init(SDL_INIT_VIDEO) != 0, "Could not create texture",
+ SDL_GetError());
+
+ END(TTF_Init() != 0, "Could not initialize TTF", TTF_GetError());
+
+
+
+ game.window = SDL_CreateWindow("balls", SDL_WINDOWPOS_UNDEFINED,
+ SDL_WINDOWPOS_UNDEFINED, game.screen_rect.w,
+ game.screen_rect.h, SDL_WINDOW_SHOWN);
+
+ END(game.window == NULL, "Could not create window", SDL_GetError());
+
+ game.renderer =
+ SDL_CreateRenderer(game.window, 0, SDL_RENDERER_ACCELERATED);
+
+ END(game.renderer == NULL, "Could not create renderer", SDL_GetError());
+
+ SDL_SetRelativeMouseMode(true);
+
+ // setColor(game->backbuffer, COLOR_BLACK);
+ // SDL_RenderClear(game->renderer);
+ game.backbuffer =
+ SDL_CreateRGBSurface(0, game.screen_rect.w, game.screen_rect.h,
+ 32, 0xFF000000, 0x00FF0000, 0x0000FF00,
+ 0x000000FF);
+ // fill backbuffer with black
+ SDL_FillRect(game.backbuffer, &game.screen_rect, 0x00000000);
+
+ // print system information
+ printf("big ending = %s\n", SDL_BYTEORDER == SDL_BIG_ENDIAN ?
+ "true": "False");
+
+ srand(time(NULL));
+ createBalls(&game);
+
+ return &game;
+}
+
+void
+Game_Quit(Game *game)
+{
+ if (game->collision_count > 0) {
+ free(game->balls_colliding);
+ game->balls_colliding = NULL;
+ }
+ SDL_DestroyWindow(game->window);
+ SDL_DestroyRenderer(game->renderer);
+ SDL_FreeSurface(game->backbuffer);
+ TTF_Quit();
+ SDL_Quit();
+}
+
+int
+main(void)
+{
+ Game *game = Game_Init();
+ Game_Update(game);
+ Game_Quit(game);
+ return 0;
+}
--- /dev/null
+= Why Your Collision-Resolution Loop Freezes and How to Fix It
+:wrap: normal
+
+[source,c]
+----
+for (int i = 0; i < BALL_COUNT; ++i) {
+ Ball *b1 = &game->balls[i];
+
+ for (int j = i + 1; j < BALL_COUNT; ++j) {
+ Ball *b2 = &game->balls[j];
+
+ if (!ballCollide(*b1, *b2)) continue;
+ colliding = calloc(sizeof(Ball *), (collision_count + 2));
+ END((!colliding), "calloc()", "could not allocate colliding()" );
+ colliding[collision_count++] = b1;
+ colliding[collision_count++] = b2;
+ float distance = getHyp(b1->px, b1->py, b2->px, b2->py);
+
+ float overlap = 0.5f * (distance - (float)b1->radius -
+ (float)b2->radius);
+ b1->px -=
+ overlap * (float)(b1->px - b2->px) / distance;
+ b1->py -=
+ overlap * (float)(b1->py - b2->py) / distance;
+ b2->px +=
+ overlap * (float)(b1->px - b2->px) / distance;
+ b2->py +=
+ overlap * (float)(b1->py - b2->py) / distance;
+
+ // all collisions must be resolved
+ // TODO
+ // fix issue that freezes program from this loop
+ while(ballCollide(*b1, *b2)) {
+ b1->px -= (float)(b1->px - b2->px) / distance;
+ b1->py -= (float)(b1->py - b2->py) / distance;
+ b2->px += (float)(b1->px - b2->px) / distance;
+ b2->py += (float)(b1->py - b2->py) / distance;
+ }
+ }
+}
+----
+
+Your code contains the classic problem of **over-correcting** and then
+**rechecking using new positions**, which makes the loop never terminate.
+Let’s walk through why this happens and how to fix it.
+
+
+== 1. The critical problem: using updated positions inside the loop
+
+Inside your main collision-resolution:
+
+[source,c]
+----
+b1->px -= overlap * (b1->px - b2->px) / distance;
+b1->py -= overlap * (b1->py - b2->py) / distance;
+b2->px += overlap * (b1->px - b2->px) / distance;
+b2->py += overlap * (b1->py - b2->py) / distance;
+----
+
+This is correct.
+
+But then you do:
+
+[source,c]
+----
+while (ballCollide(*b1, *b2)) {
+ b1->px -= (b1->px - b2->px) / distance;
+ b1->py -= (b1->py - b2->py) / distance;
+ b2->px += (b1->px - b2->px) / distance;
+ b2->py += (b1->py - b2->py) / distance;
+}
+----
+
+== ❌ Why this freezes
+
+1. `distance` stays the **old** value (before modifying positions).
+2. But `(b1->px - b2->px)` is updated each iteration.
+3. This causes steps that:
+ * overshoot
+ * oscillate
+ * sometimes increase overlap instead of decreasing it
+4. So `ballCollide()` keeps returning true forever → **infinite loop**.
+
+This is a well-known bug in naive iterative separation.
+
+== 2. Mathematical explanation
+
+Your update step behaves like:
+
+ x ← x − (x / constant)
+
+This only converges to zero if:
+
+ |1 − 1/constant| < 1
+
+But because the denominator (`distance`) is incorrect after the first
+shift, the term can jump back and forth.
+
+In other words:
+
+You are using a **fixed-length correction step based on old geometry**,
+but applying it to **new geometry**.
+
+This makes the correction unstable.
+
+
+== 3. Proper fix: recompute distance each iteration OR limit iterations
+
+Method A — Recompute distance every pass:
+
+[source,c]
+----
+int loop_guard = 0;
+while (ballCollide(*b1, *b2) && loop_guard++ < 4) {
+ float dx = b1->px - b2->px;
+ float dy = b1->py - b2->py;
+ float d = sqrtf(dx*dx + dy*dy);
+
+ if (d == 0) break;
+
+ float overlap = 0.5f * (d - b1->radius - b2->radius);
+ float nx = dx / d;
+ float ny = dy / d;
+
+ b1->px -= overlap * nx;
+ b1->py -= overlap * ny;
+ b2->px += overlap * nx;
+ b2->py += overlap * ny;
+}
+----
+
+Why this works:
+
+* `dx`, `dy`, and `distance` are recalculated from the new positions.
