Use barycentric coordinates instead of half space for triangle fill

src/window.c

@@ -1,5 +1,6 @@
 #include "window.h"
 #include "aliases/aliases.h"
+#include "math_utils.h"
 #include <SDL2/SDL_rect.h>
 #include <SDL2/SDL_render.h>
 #include <SDL2/SDL_video.h>
@@ -89,42 +90,44 @@ void draw_triangle(const window *wnd, triangle triangle, colour colour) {
   draw_line(wnd, &ln2, colour);
 }
 
-INTERNAL inline i32 min(i32 a, i32 b, i32 c) {
+INTERNAL inline bool inside_triangle(triangle tri, point p) {
-  i32 _min = a <= b ? a : b;
+  // Based on the following video:
-  return _min <= c ? _min : c;
+  // https://www.youtube.com/watch?v=HYAgJN3x4GA
+  f32 cy_min_ay = tri.p2.y - tri.p0.y;
+  f32 cx_min_ax = tri.p2.x - tri.p0.x;
+  f32 by_min_ay = tri.p1.y - tri.p0.y;
+  f32 bx_min_ax = tri.p1.x - tri.p0.x;
+
+  f32 w1 =
+      (tri.p0.x * cy_min_ay + (p.y - tri.p0.y) * cx_min_ax - p.x * cy_min_ay) /
+      (by_min_ay * cx_min_ax - bx_min_ax * cy_min_ay);
+
+  f32 w2 = (p.y - tri.p0.y - w1 * by_min_ay) / cy_min_ay;
+
+  return w1 >= 0.0f && w2 >= 0.0f && (w1 + w2) <= 1.0f;
 }
 
-INTERNAL inline i32 max(i32 a, i32 b, i32 c) {
+void fill_triangle(const window *wnd, triangle tri, colour colour) {
-  i32 _max = a >= b ? a : b;
+  // Basic triangle filling algorithm inspired by
-  return _max >= c ? _max : c;
-}
-
-INTERNAL inline i32 half_space(i32 x1, i32 x2, i32 y1, i32 y2, i32 x, i32 y) {
-  return (x2 - x1) * (y - y1) - (y2 - y1) * (x - x1);
-}
-
-void fill_triangle(const window *wnd, triangle triangle, colour colour) {
-  // Basic triangle filling algorithm from
   // https://web.archive.org/web/20050408192410/http://sw-shader.sourceforge.net/rasterizer.html
-  i32 x1 = triangle.p0.x;
+  // but uses barycentric coordinates instead of half space
-  i32 x2 = triangle.p1.x;
+  i32 x1 = tri.p0.x;
-  i32 x3 = triangle.p2.x;
+  i32 x2 = tri.p1.x;
+  i32 x3 = tri.p2.x;
 
-  i32 y1 = triangle.p0.y;
+  i32 y1 = tri.p0.y;
-  i32 y2 = triangle.p1.y;
+  i32 y2 = tri.p1.y;
-  i32 y3 = triangle.p2.y;
+  i32 y3 = tri.p2.y;
 
   // Find bounding rect
-  i32 min_x = min(x1, x2, x3);
+  i32 min_x = min(min(x1, x2), x3);
-  i32 max_x = max(x1, x2, x3);
+  i32 max_x = max(max(x1, x2), x3);
-  i32 min_y = min(y1, y2, y3);
+  i32 min_y = min(min(y1, y2), y3);
-  i32 max_y = max(y1, y2, y3);
+  i32 max_y = max(max(y1, y2), y3);
 
   for (i32 y = min_y; y < max_y; ++y) {
     for (i32 x = min_x; x < max_x; ++x) {
-      if (half_space(x2, x1, y2, y1, x, y) >= 0 &&
+      if (inside_triangle(tri, (point){x, y})) {
-          half_space(x3, x2, y3, y2, x, y) >= 0 &&
-          half_space(x1, x3, y1, y3, x, y) >= 0) {
         draw_point(wnd, (point){x, y}, colour);
       }
     }
@@ -144,8 +147,8 @@ void draw_quad(const window *wnd, quad qd, colour colour) {
 }
 
 void fill_quad(const window *wnd, quad qd, colour colour) {
-  triangle t0 = (triangle){qd.p3, qd.p1, qd.p0};
+  triangle t0 = (triangle){qd.p0, qd.p1, qd.p2};
-  triangle t1 = (triangle){qd.p0, qd.p2, qd.p3};
+  triangle t1 = (triangle){qd.p1, qd.p2, qd.p3};
 
   fill_triangle(wnd, t0, colour);
   fill_triangle(wnd, t1, colour);