split tri.h into tri.c for test purposes

Makefile

@@ -16,7 +16,10 @@ unfold: unfold.o
 wireframe: wireframe.o
 corners: corners.o stl_3d.o
 faces: faces.o stl_3d.o
-hiddenwire: hiddenwire.o camera.o
+hiddenwire: hiddenwire.o camera.o tri.o
+
+# Test the triangle intersection code
+test-intersect: test-intersect.o tri.o
 
 clean:
 	$(RM) *.o

seg.h

@@ -10,7 +10,7 @@ struct _seg_t {
 	seg_t * next;
 };
 
-seg_t *
+static inline seg_t *
 seg_new(
 	const v3_t p0,
 	const v3_t p1
@@ -29,7 +29,7 @@ seg_new(
 }
 
 
-void
+static inline void
 seg_print(
 	const seg_t * const s
 )

tri.c

@@ -0,0 +1,614 @@
+/*
+ * Triangle manipulations
+ */
+#include <stdio.h>
+#include <math.h>
+#include <stdint.h>
+#include "tri.h"
+
+
+int tri_debug = 0;
+
+
+tri_t *
+tri_new(
+	const v3_t * p_cam,
+	const v3_t * p_xyz
+)
+{
+	tri_t * const t = calloc(1, sizeof(*t));
+	if (!t)
+		return NULL;
+	for(int i = 0 ; i < 3  ; i++)
+		t->p[i] = p_cam[i];
+
+	// precompute the normals
+	t->normal = v3_norm(v3_cross(
+		v3_sub(t->p[1], t->p[0]),
+		v3_sub(t->p[2], t->p[1])
+	));
+	t->normal_xyz = v3_norm(v3_cross(
+		v3_sub(p_xyz[1], p_xyz[0]),
+		v3_sub(p_xyz[2], p_xyz[1])
+	));
+
+
+	// compute the bounding box for the triangle in camera space
+	for(int j = 0 ; j < 3 ; j++)
+	{
+		t->min[j] = min(min(t->p[0].p[j], t->p[1].p[j]), t->p[2].p[j]);
+		t->max[j] = max(max(t->p[0].p[j], t->p[1].p[j]), t->p[2].p[j]);
+	}
+
+	return t;
+}
+
+
+// insert a triangle into our z-sorted list
+void
+tri_insert(
+	tri_t ** zlist,
+	tri_t * t
+)
+{
+	while(1)
+	{
+		tri_t * const iter = *zlist;
+		if (!iter)
+			break;
+
+		// check to see if our new triangle is closer than
+		// the current triangle
+		if(iter->min[2] > t->min[2])
+			break;
+
+		zlist = &(iter->next);
+	}
+
+	// either we reached the end of the list,
+	// or we have found where our new triangle is sorted
+	t->next = *zlist;
+	t->prev = zlist;
+	*zlist = t;
+	if (t->next)
+		t->next->prev = &t->next;
+}
+
+
+void
+tri_delete(tri_t * t)
+{
+	if (t->next)
+		t->next->prev = t->prev;
+	if (t->prev)
+		*(t->prev) = t->next;
+
+	t->next = NULL;
+	t->prev = NULL;
+	free(t);
+}
+
+
+// Compute the 2D area of a triangle in screen space
+// using Heron's formula
+float
+tri_area_2d(
+	const tri_t * const t
+)
+{
+	const float a = v3_dist_2d(&t->p[0], &t->p[1]);
+	const float b = v3_dist_2d(&t->p[1], &t->p[2]);
+	const float c = v3_dist_2d(&t->p[2], &t->p[0]);
+	const float s = (a + b + c) / 2;
+
+	return sqrt(s * (s-a) * (s-b) * (s-c));
+}
+
+
+void
+tri_print(
+	const tri_t * const t
+)
+{
+	fprintf(stderr, "%.0f,%.0f,%.0f %.0f,%.0f,%.0f %.0f,%.0f,%.0f norm %.3f,%.3f,%.3f\n",
+		t->p[0].p[0],
+		t->p[0].p[1],
+		t->p[0].p[2],
+		t->p[1].p[0],
+		t->p[1].p[1],
+		t->p[1].p[2],
+		t->p[2].p[0],
+		t->p[2].p[1],
+		t->p[2].p[2],
+		t->normal.p[0],
+		t->normal.p[1],
+		t->normal.p[2]
+	);
+}
+
+
+/* Check if two triangles are coplanar and share an edge.
+ *
+ * Returns -1 if not coplanar, 0-2 for the edge in t0 that they share.
+ */
+int
+tri_coplanar(
+	const tri_t * const t0,
+	const tri_t * const t1,
+	const float coplanar_eps
+)
+{
+	// the two normals must be parallel-enough
+	const float angle = v3_mag(v3_sub(t0->normal_xyz, t1->normal_xyz));
+	if (angle < -coplanar_eps || +coplanar_eps < angle)
+		return -1;
+	
+	// find if there are two points shared
+	unsigned matches = 0;
+	for(int i = 0 ; i < 3 ; i++)
+	{
+		for(int j = 0 ; j < 3 ; j++)
+		{
+			if (!v3_eq(&t0->p[i], &t1->p[j]))
+				continue;
+			matches |= 1 << i;
+			break;
+		}
+	}
+
+	switch(matches)
+	{
+	case 0x3: return 0;
+	case 0x6: return 1;
+	case 0x5: return 2;
+	case 0x7:
+		fprintf(stderr, "uh, three points match?\n");
+		tri_print(t0);
+		tri_print(t1);
+		return -1;
+	default:
+		// no shared edge
+		return -1;
+	}
+}
+
+
+/*