+* The correction scales perfectly with the current geometry.
+* The loop is guaranteed to converge.
+
+Method B — Avoid loops entirely
+Just do **one correction step per frame**, which is how most engines and
+the Jonathan Blow code handle it.
+
+== 4. Even better fix: use Blow’s displacement formula directly
+
+His code displaces balls only **once** per collision pass:
+
+[source,c]
+----
+float fDistance = sqrtf(dx*dx + dy*dy);
+float fOverlap = 0.5f * (fDistance - r1 - r2);
+
+b1->px -= fOverlap * (dx / fDistance);
+b1->py -= fOverlap * (dy / fDistance);
+
+b2->px += fOverlap * (dx / fDistance);
+b2->py += fOverlap * (dy / fDistance);
+----
+
+This resolves overlap in **one stable pass**, so you don’t need a loop.
+
+== 5. Bonus: Your calloc() usage is also wrong
+
+You do:
+
+[source,c]
+----
+colliding = calloc(sizeof(Ball *), (collision_count + 2));
+----
+
+Correct `calloc` order is:
+
+ calloc(num_elements, element_size)
+
+So you should use:
+
+[source,c]
+----
+colliding = calloc(collision_count + 2, sizeof(Ball *));
+----
+
+== 6. Final Summary
+
+* The infinite loop comes from using **outdated distance values** while
+ updating positions.
+* This causes oscillation → `ballCollide()` never returns false.
+* Fixes:
+ - recompute distance each iteration, or
+ - apply the correct one-shot overlap resolution (recommended).
+* Also fix your `calloc` order.
+
+If you want, I can rewrite your entire collision loop into a clean,
+correct, minimal version similar to Jonathan Blow’s system.
+
--- /dev/null
+<!DOCTYPE html>
+<html lang="en">
+<head>
+<meta charset="UTF-8">
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+</head>
+<body class="article">
+<div id="header">
+<h1>Why Your Collision-Resolution Loop Freezes and How to Fix It</h1>
+</div>
+<div id="content">
+<div id="preamble">
+<div class="sectionbody">
+<div class="listingblock">
+<div class="content">
+<pre class="highlight"><code class="language-c" data-lang="c">for (int i = 0; i < BALL_COUNT; ++i) {
+ Ball *b1 = &game->balls[i];
+
+ for (int j = i + 1; j < BALL_COUNT; ++j) {
+ Ball *b2 = &game->balls[j];
+
+ if (!ballCollide(*b1, *b2)) continue;
+ colliding = calloc(sizeof(Ball *), (collision_count + 2));
+ END((!colliding), "calloc()", "could not allocate colliding()" );
+ colliding[collision_count++] = b1;
+ colliding[collision_count++] = b2;
+ float distance = getHyp(b1->px, b1->py, b2->px, b2->py);
+
+ float overlap = 0.5f * (distance - (float)b1->radius -
+ (float)b2->radius);
+ b1->px -=
+ overlap * (float)(b1->px - b2->px) / distance;
+ b1->py -=
+ overlap * (float)(b1->py - b2->py) / distance;
+ b2->px +=
+ overlap * (float)(b1->px - b2->px) / distance;
+ b2->py +=
+ overlap * (float)(b1->py - b2->py) / distance;
+
+ // all collisions must be resolved
+ // TODO
+ // fix issue that freezes program from this loop
+ while(ballCollide(*b1, *b2)) {
+ b1->px -= (float)(b1->px - b2->px) / distance;
+ b1->py -= (float)(b1->py - b2->py) / distance;
+ b2->px += (float)(b1->px - b2->px) / distance;
+ b2->py += (float)(b1->py - b2->py) / distance;
+ }
+ }
+}</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>Your code contains the classic problem of <strong>over-correcting</strong> and then
+<strong>rechecking using new positions</strong>, which makes the loop never terminate.
+Let’s walk through why this happens and how to fix it.</p>
+</div>
+</div>
+</div>
+<div class="sect1">
+<h2 id="_1_the_critical_problem_using_updated_positions_inside_the_loop">1. The critical problem: using updated positions inside the loop</h2>
+<div class="sectionbody">
+<div class="paragraph">
+<p>Inside your main collision-resolution:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="highlight"><code class="language-c" data-lang="c">b1->px -= overlap * (b1->px - b2->px) / distance;
+b1->py -= overlap * (b1->py - b2->py) / distance;
+b2->px += overlap * (b1->px - b2->px) / distance;
+b2->py += overlap * (b1->py - b2->py) / distance;</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>This is correct.</p>
+</div>
+<div class="paragraph">
+<p>But then you do:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="highlight"><code class="language-c" data-lang="c">while (ballCollide(*b1, *b2)) {
+ b1->px -= (b1->px - b2->px) / distance;
+ b1->py -= (b1->py - b2->py) / distance;
+ b2->px += (b1->px - b2->px) / distance;
+ b2->py += (b1->py - b2->py) / distance;
+}</code></pre>
+</div>
+</div>
+</div>
+</div>
+<div class="sect1">
+<h2 id="_why_this_freezes">❌ Why this freezes</h2>
+<div class="sectionbody">
+<div class="olist arabic">
+<ol class="arabic">
+<li>
+<p><code>distance</code> stays the <strong>old</strong> value (before modifying positions).</p>
+</li>
+<li>
+<p>But <code>(b1→px - b2→px)</code> is updated each iteration.</p>
+</li>
+<li>
+<p>This causes steps that:</p>
+<div class="ulist">
+<ul>
+<li>
+<p>overshoot</p>
+</li>
+<li>
+<p>oscillate</p>
+</li>
+<li>
+<p>sometimes increase overlap instead of decreasing it</p>
+</li>
+</ul>
+</div>
+</li>
+<li>
+<p>So <code>ballCollide()</code> keeps returning true forever → <strong>infinite loop</strong>.</p>
+</li>
+</ol>
+</div>
+<div class="paragraph">
+<p>This is a well-known bug in naive iterative separation.</p>
+</div>
+</div>
+</div>
+<div class="sect1">
+<h2 id="_2_mathematical_explanation">2. Mathematical explanation</h2>
+<div class="sectionbody">
+<div class="paragraph">
+<p>Your update step behaves like:</p>
+</div>
+<div class="literalblock">
+<div class="content">
+<pre>x ← x − (x / constant)</pre>
+</div>
+</div>
+<div class="paragraph">
+<p>This only converges to zero if:</p>
+</div>
+<div class="literalblock">
+<div class="content">
