made edgeptcmp public. implemented centroid for Triangle[23], and a h…

…omogeneous-to-barycentric coordinates conversion function for Triangle2.

geometry.h

@@ -56,6 +56,7 @@ Point2 lerp2(Point2, Point2, double);
 double dotvec2(Point2, Point2);
 double vec2len(Point2);
 Point2 normvec2(Point2);
+int edgeptcmp(Point2, Point2, Point2);
 int ptinpoly(Point2, Point2*, ulong);
 
 /* Point3 */
@@ -118,8 +119,12 @@ Point3 rframexform3(Point3, RFrame3);
 Point2 invrframexform(Point2, RFrame);
 Point3 invrframexform3(Point3, RFrame3);
 
+/* Triangle2 */
+Point2 centroid(Triangle2);
+Point3 barycoords(Triangle2, Point2);
+
 /* Triangle3 */
-Point3 centroid(Triangle3);
+Point3 centroid3(Triangle3);
 
 /* Fmt */
 #pragma varargck type "v" Point2

point.c

@@ -79,6 +79,11 @@ normvec2(Point2 v)
  *
  * Juan Pineda, “A Parallel Algorithm for Polygon Rasterization”,
  * Computer Graphics, Vol. 22, No. 8, August 1988
+ *
+ * comparison of a point p with an edge [e0 e1]
+ * p to the right: +
+ * p to the left: -
+ * p on the edge: 0
  */
 int
 edgeptcmp(Point2 e0, Point2 e1, Point2 p)

triangle.c

@@ -2,8 +2,39 @@
 #include <libc.h>
 #include <geometry.h>
 
+/* 2D */
+
+Point2
+centroid(Triangle2 t)
+{
+	return divpt2(addpt2(t.p0, addpt2(t.p1, t.p2)), 3);
+}
+
+/*
+ * based on the implementation from:
+ *
+ * Dmitry V. Sokolov, “Tiny Renderer: Lesson 2”,
+ * https://github.com/ssloy/tinyrenderer/wiki/Lesson-2:-Triangle-rasterization-and-back-face-culling
+ */
+Point3
+barycoords(Triangle2 t, Point2 p)
+{
+	Point2 p0p1 = subpt2(t.p1, t.p0);
+	Point2 p0p2 = subpt2(t.p2, t.p0);
+	Point2 pp0  = subpt2(t.p0, p);
+
+	Point3 v = crossvec3(Vec3(p0p2.x, p0p1.x, pp0.x), Vec3(p0p2.y, p0p1.y, pp0.y));
+
+	/* handle degenerate triangles—i.e. the ones where every point lies on the same line */
+	if(fabs(v.z) < 1)
+		return Pt3(-1,-1,-1,1);
+	return Pt3(1 - (v.x + v.y)/v.z, v.y/v.z, v.x/v.z, 1);
+}
+
+/* 3D */
+
 Point3
-centroid(Triangle3 t)
+centroid3(Triangle3 t)
 {
 	return divpt3(addpt3(t.p0, addpt3(t.p1, t.p2)), 3);
 }