+ * Find the Z point of an XY coordinate in a triangle.
+ *
+ * p can be written as a combination of t01 and t02,
+ * p - t0 = a * (t1 - t0) + b * (t2 - t0)
+ * setting t0 to 0, this becomes:
+ * p = a * t1 + b * t2
+ * which is two equations with two unknowns
+ *
+ * Returns true if the point is inside the triangle
+ */
+int
+tri_find_z(
+	const tri_t * const t,
+	const v3_t * const p,
+	float * const zout
+)
+{
+	const float t1x = t->p[1].p[0] - t->p[0].p[0];
+	const float t1y = t->p[1].p[1] - t->p[0].p[1];
+	const float t1z = t->p[1].p[2] - t->p[0].p[2];
+	const float t2x = t->p[2].p[0] - t->p[0].p[0];
+	const float t2y = t->p[2].p[1] - t->p[0].p[1];
+	const float t2z = t->p[2].p[2] - t->p[0].p[2];
+	const float px = p->p[0] - t->p[0].p[0];
+	const float py = p->p[1] - t->p[0].p[1];
+
+	const float a = (px * t2y - py * t2x) / (t1x * t2y - t2x * t1y);
+	const float b = (px * t1y - py * t1x) / (t2x * t1y - t1x * t2y);
+
+	const float z = t->p[0].p[2] + a * t1z + b * t2z;
+
+	if (zout)
+		*zout = z;
+
+	return 0 <= a && 0 <= b && a + b <= 1;
+}
+
+
+/** Compute the points of intersection for two segments in 2d, and z points.
+ *
+ * This is a specialized ray intersection algorithm for the
+ * hidden wire-frame removal code that computes the intersection
+ * points for two rays (in 2D, "orthographic") and then computes
+ * the Z depth for the intersections along each of the segments.
+ *
+ * Returns -1 for non-intersecting, otherwise a ratio of how far
+ * along the intersection is on the l0.
+ */
+float
+hidden_intersect(
+	const v3_t * const p0,
+	const v3_t * const p1,
+	const v3_t * const p2,
+	const v3_t * const p3,
+	v3_t * const l0_int,
+	v3_t * const l1_int
+)
+{
+	const float p0_x = p0->p[0];
+	const float p0_y = p0->p[1];
+	const float p0_z = p0->p[2];
+	const float p1_x = p1->p[0];
+	const float p1_y = p1->p[1]; 
+	const float p1_z = p1->p[2];
+	const float p2_x = p2->p[0];
+	const float p2_y = p2->p[1];
+	const float p2_z = p2->p[2];
+	const float p3_x = p3->p[0];
+	const float p3_y = p3->p[1];
+	const float p3_z = p3->p[2];
+
+	const float s1_x = p1_x - p0_x;
+	const float s1_y = p1_y - p0_y;
+	const float s2_x = p3_x - p2_x;
+	const float s2_y = p3_y - p2_y;
+
+	// compute r x s
+	const float d = -s2_x * s1_y + s1_x * s2_y;
+
+	// if they are close to parallel, then we do not need to check
+	// for intersection (we define that as "non-intersecting")
+	if (-EPS < d && d < EPS)
+		return -1;
+
+	// Compute how far along each line they would interesect
+	const float r0 = ( s2_x * (p0_y - p2_y) - s2_y * (p0_x - p2_x)) / d;
+	const float r1 = (-s1_y * (p0_x - p2_x) + s1_x * (p0_y - p2_y)) / d;
+
+	// if they are not within the ratio (0,1), then the intersecton occurs
+	// outside of the segments and is not of concern
+	if (r0 < 0 || r0 > 1)
+		return -1;
+	if (r1 < 0 || r1 > 1)
+		return -1;
+
+	// Collision detected with the segments
+if(0) fprintf(stderr, "collision: %.0f,%.0f,%.0f->%.0f,%.0f,%.0f %.0f,%.0f,%.0f->%.0f,%.0f,%.0f == %.3f,%.3f\n",
+		p0_x, p0_y, p0_z,
+		p1_x, p1_y, p1_z,
+		p2_x, p2_y, p2_z,
+		p3_x, p3_y, p2_z,
+		r0,
+		r1
+	);
+
+	const float ix = p0_x + (r0 * s1_x);
+	const float iy = p0_y + (r0 * s1_y);
+
+	// compute the z intercept for each on the two different coordinates
+	if(l0_int)
+	{
+		*l0_int = (v3_t){{
+			ix,
+			iy,
+			p0_z + r0 * (p1_z - p0_z)
+		}};
+	}
+
+	if(l1_int)
+	{
+		*l1_int = (v3_t){{
+			ix,
+			iy,
+			p2_z + r1 * (p3_z - p2_z)
+		}};
+	}
+
+	return r0;
+}
+
+
+/*
+ * Recursive algorithm:
+ * Given a line segment and a list of triangles,
+ * find if the line segment crosses any triangle.
+ * If it crosses a triangle the segment will be shortened
+ * and an additional one might be created.
+ * Recusively try intersecting the new segment (starting at the same triangle)
+ * and then continue trying the shortened segment.