+<pre>|1 − 1/constant| < 1</pre>
+</div>
+</div>
+<div class="paragraph">
+<p>But because the denominator (<code>distance</code>) is incorrect after the first
+shift, the term can jump back and forth.</p>
+</div>
+<div class="paragraph">
+<p>In other words:</p>
+</div>
+<div class="paragraph">
+<p>You are using a <strong>fixed-length correction step based on old geometry</strong>,
+but applying it to <strong>new geometry</strong>.</p>
+</div>
+<div class="paragraph">
+<p>This makes the correction unstable.</p>
+</div>
+</div>
+</div>
+<div class="sect1">
+<h2 id="_3_proper_fix_recompute_distance_each_iteration_or_limit_iterations">3. Proper fix: recompute distance each iteration OR limit iterations</h2>
+<div class="sectionbody">
+<div class="paragraph">
+<p>Method A — Recompute distance every pass:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="highlight"><code class="language-c" data-lang="c">int loop_guard = 0;
+while (ballCollide(*b1, *b2) && loop_guard++ < 4) {
+ float dx = b1->px - b2->px;
+ float dy = b1->py - b2->py;
+ float d = sqrtf(dx*dx + dy*dy);
+
+ if (d == 0) break;
+
+ float overlap = 0.5f * (d - b1->radius - b2->radius);
+ float nx = dx / d;
+ float ny = dy / d;
+
+ b1->px -= overlap * nx;
+ b1->py -= overlap * ny;
+ b2->px += overlap * nx;
+ b2->py += overlap * ny;
+}</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>Why this works:</p>
+</div>
+<div class="ulist">
+<ul>
+<li>
+<p><code>dx</code>, <code>dy</code>, and <code>distance</code> are recalculated from the new positions.</p>
+</li>
+<li>
+<p>The correction scales perfectly with the current geometry.</p>
+</li>
+<li>
+<p>The loop is guaranteed to converge.</p>
+</li>
+</ul>
+</div>
+<div class="paragraph">
+<p>Method B — Avoid loops entirely
+Just do <strong>one correction step per frame</strong>, which is how most engines and
+the Jonathan Blow code handle it.</p>
+</div>
+</div>
+</div>
+<div class="sect1">
+<h2 id="_4_even_better_fix_use_blows_displacement_formula_directly">4. Even better fix: use Blow’s displacement formula directly</h2>
+<div class="sectionbody">
+<div class="paragraph">
+<p>His code displaces balls only <strong>once</strong> per collision pass:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="highlight"><code class="language-c" data-lang="c">float fDistance = sqrtf(dx*dx + dy*dy);
+float fOverlap = 0.5f * (fDistance - r1 - r2);
+
+b1->px -= fOverlap * (dx / fDistance);
+b1->py -= fOverlap * (dy / fDistance);
+
+b2->px += fOverlap * (dx / fDistance);
+b2->py += fOverlap * (dy / fDistance);</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>This resolves overlap in <strong>one stable pass</strong>, so you don’t need a loop.</p>
+</div>
+</div>
+</div>
+<div class="sect1">
+<h2 id="_5_bonus_your_calloc_usage_is_also_wrong">5. Bonus: Your calloc() usage is also wrong</h2>
+<div class="sectionbody">
+<div class="paragraph">
+<p>You do:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="highlight"><code class="language-c" data-lang="c">colliding = calloc(sizeof(Ball *), (collision_count + 2));</code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>Correct <code>calloc</code> order is:</p>
+</div>
+<div class="literalblock">
+<div class="content">
+<pre>calloc(num_elements, element_size)</pre>
+</div>
+</div>
+<div class="paragraph">
+<p>So you should use:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="highlight"><code class="language-c" data-lang="c">colliding = calloc(collision_count + 2, sizeof(Ball *));</code></pre>
+</div>
+</div>
+</div>
+</div>
+<div class="sect1">
+<h2 id="_6_final_summary">6. Final Summary</h2>
+<div class="sectionbody">
+<div class="ulist">
+<ul>
+<li>
+<p>The infinite loop comes from using <strong>outdated distance values</strong> while
+updating positions.</p>
+</li>
+<li>
+<p>This causes oscillation → <code>ballCollide()</code> never returns false.</p>
+</li>
+<li>
+<p>Fixes:</p>
+<div class="ulist">
+<ul>
+<li>
+<p>recompute distance each iteration, or</p>
+</li>
+<li>
+<p>apply the correct one-shot overlap resolution (recommended).</p>
+</li>
+</ul>
+</div>
+</li>
+<li>
+<p>Also fix your <code>calloc</code> order.</p>
+</li>
+</ul>
+</div>
+<div class="paragraph">
+<p>If you want, I can rewrite your entire collision loop into a clean,
+correct, minimal version similar to Jonathan Blow’s system.</p>
+</div>
+</div>
+</div>
+</div>
+<div id="footer">
+<div id="footer-text">
+Last updated 2025-12-23 12:07:18 -0500
+</div>
+</div>
+</body>
+</html>
\ No newline at end of file
--- /dev/null
+= Why Recomputing Distance Still Freezes the Loop
+Even when recomputing `distance` inside the loop, it can still freeze. This
+happens when:
+
+* The distance between ball centers becomes **zero or extremely close to zero**.
+* The overlap becomes **very tiny** but never fully resolves because floating-
+ point error prevents the condition from becoming false.
+* The collision logic attempts to normalize a zero-length vector.
+
+Below is the real reason and the correct fix.
+
+== The Real Crash Scenario: Distance == 0
+If two balls overlap **perfectly**, meaning:
+
+----
+b1->px == b2->px
+b1->py == b2->py
+----
+
+Then:
+
+----
+dx = 0
+dy = 0
+distance = sqrt(0 + 0) = 0
+----
+
+Normalizing `(dx, dy)` becomes:
+
+----
+nx = dx / distance --> division by zero
+----
+
+This produces `NaN`, and once NaNs enter your coordinates, your loop **never
+terminates**, because every test becomes nonsense.
+
+== Why This Happens
+Your simulation allows balls to be pushed so close together (or initialized too
+close) that they fully overlap before you start resolving.
+
+Your while-loop approach *cannot* recover when distance reaches 0.