+ */
+
+void
+tri_seg_intersect(
+	const tri_t * zlist,
+	seg_t * s,
+	seg_t ** slist_visible
+)
+{
+	const float p0z = s->p[0].p[2];
+	const float p1z = s->p[1].p[2];
+	const float seg_max_z = max(p0z, p1z);
+
+	// avoid processing empty segments
+	const float seg_len = v3_len(&s->p[0], &s->p[1]);
+	if (seg_len < EPS)
+		return;
+
+static int recursive;
+recursive++;
+
+//fprintf(stderr, "%d: processing segment ", recursive); seg_print(s);
+	fprintf(stderr, "--- recursive %d\n", recursive);
+	seg_print(s);
+
+	for( const tri_t * t = zlist ; t ; t = t->next )
+	{
+		// if the segment is closer than the triangle,
+		// then we no longer have to check any further into
+		// the zlist (it is sorted by depth).
+		if (seg_max_z <= t->min[2])
+			break;
+
+#if 0
+		// make sure that we're not comparing to our own triangle
+		// or one that shares an edge with us (which might be in
+		// a different order)
+		if (v2_eq(s->src[0].p, t->p[0].p, 0.0005)
+		&&  v2_eq(s->src[1].p, t->p[1].p, 0.0005))
+			continue;
+		if (v2_eq(s->src[0].p, t->p[1].p, 0.0005)
+		&&  v2_eq(s->src[1].p, t->p[2].p, 0.0005))
+			continue;
+		if (v2_eq(s->src[0].p, t->p[2].p, 0.0005)
+		&&  v2_eq(s->src[1].p, t->p[0].p, 0.0005))
+			continue;
+		if (v2_eq(s->src[0].p, t->p[1].p, 0.0005)
+		&&  v2_eq(s->src[1].p, t->p[0].p, 0.0005))
+			continue;
+		if (v2_eq(s->src[0].p, t->p[2].p, 0.0005)
+		&&  v2_eq(s->src[1].p, t->p[1].p, 0.0005))
+			continue;
+		if (v2_eq(s->src[0].p, t->p[0].p, 0.0005)
+		&&  v2_eq(s->src[1].p, t->p[2].p, 0.0005))
+			continue;
+#endif
+
+		if (tri_debug >= 2)
+			tri_print(t);
+/*
+		// if the segment is co-linear to any of the
+		// triangle edges, include it
+		for(int i = 0 ; i < 3 ; i++)
+		{
+			if (parallel(
+				&s->p[0], &s->p[1],
+				&t->p[i], &t->p[(i+1)%3]
+			))
+				goto next_segment;
+		}
+*/
+
+		float z0, z1;
+		int inside0 = tri_find_z(t, &s->p[0], &z0);
+		int inside1 = tri_find_z(t, &s->p[1], &z1);
+
+		if (tri_debug >= 2 && (inside0 || inside1))
+		{
+			fprintf(stderr, "inside %d %d\n", inside0, inside1);
+		}
+
+		// if both are inside but the segment is infront of the
+		// triangle, then we retain the segment.
+		// otherwies we discard the segment
+		if (inside0 && inside1)
+		{
+			if (s->p[0].p[2] <= z0
+			&&  s->p[1].p[2] <= z1)
+				continue;
+			if (tri_debug >= 2)
+				fprintf(stderr, "BOTH INSIDE\n");
+			recursive--;
+			return;
+		}
+
+		// split the segment for each intersection with the
+		// triangle segments and add it to the work queue.
+		int intersections = 0;
+		v3_t is[3] = {}; // 3d point of segment intercept
+		v3_t it[3] = {}; // 3d point of triangle intercept
+
+		for(int j = 0 ; j < 3 ; j++)
+		{
+			float ratio = hidden_intersect(
+				&s->p[0], &s->p[1],
+				&t->p[j], &t->p[(j+1)%3],
+				&is[intersections],
+				&it[intersections]
+			);
+
+			if (ratio < 0)
+				continue;
+
+			if (tri_debug >= 2)
+				fprintf(stderr, "%d ratio=%.2f\n", j, ratio);
+			intersections++;
+		}
+
+
+		// if none of them intersect, we keep looking
+		if (intersections == 0)
+			continue;
+
+		if (tri_debug >= 2)
+			fprintf(stderr, "%d intersections\n", intersections);
+
+		if (intersections == 3)
+		{
+			// this likely means that the triangle is very, very
+			// small, so let's just ignore this triangle
+			if (tri_debug >= 2)
+				fprintf(stderr, "Three intersections\n");
+			continue;
+		}
+
+
+		if (intersections == 2)
+		{
+			// figure out how far it is to each of the intersections
+			const float d00 = v3_len(&s->p[0], &is[0]);
+			const float d01 = v3_len(&s->p[0], &is[1]);
+			const float d10 = v3_len(&s->p[1], &is[0]);
+			const float d11 = v3_len(&s->p[1], &is[1]);
+
+			if (tri_debug >= 2)
+				fprintf(stderr, "Two intersections\n");
+
+			// discard segments that have two interesections that match