+
+== The Fix: Replace the Loop With One Guaranteed Separation Step
+Physics engines never use repeated loops; they use one mathematically correct
+position correction.
+
+Here is the correct safe displacement code:
+
+[source,c]
+----
+float dx = b1->px - b2->px;
+float dy = b1->py - b2->py;
+float d2 = dx*dx + dy*dy;
+
+// If centers are identical, push them apart arbitrarily
+if (d2 == 0.0f) {
+ dx = 1.0f;
+ dy = 0.0f;
+ d2 = 1.0f;
+}
+
+float distance = sqrtf(d2);
+float overlap = (b1->radius + b2->radius) - distance;
+
+if (overlap > 0.0f) {
+ float nx = dx / distance;
+ float ny = dy / distance;
+
+ float half = overlap * 0.5f;
+
+ b1->px += nx * half;
+ b1->py += ny * half;
+
+ b2->px -= nx * half;
+ b2->py -= ny * half;
+}
+----
+
+== Why This Works
+* **No loop**, so it can’t freeze.
+* Handles the `distance == 0` case safely.
+* Fully resolves the overlap mathematically.
+* Guaranteed to stop balls from colliding in a single step.
+* `collision_count` will now drop to zero.
+
+== Summary
+Recomputing distance didn't fix the freeze because the loop becomes invalid
+whenever the distance is zero or extremely tiny.
+The correct solution is to completely remove the loop and use one safe,
+mathematically correct separation step.
+
+== Want the Full Fixed Version?
+If you want, I can rewrite your entire collision detection and resolution block
+into clean, safe, minimal C code.
+
--- /dev/null
+<!DOCTYPE html>
+<html lang="en">
+<head>
+<meta charset="UTF-8">
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+<meta name="author" content="Even when recomputing `distance` inside the loop, it can still freeze. This">
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+@media amzn-kf8{#header,#content,#footnotes,#footer{padding:0}}
+</style>
+</head>
+<body class="article">
+<div id="header">
+<h1>Why Recomputing Distance Still Freezes the Loop</h1>
+<div class="details">
+<span id="author" class="author">Even when recomputing `distance` inside the loop, it can still freeze. This</span><br>
+<span id="revdate">happens when</span>
+<br><span id="revremark"></span>
+</div>
+</div>
+<div id="content">
+<div id="preamble">
+<div class="sectionbody">
+<div class="ulist">
+<ul>
+<li>
+<p>The distance between ball centers becomes <strong>zero or extremely close to zero</strong>.</p>
+</li>
+<li>
+<p>The overlap becomes <strong>very tiny</strong> but never fully resolves because floating-
+point error prevents the condition from becoming false.</p>
+</li>
+<li>
+<p>The collision logic attempts to normalize a zero-length vector.</p>
+</li>
+</ul>
+</div>
+<div class="paragraph">
+<p>Below is the real reason and the correct fix.</p>
+</div>
+</div>
+</div>
+<div class="sect1">
+<h2 id="_the_real_crash_scenario_distance_0">The Real Crash Scenario: Distance == 0</h2>
+<div class="sectionbody">
+<div class="paragraph">
+<p>If two balls overlap <strong>perfectly</strong>, meaning:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre>b1->px == b2->px
+b1->py == b2->py</pre>
+</div>
+</div>
+<div class="paragraph">
+<p>Then:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre>dx = 0
+dy = 0
+distance = sqrt(0 + 0) = 0</pre>
+</div>
+</div>
+<div class="paragraph">
+<p>Normalizing <code>(dx, dy)</code> becomes:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre>nx = dx / distance --> division by zero</pre>
+</div>
+</div>
+<div class="paragraph">
+<p>This produces <code>NaN</code>, and once NaNs enter your coordinates, your loop <strong>never
+terminates</strong>, because every test becomes nonsense.</p>
+</div>
+</div>
+</div>
+<div class="sect1">
+<h2 id="_why_this_happens">Why This Happens</h2>
+<div class="sectionbody">
+<div class="paragraph">
+<p>Your simulation allows balls to be pushed so close together (or initialized too
+close) that they fully overlap before you start resolving.</p>
+</div>
+<div class="paragraph">
+<p>Your while-loop approach <strong>cannot</strong> recover when distance reaches 0.</p>
+</div>
+</div>
+</div>
+<div class="sect1">
+<h2 id="_the_fix_replace_the_loop_with_one_guaranteed_separation_step">The Fix: Replace the Loop With One Guaranteed Separation Step</h2>
+<div class="sectionbody">
+<div class="paragraph">
+<p>Physics engines never use repeated loops; they use one mathematically correct
+position correction.</p>
+</div>
+<div class="paragraph">
+<p>Here is the correct safe displacement code:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="highlight"><code class="language-c" data-lang="c">float dx = b1->px - b2->px;
+float dy = b1->py - b2->py;
+float d2 = dx*dx + dy*dy;
+
+// If centers are identical, push them apart arbitrarily
+if (d2 == 0.0f) {
+ dx = 1.0f;
+ dy = 0.0f;
+ d2 = 1.0f;
+}
+
+float distance = sqrtf(d2);
+float overlap = (b1->radius + b2->radius) - distance;
+
+if (overlap > 0.0f) {
+ float nx = dx / distance;
+ float ny = dy / distance;
+
+ float half = overlap * 0.5f;
+
+ b1->px += nx * half;
+ b1->py += ny * half;
+
+ b2->px -= nx * half;
+ b2->py -= ny * half;
+}</code></pre>
+</div>
+</div>
+</div>
+</div>
+<div class="sect1">
+<h2 id="_why_this_works">Why This Works</h2>
+<div class="sectionbody">
+<div class="ulist">
+<ul>
+<li>
+<p><strong>No loop</strong>, so it can’t freeze.</p>
+</li>
+<li>
+<p>Handles the <code>distance == 0</code> case safely.</p>
+</li>
+<li>
+<p>Fully resolves the overlap mathematically.</p>
+</li>
+<li>
+<p>Guaranteed to stop balls from colliding in a single step.</p>
+</li>
+<li>
+<p><code>collision_count</code> will now drop to zero.</p>
+</li>
+</ul>
+</div>
+</div>
+</div>
+<div class="sect1">
+<h2 id="_summary">Summary</h2>
+<div class="sectionbody">
+<div class="paragraph">
+<p>Recomputing distance didn’t fix the freeze because the loop becomes invalid
+whenever the distance is zero or extremely tiny.
+The correct solution is to completely remove the loop and use one safe,
+mathematically correct separation step.</p>
+</div>
+</div>
+</div>
+<div class="sect1">
+<h2 id="_want_the_full_fixed_version">Want the Full Fixed Version?</h2>
+<div class="sectionbody">
+<div class="paragraph">
+<p>If you want, I can rewrite your entire collision detection and resolution block
+into clean, safe, minimal C code.</p>
+</div>
+</div>
+</div>
+</div>
+<div id="footer">
+<div id="footer-text">
+Last updated 2025-12-23 12:07:18 -0500
+</div>
+</div>
+</body>
+</html>
\ No newline at end of file
--- /dev/null
+:stem: latexmath
+:source-highlighter: pygments
+:pygments-style: monokai
+:wrap: normal
+
+= Formulas
+
+* Dot Product
+
+[stem]
+++++
+\overrightarrow{a} \cdot \overrightarrow{b} \\
+\left[ \begin{array}{c}
+a_{1} \\
+a_{2} \\
+\vdots \\
+a_{n}
+\end{array} \right]
+
+\cdot
+
+\left[ \begin{array}{c}
+b_{1} \\
+b_{2} \\
+\vdots \\
+b_{n}
+\end{array} \right]
+=
+a_{1} * b_{1} + a_{2} * b_{2} + * a_{n} * b_{n}
+++++
+
+* Circle Overlapping
+
+[stem]
+++++
+|\sqrt{a^2 + b^2}| <= r_1 + r_2
+++++
+
+NOTE: a and a is the opposite and adjacent sides found from
+ the centers of both circles
+
+
+* Pythagrean Thereom to find distancce between balls centers
+
+[stem]
+++++
+a^2 + b^2 = c^2
+++++
+
+* Vector Normalization
+
+[stem]
+++++
+\hat{u} = \frac{\overrightarrow{v}}{|\overrightarrow{v}|}
+++++
+
+
+* Magnitude of a Vector
+
+[stem]
+++++
+|\overrightarrow{a}| = \sqrt{a_{1}^2 + a_{2}^2 + \dots a_{n}^2}
+++++
+
+* Finding tangent vector
+
+[stem]
+++++
+x = -y, y = x
+++++
+
+* 1D Conservation of Momentum
+
+[stem]
+++++
+m_1 v_1 + m_2 v_2 = m_1 v_1 + m_2 v_2
+++++
+
+* 1D Elastic Collision
+
+[stem]
+++++
+v_1' = (v_1 * (m_1-m_2) + 2 * m_2 * v_2)) / (m_1 + m_2) \\
+v_2' = (v_2 * (m_2-m_1) + 2 * m_1 * v_1)) / (m_1 + m_2)
+++++
+
+* Finding magnitude in a specific direction
+
+[stem]
+++++
+|\overrightarrow{v}| = \overrightarrow{n} \cdot \overrightarrow{v}
+++++
+
+* Distinct unordered pairs
+
+[stem]
+++++
+(n,2) = \frac{n(n-1)}{2}]
+++++
+
+
+== Seeing if circle collide
+Instead of doing this:
+
+[source,c]
+----
+sqrtf((x1 - x2)*(x1 - x2) + (y1 - y2)*(y1 - y2)) <= (r1 + r2);
+----
+
+We can save some computing speed by removing the square root and just
+multiplying the left side by itself:
+
+[source,c]
+----
+fabs((x1 - x2)*(x1 - x2) + (y1 - y2)*(y1 - y2)) <= (r1 + r2)*(r1 + r2);
+----
+
+== Clamping Velocity
+
+We can use the dot product to find the velocity in specific direction and then
+clamp it
+
+[source,c]
+----
+if (fabs(ball.vx*ball.vx + ball.vy*ball.vy) < 0.01f)
+----
--- /dev/null
+<!DOCTYPE html>
+<html lang="en">
+<head>
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+body.book #header .details br{display:block}
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+body.book #toc{border:0!important;text-align:left!important;padding:0!important;margin:0!important}
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+</style>
+</head>
+<body class="article">
+<div id="header">
+<h1>Formulas</h1>
+</div>
+<div id="content">
+<div id="preamble">
+<div class="sectionbody">
+<div class="ulist">
+<ul>
+<li>
+<p>Dot Product</p>
+</li>
+</ul>
+</div>
+<div class="stemblock">
+<div class="content">
+\[\overrightarrow{a} \cdot \overrightarrow{b} \\
+\left[ \begin{array}{c}
+a_{1} \\
+a_{2} \\
+\vdots \\
+a_{n}
+\end{array} \right]
+
+\cdot
+
+\left[ \begin{array}{c}
+b_{1} \\
+b_{2} \\
+\vdots \\
+b_{n}
+\end{array} \right]
+=
+a_{1} * b_{1} + a_{2} * b_{2} + * a_{n} * b_{n}\]
+</div>
+</div>
+<div class="ulist">
+<ul>
+<li>
+<p>Circle Overlapping</p>
+</li>
+</ul>
+</div>
+<div class="stemblock">
+<div class="content">
+\[|\sqrt{a^2 + b^2}| <= r_1 + r_2\]
+</div>
+</div>
+<div class="admonitionblock note">
+<table>
+<tr>
+<td class="icon">
+<div class="title">Note</div>
+</td>
+<td class="content">
+a and a is the opposite and adjacent sides found from
+ the centers of both circles
+</td>
+</tr>
+</table>
+</div>
+<div class="ulist">
+<ul>
+<li>
+<p>Pythagrean Thereom to find distancce between balls centers</p>
+</li>
+</ul>
+</div>
+<div class="stemblock">
+<div class="content">
+\[a^2 + b^2 = c^2\]
+</div>
+</div>
+<div class="ulist">
+<ul>
+<li>
+<p>Vector Normalization</p>
+</li>
+</ul>
+</div>
+<div class="stemblock">
+<div class="content">
+\[\hat{u} = \frac{\overrightarrow{v}}{|\overrightarrow{v}|}\]
+</div>
+</div>
+<div class="ulist">
+<ul>
+<li>
+<p>Magnitude of a Vector</p>
+</li>
+</ul>
+</div>
+<div class="stemblock">
+<div class="content">
+\[|\overrightarrow{a}| = \sqrt{a_{1}^2 + a_{2}^2 + \dots a_{n}^2}\]
+</div>
+</div>
+<div class="ulist">
+<ul>
+<li>
+<p>Finding tangent vector</p>
+</li>
+</ul>
+</div>
+<div class="stemblock">
+<div class="content">
+\[x = -y, y = x\]
+</div>
+</div>
+<div class="ulist">
+<ul>
+<li>
+<p>1D Conservation of Momentum</p>
+</li>
+</ul>
+</div>
+<div class="stemblock">
+<div class="content">
+\[m_1 v_1 + m_2 v_2 = m_1 v_1 + m_2 v_2\]
+</div>
+</div>
+<div class="ulist">
+<ul>
+<li>
+<p>1D Elastic Collision</p>
+</li>
+</ul>
+</div>
+<div class="stemblock">
+<div class="content">
+\[v_1' = (v_1 * (m_1-m_2) + 2 * m_2 * v_2)) / (m_1 + m_2) \\
+v_2' = (v_2 * (m_2-m_1) + 2 * m_1 * v_1)) / (m_1 + m_2)\]
+</div>
+</div>
+<div class="ulist">
+<ul>
+<li>
+<p>Finding magnitude in a specific direction</p>
+</li>
+</ul>
+</div>
+<div class="stemblock">
+<div class="content">
+\[|\overrightarrow{v}| = \overrightarrow{n} \cdot \overrightarrow{v}\]
+</div>
+</div>
+<div class="ulist">
+<ul>
+<li>
+<p>Distinct unordered pairs</p>
+</li>
+</ul>
+</div>
+<div class="stemblock">
+<div class="content">
+\[(n,2) = \frac{n(n-1)}{2}]\]
+</div>
+</div>
+</div>
+</div>
+<div class="sect1">
+<h2 id="_seeing_if_circle_collide">Seeing if circle collide</h2>
+<div class="sectionbody">
+<div class="paragraph">