+			// the segment exactly (distance from segment ends to
+			// intersection point close enough to zero).
+			if (d00 < EPS && d11 < EPS)
+			{
+				recursive--;
+				return;
+			}
+			if (d01 < EPS && d10 < EPS)
+			{
+				recursive--;
+				return;
+			}
+
+			// if the segment intersection is closer than the triangle,
+			// then we do nothing. degenerate cases are not handled
+			if (d00 <= d01
+			&& is[0].p[2] <= it[0].p[2]
+			&& is[1].p[2] <= it[1].p[2])
+				continue;
+			if (d00 > d01
+			&& is[1].p[2] <= it[0].p[2]
+			&& is[0].p[2] <= it[1].p[2])
+				continue;
+
+			// segment is behind the triangle,
+			// we have to create a new segment
+			// and shorten the existing segment
+			// find the two intersections that we have
+			// update the src field
+
+			// we need to create a new segment
+			seg_t * news;
+			if (d00 < d01)
+			{
+				// split from p0 to ix0
+				news = seg_new(s->p[0], is[0]);
+				news->src[0] = s->src[0];
+				news->src[1] = s->src[1];
+				s->p[0] = is[1];
+			} else {
+				// split from p0 to ix1
+				news = seg_new(s->p[0], is[1]);
+				news->src[0] = s->src[0];
+				news->src[1] = s->src[1];
+				s->p[0] = is[0];
+			}
+
+			// recursively start splitting the new segment
+			// starting at the next triangle down the z-depth
+			tri_seg_intersect(zlist->next, news, slist_visible);
+
+			// continue splitting our current segment
+			continue;
+		}
+
+		if (intersections == 1)
+		{
+			// if there is an intersection, but the segment intercept
+			// is closer than the triangle intercept, then no problem.
+			// we do not bother with degenerate cases of intersecting
+			// triangles
+			if (is[0].p[2] <= it[0].p[2]
+			&&  is[1].p[2] <= it[0].p[2])
+			{
+				//svg_line("#00FF00", s->p[0].p, s->p[1].p, 10);
+				continue;
+			}
+
+			if (inside0)
+			{
+				// shorten it on the 0 side
+				s->p[0] = is[0];
+// huh? shouldn't we process this one?
+return;
+				continue;
+			} else
+			if (inside1)
+			{
+				// shorten it on the 1 side
+				s->p[1] = is[0];
+// huh? shouldn't we process this one?
+return;
+				continue;
+			} else {
+				// both outside, but an intersection?
+				// split at that point and hope for the best
+				seg_t * const news = seg_new(s->p[0], is[0]);
+				news->src[0] = s->src[0];
+				news->src[1] = s->src[1];
+				s->p[0] = is[0];
+
+				tri_seg_intersect(zlist->next, news, slist_visible);
+				// continue splitting our current segment
+				continue;
+			}
+		}
+
+next_segment:
+		continue;
+	}
+
+	// if we've reached here the segment is visible
+	// and should be added to the visible list
+	s->next = *slist_visible;
+	*slist_visible = s;
+	recursive--;
+}
+
+
+/*
+ * Fast check to see if t2 is entire occluded by t.
+ */
+int
+tri_behind(
+	const tri_t * const t,
+	const tri_t * const t2
+)
+{
+	float z0, z1, z2;
+	int inside0 = tri_find_z(t, &t2->p[0], &z0);
+	int inside1 = tri_find_z(t, &t2->p[1], &z1);
+	int inside2 = tri_find_z(t, &t2->p[2], &z2);
+
+	// easy check -- if none of the points are inside,
+	// t2 is not entirely occluded
+	if (!inside0 || !inside1 || !inside2)
+		return 0;
+
+	// are all of the intersection points ahead of t2?
+	int behind0 = t2->p[0].p[2] >= z0;
+	int behind1 = t2->p[1].p[2] >= z1;
+	int behind2 = t2->p[2].p[2] >= z2;
+	if (behind0 && behind1 && behind2)
+		return 1;
+
+	// it is a STL violation if they are not all on the
+	// same side (this would indicate that t and t2 intersect
+	// go ahead and prune since it will cause problems
+	if (behind0 || behind1 || behind2)
+	{
+/*
+		fprintf(stderr, "WARNING: triangles intersect %.0f %.0f %.0f inside %d %d %d behind %d %d %d\n", z0, z1, z2, inside0, inside1, inside2, behind0, behind1, behind2);
+		tri_print(t);
+		tri_print(t2);
+*/
+		return 1;
+	}
+
+	// they are all on the same side
+	return 0;
+}