+<p>Instead of doing this:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="pygments highlight"><code data-lang="c"><span></span><span class="tok-n">sqrtf</span><span class="tok-p">((</span><span class="tok-n">x1</span><span class="tok-w"> </span><span class="tok-o">-</span><span class="tok-w"> </span><span class="tok-n">x2</span><span class="tok-p">)</span><span class="tok-o">*</span><span class="tok-p">(</span><span class="tok-n">x1</span><span class="tok-w"> </span><span class="tok-o">-</span><span class="tok-w"> </span><span class="tok-n">x2</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-o">+</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-n">y1</span><span class="tok-w"> </span><span class="tok-o">-</span><span class="tok-w"> </span><span class="tok-n">y2</span><span class="tok-p">)</span><span class="tok-o">*</span><span class="tok-p">(</span><span class="tok-n">y1</span><span class="tok-w"> </span><span class="tok-o">-</span><span class="tok-w"> </span><span class="tok-n">y2</span><span class="tok-p">))</span><span class="tok-w"> </span><span class="tok-o"><=</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-n">r1</span><span class="tok-w"> </span><span class="tok-o">+</span><span class="tok-w"> </span><span class="tok-n">r2</span><span class="tok-p">);</span></code></pre>
+</div>
+</div>
+<div class="paragraph">
+<p>We can save some computing speed by removing the square root and just
+multiplying the left side by itself:</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="pygments highlight"><code data-lang="c"><span></span><span class="tok-n">fabs</span><span class="tok-p">((</span><span class="tok-n">x1</span><span class="tok-w"> </span><span class="tok-o">-</span><span class="tok-w"> </span><span class="tok-n">x2</span><span class="tok-p">)</span><span class="tok-o">*</span><span class="tok-p">(</span><span class="tok-n">x1</span><span class="tok-w"> </span><span class="tok-o">-</span><span class="tok-w"> </span><span class="tok-n">x2</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-o">+</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-n">y1</span><span class="tok-w"> </span><span class="tok-o">-</span><span class="tok-w"> </span><span class="tok-n">y2</span><span class="tok-p">)</span><span class="tok-o">*</span><span class="tok-p">(</span><span class="tok-n">y1</span><span class="tok-w"> </span><span class="tok-o">-</span><span class="tok-w"> </span><span class="tok-n">y2</span><span class="tok-p">))</span><span class="tok-w"> </span><span class="tok-o"><=</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-n">r1</span><span class="tok-w"> </span><span class="tok-o">+</span><span class="tok-w"> </span><span class="tok-n">r2</span><span class="tok-p">)</span><span class="tok-o">*</span><span class="tok-p">(</span><span class="tok-n">r1</span><span class="tok-w"> </span><span class="tok-o">+</span><span class="tok-w"> </span><span class="tok-n">r2</span><span class="tok-p">);</span></code></pre>
+</div>
+</div>
+</div>
+</div>
+<div class="sect1">
+<h2 id="_clamping_velocity">Clamping Velocity</h2>
+<div class="sectionbody">
+<div class="paragraph">
+<p>We can use the dot product to find the velocity in specific direction and then
+clamp it</p>
+</div>
+<div class="listingblock">
+<div class="content">
+<pre class="pygments highlight"><code data-lang="c"><span></span><span class="tok-k">if</span><span class="tok-w"> </span><span class="tok-p">(</span><span class="tok-n">fabs</span><span class="tok-p">(</span><span class="tok-n">ball</span><span class="tok-p">.</span><span class="tok-n">vx</span><span class="tok-o">*</span><span class="tok-n">ball</span><span class="tok-p">.</span><span class="tok-n">vx</span><span class="tok-w"> </span><span class="tok-o">+</span><span class="tok-w"> </span><span class="tok-n">ball</span><span class="tok-p">.</span><span class="tok-n">vy</span><span class="tok-o">*</span><span class="tok-n">ball</span><span class="tok-p">.</span><span class="tok-n">vy</span><span class="tok-p">)</span><span class="tok-w"> </span><span class="tok-o"><</span><span class="tok-w"> </span><span class="tok-mf">0.01f</span><span class="tok-p">)</span></code></pre>
+</div>
+</div>
+</div>
+</div>
+</div>
+<div id="footer">
+<div id="footer-text">
+Last updated 2025-12-23 12:07:18 -0500
+</div>
+</div>
+<script type="text/x-mathjax-config">
+MathJax.Hub.Config({
+ messageStyle: "none",
+ tex2jax: {
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+</html>
\ No newline at end of file
--- /dev/null
+#!/usr/bin/env bash
+HOSTNAME=nyquistdev.net
+DOCINFODIR=/usr/local/share/readme-to-html
--- /dev/null
+== GDB
+
+remember that conditional break points exist
+
+== Links
+* https://www.youtube.com/watch?v=nXrEX6j-Mws&list=PLkhTWnF-dZA7fqD7CF8koSTsRbmfBfr2_
+* https://www.unitconverters.net/typography/pixel-x-to-meter.htm[pixels to meters]
+* https://simulationshub.com/ball-drop/[interactive ball]
+* https://www.physicslens.com/simulation-of-a-bouncing-ball/
+* https://www.youtube.com/watch?v=hG9SzQxaCm8
+* https://en.wikipedia.org/wiki/Bouncing_ball
+* https://youtu.be/LPzyNOHY3A4?si=Vv4pVQ0cbLwPI9Zt[javidx9]
--- /dev/null
+<!DOCTYPE html>
+<html lang="en">
+<head>
+<meta charset="UTF-8">
+<meta http-equiv="X-UA-Compatible" content="IE=edge">
+<meta name="viewport" content="width=device-width, initial-scale=1.0">
+<meta name="generator" content="Asciidoctor 2.0.20">
+<title>Balls</title>
+<link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Open+Sans:300,300italic,400,400italic,600,600italic%7CNoto+Serif:400,400italic,700,700italic%7CDroid+Sans+Mono:400,700">
+<style>
+/*! Asciidoctor default stylesheet | MIT License | https://asciidoctor.org */
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+/* @import "https://fonts.googleapis.com/css?family=Open+Sans:300,300italic,400,400italic,600,600italic%7CNoto+Serif:400,400italic,700,700italic%7CDroid+Sans+Mono:400,700"; */
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+html,body{font-size:100%}
+body{background:#fff;color:rgba(0,0,0,.8);padding:0;margin:0;font-family:"Noto Serif","DejaVu Serif",serif;line-height:1;position:relative;cursor:auto;-moz-tab-size:4;-o-tab-size:4;tab-size:4;word-wrap:anywhere;-moz-osx-font-smoothing:grayscale;-webkit-font-smoothing:antialiased}
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+@page{margin:1.25cm .75cm}
+@media print{*{box-shadow:none!important;text-shadow:none!important}
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+#toc,.sidebarblock,.exampleblock>.content{background:none!important}
+#toc{border-bottom:1px solid #dddddf!important;padding-bottom:0!important}
+body.book #header{text-align:center}
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+body.book #header .details{border:0!important;display:block;padding:0!important}
+body.book #header .details span:first-child{margin-left:0!important}
+body.book #header .details br{display:block}
+body.book #header .details br+span::before{content:none!important}
+body.book #toc{border:0!important;text-align:left!important;padding:0!important;margin:0!important}
+body.book #toc,body.book #preamble,body.book h1.sect0,body.book .sect1>h2{page-break-before:always}
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+@media amzn-kf8{#header,#content,#footnotes,#footer{padding:0}}
+</style>
+<link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/4.7.0/css/font-awesome.min.css">
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+<!-- <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=DotGothic16"> -->
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+<!-- <link href="https://fonts.googleapis.com/css2?family=Abril+Fatface&display=swap" rel="stylesheet"> -->
+<style>
+
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+}
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+.title {
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+cite {
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+.tableblock {
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+ max-width: 95%;
+}
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+ background-color: var(--gruvbox-black3);
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+ max-width: 97%;
+}
+
+code:not([data-lang]) {
+ background-color: var(--gruvbox-bg2) !important;
+ color: var(--gruvbox-white);
+ text-shadow: none;
+}
+
+.checklist {
+ text-align: left;
+ font-size: .8em;
+}
+
+.checklist li ul { margin-left: 3%;
+}
+
+#content, h1, pre {
+ border-radius: 8px !important;
+}
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+#header, #content, #footnotes, #footer {
+ padding-left: 0 !important;
+ padding-right: 0 !important;
+}
+
+.api-type a:hover {
+ text-decoration: underline;
+}
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+.api-type, .api-type a {
+ color: var(--gruvbox-green);
+ text-decoration: none;
+}
+
+pre {
+ border-style: solid !important;
+ border-color: white !important;
+ border-width: 2px !important;
+}
+
+h1 {
+ /* font-family: "DotGothic16", sans-serif !important;*/
+
+
+ background-color: var(--gruvbox-white2) !important;
+ color: var(--gruvbox-black) !important;
+}
+
+.admonitionblock > table td.content {
+ color: var(--gruvbox-white) !important;
+}
+
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+ margin: 0;
+ height: 100%;
+ width: 100%;
+}
+
+
+*/
+/*html {*/
+
+body {
+ /*background: black url("background-image-space.jpeg") no-repeat fixed center;*/
+ /*background-color: black;*/
+ background-color: var(--gruvbox-black);
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+ background-size: cover;
+ overflow-y: scroll;
+ /*
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+ height: 100%;
+ width: 100%;
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+}
+
+
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+ overflow-y: scroll;
+ background: rgba(0,0,0,0);
+ height: 100%;
+ margin: 2%;
+}
+*/
+
+#toc {
+ background-color: var(--gruvbox-black2) !important;
+ /*opacity: .9;*/
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+
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+ color: var(--gruvbox-yellow);
+}
+
+a {
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+ background: var(--gruvbox-black);
+ /*opacity: .9;*/
+}
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+ border-bottom: none !important;
+ background-color: rgba(0, 0, 0, .1);
+ padding-left: 2%;
+}
+
+.sect1 + .sect1 {
+ border-top: none !important;
+}
+
+.sect1 h2 {
+ background-size: cover;
+ background-attachment: fixed;
+ /*
+ border-bottom: 1px solid var(--gruvbox-white);
+ border-top: 1px solid var(--gruvbox-white);
+ */
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+ text-align: left;
+ color: var(--gruvbox-red) !important;
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+}
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+ color: var(--gruvbox-yellow) !important;
+}
+
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+ color: #83a598 !important;
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+ margin-left: .5em;
+}
+
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+ max-width: 97% !important;
+ white-space: pre;
+ overflow-x: scroll !important;
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+ /*makes sure that the programming language that show up on hover is within
+ pre tag*/
+ padding-right: 3%;
+}
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+ .checklist li ul {
+ margin-left: 6% !important;
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+ padding-left: 10px;
+ }
+
+ footer {
+ margin-bottom: 10px !important;
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+ html {
+ margin-bottom: 10px !important;
+ }
+}
+@media screen and (max-width: 535px) {
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+ margin-left: 0 !important;