tri.h

@@ -7,6 +7,7 @@
 #include "v3.h"
 #include "seg.h"
 
+extern int tri_debug;
 
 typedef struct _tri_t tri_t;
 struct _tri_t
@@ -21,39 +22,11 @@ struct _tri_t
 };
 
 
-
 tri_t *
 tri_new(
 	const v3_t * p_cam,
 	const v3_t * p_xyz
-)
+);
-{
-	tri_t * const t = calloc(1, sizeof(*t));
-	if (!t)
-		return NULL;
-	for(int i = 0 ; i < 3  ; i++)
-		t->p[i] = p_cam[i];
-
-	// precompute the normals
-	t->normal = v3_norm(v3_cross(
-		v3_sub(t->p[1], t->p[0]),
-		v3_sub(t->p[2], t->p[1])
-	));
-	t->normal_xyz = v3_norm(v3_cross(
-		v3_sub(p_xyz[1], p_xyz[0]),
-		v3_sub(p_xyz[2], p_xyz[1])
-	));
-
-
-	// compute the bounding box for the triangle in camera space
-	for(int j = 0 ; j < 3 ; j++)
-	{
-		t->min[j] = min(min(t->p[0].p[j], t->p[1].p[j]), t->p[2].p[j]);
-		t->max[j] = max(max(t->p[0].p[j], t->p[1].p[j]), t->p[2].p[j]);
-	}
-
-	return t;
-}
 
 
 // insert a triangle into our z-sorted list
@@ -61,44 +34,11 @@ void
 tri_insert(
 	tri_t ** zlist,
 	tri_t * t
-)
+);
-{
-	while(1)
-	{
-		tri_t * const iter = *zlist;
-		if (!iter)
-			break;
-
-		// check to see if our new triangle is closer than
-		// the current triangle
-		if(iter->min[2] > t->min[2])
-			break;
-
-		zlist = &(iter->next);
-	}
-
-	// either we reached the end of the list,
-	// or we have found where our new triangle is sorted
-	t->next = *zlist;
-	t->prev = zlist;
-	*zlist = t;
-	if (t->next)
-		t->next->prev = &t->next;
-}
 
 
 void
-tri_delete(tri_t * t)
+tri_delete(tri_t * t);
-{
-	if (t->next)
-		t->next->prev = t->prev;
-	if (t->prev)
-		*(t->prev) = t->next;
-
-	t->next = NULL;
-	t->prev = NULL;
-	free(t);
-}
 
 
 // Compute the 2D area of a triangle in screen space
@@ -106,37 +46,13 @@ tri_delete(tri_t * t)
 float
 tri_area_2d(
 	const tri_t * const t
-)
+);
-{
-	const float a = v3_dist_2d(&t->p[0], &t->p[1]);
-	const float b = v3_dist_2d(&t->p[1], &t->p[2]);
-	const float c = v3_dist_2d(&t->p[2], &t->p[0]);
-	const float s = (a + b + c) / 2;
-
-	return sqrt(s * (s-a) * (s-b) * (s-c));
-}
 
 
 void
 tri_print(
 	const tri_t * const t
-)
-{
-	fprintf(stderr, "%.0f,%.0f,%.0f %.0f,%.0f,%.0f %.0f,%.0f,%.0f norm %.3f,%.3f,%.3f\n",
-		t->p[0].p[0],
-		t->p[0].p[1],
-		t->p[0].p[2],
-		t->p[1].p[0],
-		t->p[1].p[1],
-		t->p[1].p[2],
-		t->p[2].p[0],
-		t->p[2].p[1],
-		t->p[2].p[2],
-		t->normal.p[0],
-		t->normal.p[1],
-		t->normal.p[2]
 );
-}
 