+ }
+
+ footer {
+ margin-bottom: 10px !important;
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+ margin-bottom: 10px !important;
+ }
+}
+h3 ~ *:not(h2):not(h3) {
+ margin-left: 1.5em;
+}
+
+h4 ~ *:not(h2):not(h3):not(.h3):not(h4) {
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+}
+h5 ~ *:not(h2):not(h3):not(.h3):not(h4):not(.h4):not(h5) {
+ margin-left: 2.5em;
+}
+
+
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+
+ /*
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+ to bottom,
+ rgba(251, 189, 47, 0.2), /* yellow */
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+ );
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+ /*opacity: .9;*/
+ }
+
+#preamble p{
+ padding-left: 10px;
+ color: var(--gruvbox-white) !important;
+}
+
+#footer {
+ max-width: 62.5em !important;
+ padding-left: 10px !important;
+ text-align: center;
+}
+
+.logo img {
+ display: block !important;
+ margin-left: auto !important;
+ margin-right: auto !important;
+}
+
+#header > h1:first-child {
+ margin-top: .3em !important;
+ padding-top: .2em !important;
+ text-align: center;
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+
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+ max-width: 62.5em;
+ margin-left: auto;
+ margin-right: auto;
+ display: block;
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+ /* display: none;*/
+ border-top: none;
+ content: "▼";
+ margin-top: -12px;
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+ border: solid;
+ font-size: 2vw;
+ max-width: 40%;
+ margin: auto;
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+ max-width: 500px;
+ display: flex;
+ justify-content: center;
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+
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+ margin-right: 5%;
+ display: inline-block;
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+
+</style>
+
+</head>
+
+<script src="docinfo.js"></script>
+
+
+</head>
+<body class="article">
+<div id="header">
+<h1>Balls</h1>
+</div>
+<div id="content">
+<div id="preamble">
+<div class="sectionbody">
+<div class="paragraph">
+<p>This repository has physics examples using balls. Each folder has a different
+example, with a link to the formulas used in the readme’s.</p>
+</div>
+</div>
+</div>
+<div class="sect1">
+<h2 id="_2d_projectile_motion">2D Projectile Motion</h2>
+<div class="sectionbody">
+<div class="paragraph">
+<p>checkout this link
+<a href="https://nyquistdev.net/git/?p=balls.git;a=blob_plain;f=2d-projectile-motion/docs/formulas.html;hb=HEAD">formulas</a>.
+for a list of forumlas used.</p>
+</div>
+<table class="tableblock frame-all grid-all stretch">
+<colgroup>
+<col style="width: 50%;">
+<col style="width: 50%;">
+</colgroup>
+<thead>
+<tr>
+<th class="tableblock halign-left valign-top">control</th>
+<th class="tableblock halign-left valign-top">action</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">right-click and drag</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">determine direction and velocity of ball</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">right-click release</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">launch ball</p></td>
+</tr>
+</tbody>
+</table>
+</div>
+</div>
+<div class="sect1">
+<h2 id="_bouncing">Bouncing</h2>
+<div class="sectionbody">
+<div class="paragraph">
+<p>check out this link
+<a href="https://nyquistdev.net/git/?p=balls.git;a=blob_plain;f=bounce/docs/formulas.html;hb=HEAD">formulas</a>.
+for the formulas used.</p>
+</div>
+</div>
+</div>
+<div class="sect1">
+<h2 id="_collisions">Collisions</h2>
+<div class="sectionbody">
+<div class="paragraph">
+<p>Creates random balls. These balls will resolve any collision issues. Launching a
+ball will show you an example of elastic collision.</p>
+</div>
+<div class="paragraph">
+<p>checkout this link
+<a href="https://nyquistdev.net/git/?p=balls.git;a=blob_plain;f=collisions/docs/formulas.html;hb=HEAD">formulas</a>.
+for a list of forumlas used.</p>
+</div>
+<table class="tableblock frame-all grid-all stretch">
+<colgroup>
+<col style="width: 50%;">
+<col style="width: 50%;">
+</colgroup>
+<thead>
+<tr>
+<th class="tableblock halign-left valign-top">control</th>
+<th class="tableblock halign-left valign-top">action</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">right-click</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">select ball</p></td>
+</tr>
+<tr>
+<td class="tableblock halign-left valign-top"><p class="tableblock">right-click and left-click and drag</p></td>
+<td class="tableblock halign-left valign-top"><p class="tableblock">flings ball on release, the distance
+ away from the ball determines the amount
+ of velocity to launch the ball at</p></td>
+</tr>
+</tbody>
+</table>
+</div>
+</div>
+<div class="sect1">
+<h2 id="_building_html_from_formula_adoc_files">Building html from formula <em>.adoc</em> files</h2>
+<div class="sectionbody">
+<div class="listingblock">
+<div class="content">
+<pre>./Makehtml make</pre>
+</div>
+</div>
+</div>
+</div>
+<div class="sect1">
+<h2 id="_links">Links</h2>
+<div class="sectionbody">
+<div class="ulist">
+<ul>
+<li>
+<p><a href="https://www.studyplan.dev/sdl2/sdl2-relative-mode">sdl2-relative-mouse-mode</a></p>
+</li>
+<li>
+<p><a href="https://www.youtube.com/watch?v=XJnIdRXUi7A&t=315s">permutations and combinations</a></p>
+</li>
+<li>
+<p><a href="https://www.youtube.com/watch?v=CFbo_nBdBco">OCT | Elastic Collisions</a></p>
+</li>
+<li>
+<p><a href="https://www.wikihow.com/Normalize-a-Vector">Normalizing a Vector</a></p>
+</li>
+<li>
+<p><a href="https://www.youtube.com/watch?v=Fp7D5D8Bqjc">conservation of Momentum</a></p>
+</li>
+</ul>
+</div>
+</div>
+</div>
+</div>
+<script type="text/x-mathjax-config">
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\ No newline at end of file
projects / balls.git / commitdiff