 
 /* Check if two triangles are coplanar and share an edge.
@@ -148,41 +64,7 @@ tri_coplanar(
 	const tri_t * const t0,
 	const tri_t * const t1,
 	const float coplanar_eps
-)
+);
-{
-	// the two normals must be parallel-enough
-	const float angle = v3_mag(v3_sub(t0->normal_xyz, t1->normal_xyz));
-	if (angle < -coplanar_eps || +coplanar_eps < angle)
-		return -1;
-	
-	// find if there are two points shared
-	unsigned matches = 0;
-	for(int i = 0 ; i < 3 ; i++)
-	{
-		for(int j = 0 ; j < 3 ; j++)
-		{
-			if (!v3_eq(&t0->p[i], &t1->p[j]))
-				continue;
-			matches |= 1 << i;
-			break;
-		}
-	}
-
-	switch(matches)
-	{
-	case 0x3: return 0;
-	case 0x6: return 1;
-	case 0x5: return 2;
-	case 0x7:
-		fprintf(stderr, "uh, three points match?\n");
-		tri_print(t0);
-		tri_print(t1);
-		return -1;
-	default:
-		// no shared edge
-		return -1;
-	}
-}
 
 
 /*
@@ -201,27 +83,7 @@ tri_find_z(
 	const tri_t * const t,
 	const v3_t * const p,
 	float * const zout
-)
+);
-{
-	const float t1x = t->p[1].p[0] - t->p[0].p[0];
-	const float t1y = t->p[1].p[1] - t->p[0].p[1];
-	const float t1z = t->p[1].p[2] - t->p[0].p[2];
-	const float t2x = t->p[2].p[0] - t->p[0].p[0];
-	const float t2y = t->p[2].p[1] - t->p[0].p[1];
-	const float t2z = t->p[2].p[2] - t->p[0].p[2];
-	const float px = p->p[0] - t->p[0].p[0];
-	const float py = p->p[1] - t->p[0].p[1];
-
-	const float a = (px * t2y - py * t2x) / (t1x * t2y - t2x * t1y);
-	const float b = (px * t1y - py * t1x) / (t2x * t1y - t1x * t2y);
-
-	const float z = t->p[0].p[2] + a * t1z + b * t2z;
-
-	if (zout)
-		*zout = z;
-
-	return 0 <= a && 0 <= b && a + b <= 1;
-}
 
 
 /** Compute the points of intersection for two segments in 2d, and z points.
@@ -242,80 +104,8 @@ hidden_intersect(
 	const v3_t * const p3,
 	v3_t * const l0_int,
 	v3_t * const l1_int
-)
-{
-	const float p0_x = p0->p[0];
-	const float p0_y = p0->p[1];
-	const float p0_z = p0->p[2];
-	const float p1_x = p1->p[0];
-	const float p1_y = p1->p[1]; 
-	const float p1_z = p1->p[2];
-	const float p2_x = p2->p[0];
-	const float p2_y = p2->p[1];
-	const float p2_z = p2->p[2];
-	const float p3_x = p3->p[0];
-	const float p3_y = p3->p[1];
-	const float p3_z = p3->p[2];
-
-	const float s1_x = p1_x - p0_x;
-	const float s1_y = p1_y - p0_y;
-	const float s2_x = p3_x - p2_x;
-	const float s2_y = p3_y - p2_y;
-
-	// compute r x s
-	const float d = -s2_x * s1_y + s1_x * s2_y;
-
-	// if they are close to parallel, then we do not need to check
-	// for intersection (we define that as "non-intersecting")
-	if (-EPS < d && d < EPS)
-		return -1;
-
-	// Compute how far along each line they would interesect
-	const float r0 = ( s2_x * (p0_y - p2_y) - s2_y * (p0_x - p2_x)) / d;
-	const float r1 = (-s1_y * (p0_x - p2_x) + s1_x * (p0_y - p2_y)) / d;
-
-	// if they are not within the ratio (0,1), then the intersecton occurs
-	// outside of the segments and is not of concern
-	if (r0 < 0 || r0 > 1)
-		return -1;
-	if (r1 < 0 || r1 > 1)
-		return -1;
-
-	// Collision detected with the segments
-if(0) fprintf(stderr, "collision: %.0f,%.0f,%.0f->%.0f,%.0f,%.0f %.0f,%.0f,%.0f->%.0f,%.0f,%.0f == %.3f,%.3f\n",
-		p0_x, p0_y, p0_z,
-		p1_x, p1_y, p1_z,
-		p2_x, p2_y, p2_z,
-		p3_x, p3_y, p2_z,
-		r0,
-		r1
 );
 
-	const float ix = p0_x + (r0 * s1_x);
-	const float iy = p0_y + (r0 * s1_y);
-
-	// compute the z intercept for each on the two different coordinates
-	if(l0_int)
-	{
-		*l0_int = (v3_t){{
-			ix,
-			iy,
-			p0_z + r0 * (p1_z - p0_z)
-		}};
-	}
-
-	if(l1_int)
-	{
-		*l1_int = (v3_t){{
-			ix,
-			iy,
-			p2_z + r1 * (p3_z - p2_z)
-		}};
-	}
-
-	return r0;
-}
-
 
 /*
  * Recursive algorithm:
@@ -332,255 +122,8 @@ tri_seg_intersect(
 	const tri_t * zlist,
 	seg_t * s,
 	seg_t ** slist_visible
-)
-{
-	const float p0z = s->p[0].p[2];
-	const float p1z = s->p[1].p[2];
-	const float seg_max_z = max(p0z, p1z);
-
-	// avoid processing empty segments
-	const float seg_len = v3_len(&s->p[0], &s->p[1]);
-	if (seg_len < EPS)
-		return;
-
-static int recursive;
-recursive++;
-
-//fprintf(stderr, "%d: processing segment ", recursive); seg_print(s);
-	fprintf(stderr, "--- recursive %d\n", recursive);
-	seg_print(s);
-
-	for( const tri_t * t = zlist ; t ; t = t->next )
-	{
-		// if the segment is closer than the triangle,
-		// then we no longer have to check any further into
-		// the zlist (it is sorted by depth).
-		if (seg_max_z <= t->min[2])
-			break;
-
-#if 0
-		// make sure that we're not comparing to our own triangle
-		// or one that shares an edge with us (which might be in
-		// a different order)
-		if (v2_eq(s->src[0].p, t->p[0].p, 0.0005)
-		&&  v2_eq(s->src[1].p, t->p[1].p, 0.0005))
-			continue;
-		if (v2_eq(s->src[0].p, t->p[1].p, 0.0005)
-		&&  v2_eq(s->src[1].p, t->p[2].p, 0.0005))
-			continue;
-		if (v2_eq(s->src[0].p, t->p[2].p, 0.0005)
-		&&  v2_eq(s->src[1].p, t->p[0].p, 0.0005))
-			continue;
-		if (v2_eq(s->src[0].p, t->p[1].p, 0.0005)
-		&&  v2_eq(s->src[1].p, t->p[0].p, 0.0005))
-			continue;
-		if (v2_eq(s->src[0].p, t->p[2].p, 0.0005)
-		&&  v2_eq(s->src[1].p, t->p[1].p, 0.0005))
-			continue;
-		if (v2_eq(s->src[0].p, t->p[0].p, 0.0005)
-		&&  v2_eq(s->src[1].p, t->p[2].p, 0.0005))
-			continue;
-#endif
-
-		if (debug >= 2)
-			tri_print(t);
-/*
-		// if the segment is co-linear to any of the
-		// triangle edges, include it
-		for(int i = 0 ; i < 3 ; i++)
-		{
-			if (parallel(
-				&s->p[0], &s->p[1],
-				&t->p[i], &t->p[(i+1)%3]
-			))
-				goto next_segment;
-		}
-*/
-
-		float z0, z1;
-		int inside0 = tri_find_z(t, &s->p[0], &z0);
-		int inside1 = tri_find_z(t, &s->p[1], &z1);
-
-		if (debug >= 2 && (inside0 || inside1))
-		{
-			fprintf(stderr, "inside %d %d\n", inside0, inside1);
-		}
-
-		// if both are inside but the segment is infront of the
-		// triangle, then we retain the segment.
-		// otherwies we discard the segment
-		if (inside0 && inside1)
-		{
-			if (s->p[0].p[2] <= z0
-			&&  s->p[1].p[2] <= z1)
-				continue;
-			if (debug >= 2)
-				fprintf(stderr, "BOTH INSIDE\n");
-			recursive--;
-			return;
-		}
-
-		// split the segment for each intersection with the
-		// triangle segments and add it to the work queue.
-		int intersections = 0;
-		v3_t is[3] = {}; // 3d point of segment intercept
-		v3_t it[3] = {}; // 3d point of triangle intercept
-
-		for(int j = 0 ; j < 3 ; j++)
-		{
-			float ratio = hidden_intersect(
-				&s->p[0], &s->p[1],
-				&t->p[j], &t->p[(j+1)%3],
-				&is[intersections],
-				&it[intersections]
 );
 
-			if (ratio < 0)
-				continue;
-
-			if (debug >= 2)
-				fprintf(stderr, "%d ratio=%.2f\n", j, ratio);
-			intersections++;
-		}
-
-
-		// if none of them intersect, we keep looking
-		if (intersections == 0)
-			continue;
-
-		if (debug >= 2)
-			fprintf(stderr, "%d intersections\n", intersections);
-
-		if (intersections == 3)
-		{
-			// this likely means that the triangle is very, very
-			// small, so let's just ignore this triangle
-			if (debug >= 2)
-				fprintf(stderr, "Three intersections\n");
-			continue;
-		}
-
-
-		if (intersections == 2)
-		{
-			// figure out how far it is to each of the intersections
-			const float d00 = v3_len(&s->p[0], &is[0]);
-			const float d01 = v3_len(&s->p[0], &is[1]);
-			const float d10 = v3_len(&s->p[1], &is[0]);
-			const float d11 = v3_len(&s->p[1], &is[1]);
-
-			if (debug >= 2)
-				fprintf(stderr, "Two intersections\n");
-
-			// discard segments that have two interesections that match
-			// the segment exactly (distance from segment ends to
-			// intersection point close enough to zero).
-			if (d00 < EPS && d11 < EPS)
-			{
-				recursive--;
-				return;
-			}
-			if (d01 < EPS && d10 < EPS)
-			{
-				recursive--;
-				return;
-			}
-
-			// if the segment intersection is closer than the triangle,
-			// then we do nothing. degenerate cases are not handled
-			if (d00 <= d01
-			&& is[0].p[2] <= it[0].p[2]
-			&& is[1].p[2] <= it[1].p[2])
-				continue;
-			if (d00 > d01
-			&& is[1].p[2] <= it[0].p[2]
-			&& is[0].p[2] <= it[1].p[2])
-				continue;
-
-			// segment is behind the triangle,
-			// we have to create a new segment
-			// and shorten the existing segment
-			// find the two intersections that we have
-			// update the src field
-
-			// we need to create a new segment
-			seg_t * news;
-			if (d00 < d01)
-			{
-				// split from p0 to ix0
-				news = seg_new(s->p[0], is[0]);
-				news->src[0] = s->src[0];
-				news->src[1] = s->src[1];
-				s->p[0] = is[1];
-			} else {
-				// split from p0 to ix1
-				news = seg_new(s->p[0], is[1]);
-				news->src[0] = s->src[0];
-				news->src[1] = s->src[1];
-				s->p[0] = is[0];
-			}
-
-			// recursively start splitting the new segment
-			// starting at the next triangle down the z-depth
-			tri_seg_intersect(zlist->next, news, slist_visible);
-
-			// continue splitting our current segment
-			continue;
-		}
-
-		if (intersections == 1)
-		{
-			// if there is an intersection, but the segment intercept
-			// is closer than the triangle intercept, then no problem.
-			// we do not bother with degenerate cases of intersecting
-			// triangles
-			if (is[0].p[2] <= it[0].p[2]
-			&&  is[1].p[2] <= it[0].p[2])
-			{
-				//svg_line("#00FF00", s->p[0].p, s->p[1].p, 10);
-				continue;
-			}
-
-			if (inside0)
-			{
-				// shorten it on the 0 side
-				s->p[0] = is[0];
-// huh? shouldn't we process this one?
-return;
-				continue;
-			} else
-			if (inside1)
-			{
-				// shorten it on the 1 side
-				s->p[1] = is[0];
-// huh? shouldn't we process this one?
-return;
-				continue;
-			} else {
-				// both outside, but an intersection?
-				// split at that point and hope for the best
-				seg_t * const news = seg_new(s->p[0], is[0]);
-				news->src[0] = s->src[0];
-				news->src[1] = s->src[1];
-				s->p[0] = is[0];
-
-				tri_seg_intersect(zlist->next, news, slist_visible);
-				// continue splitting our current segment
-				continue;
-			}
-		}
-
-next_segment:
-		continue;
-	}
-
-	// if we've reached here the segment is visible
-	// and should be added to the visible list
-	s->next = *slist_visible;
-	*slist_visible = s;
-	recursive--;
-}
-
 
 /*
  * Fast check to see if t2 is entire occluded by t.
@@ -589,40 +132,6 @@ int
 tri_behind(
 	const tri_t * const t,
 	const tri_t * const t2
-)
+);
-{
-	float z0, z1, z2;
-	int inside0 = tri_find_z(t, &t2->p[0], &z0);
-	int inside1 = tri_find_z(t, &t2->p[1], &z1);
-	int inside2 = tri_find_z(t, &t2->p[2], &z2);
-
-	// easy check -- if none of the points are inside,
-	// t2 is not entirely occluded
-	if (!inside0 || !inside1 || !inside2)
-		return 0;
-
-	// are all of the intersection points ahead of t2?
-	int behind0 = t2->p[0].p[2] >= z0;
-	int behind1 = t2->p[1].p[2] >= z1;
-	int behind2 = t2->p[2].p[2] >= z2;
-	if (behind0 && behind1 && behind2)
-		return 1;
-
-	// it is a STL violation if they are not all on the
-	// same side (this would indicate that t and t2 intersect
-	// go ahead and prune since it will cause problems
-	if (behind0 || behind1 || behind2)
-	{
-/*
-		fprintf(stderr, "WARNING: triangles intersect %.0f %.0f %.0f inside %d %d %d behind %d %d %d\n", z0, z1, z2, inside0, inside1, inside2, behind0, behind1, behind2);
-		tri_print(t);
-		tri_print(t2);
-*/
-		return 1;
-	}
-
-	// they are all on the same side
-	return 0;
-}
 
 #endif