629 lines
14 KiB
C
629 lines
14 KiB
C
/*
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* Triangle manipulations
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*/
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#ifndef _tri_h_
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#define _tri_h_
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#include "v3.h"
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#include "seg.h"
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typedef struct _tri_t tri_t;
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struct _tri_t
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{
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v3_t p[3]; // camera space
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v3_t normal; // camera space
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v3_t normal_xyz; // original xyz space
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float min[3]; // camera space
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float max[3]; // camera space
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tri_t * next;
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tri_t ** prev;
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};
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tri_t *
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tri_new(
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const v3_t * p_cam,
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const v3_t * p_xyz
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)
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{
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tri_t * const t = calloc(1, sizeof(*t));
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if (!t)
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return NULL;
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for(int i = 0 ; i < 3 ; i++)
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t->p[i] = p_cam[i];
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// precompute the normals
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t->normal = v3_norm(v3_cross(
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v3_sub(t->p[1], t->p[0]),
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v3_sub(t->p[2], t->p[1])
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));
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t->normal_xyz = v3_norm(v3_cross(
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v3_sub(p_xyz[1], p_xyz[0]),
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v3_sub(p_xyz[2], p_xyz[1])
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));
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// compute the bounding box for the triangle in camera space
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for(int j = 0 ; j < 3 ; j++)
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{
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t->min[j] = min(min(t->p[0].p[j], t->p[1].p[j]), t->p[2].p[j]);
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t->max[j] = max(max(t->p[0].p[j], t->p[1].p[j]), t->p[2].p[j]);
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}
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return t;
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}
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// insert a triangle into our z-sorted list
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void
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tri_insert(
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tri_t ** zlist,
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tri_t * t
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)
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{
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while(1)
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{
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tri_t * const iter = *zlist;
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if (!iter)
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break;
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// check to see if our new triangle is closer than
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// the current triangle
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if(iter->min[2] > t->min[2])
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break;
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zlist = &(iter->next);
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}
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// either we reached the end of the list,
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// or we have found where our new triangle is sorted
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t->next = *zlist;
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t->prev = zlist;
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*zlist = t;
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if (t->next)
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t->next->prev = &t->next;
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}
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void
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tri_delete(tri_t * t)
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{
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if (t->next)
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t->next->prev = t->prev;
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if (t->prev)
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*(t->prev) = t->next;
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t->next = NULL;
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t->prev = NULL;
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free(t);
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}
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// Compute the 2D area of a triangle in screen space
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// using Heron's formula
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float
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tri_area_2d(
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const tri_t * const t
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)
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{
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const float a = v3_dist_2d(&t->p[0], &t->p[1]);
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const float b = v3_dist_2d(&t->p[1], &t->p[2]);
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const float c = v3_dist_2d(&t->p[2], &t->p[0]);
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const float s = (a + b + c) / 2;
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return sqrt(s * (s-a) * (s-b) * (s-c));
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}
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void
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tri_print(
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const tri_t * const t
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)
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{
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fprintf(stderr, "%.0f,%.0f,%.0f %.0f,%.0f,%.0f %.0f,%.0f,%.0f norm %.3f,%.3f,%.3f\n",
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t->p[0].p[0],
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t->p[0].p[1],
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t->p[0].p[2],
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t->p[1].p[0],
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t->p[1].p[1],
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t->p[1].p[2],
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t->p[2].p[0],
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t->p[2].p[1],
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t->p[2].p[2],
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t->normal.p[0],
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t->normal.p[1],
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t->normal.p[2]
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);
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}
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/* Check if two triangles are coplanar and share an edge.
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*
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* Returns -1 if not coplanar, 0-2 for the edge in t0 that they share.
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*/
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int
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tri_coplanar(
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const tri_t * const t0,
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const tri_t * const t1,
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const float coplanar_eps
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)
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{
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// the two normals must be parallel-enough
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const float angle = v3_mag(v3_sub(t0->normal_xyz, t1->normal_xyz));
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if (angle < -coplanar_eps || +coplanar_eps < angle)
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return -1;
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// find if there are two points shared
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unsigned matches = 0;
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for(int i = 0 ; i < 3 ; i++)
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{
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for(int j = 0 ; j < 3 ; j++)
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{
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if (!v3_eq(&t0->p[i], &t1->p[j]))
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continue;
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matches |= 1 << i;
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break;
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}
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}
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switch(matches)
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{
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case 0x3: return 0;
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case 0x6: return 1;
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case 0x5: return 2;
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case 0x7:
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fprintf(stderr, "uh, three points match?\n");
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tri_print(t0);
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tri_print(t1);
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return -1;
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default:
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// no shared edge
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return -1;
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}
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}
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/*
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* Find the Z point of an XY coordinate in a triangle.
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*
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* p can be written as a combination of t01 and t02,
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* p - t0 = a * (t1 - t0) + b * (t2 - t0)
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* setting t0 to 0, this becomes:
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* p = a * t1 + b * t2
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* which is two equations with two unknowns
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*
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* Returns true if the point is inside the triangle
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*/
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int
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tri_find_z(
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const tri_t * const t,
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const v3_t * const p,
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float * const zout
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)
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{
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const float t1x = t->p[1].p[0] - t->p[0].p[0];
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const float t1y = t->p[1].p[1] - t->p[0].p[1];
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const float t1z = t->p[1].p[2] - t->p[0].p[2];
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const float t2x = t->p[2].p[0] - t->p[0].p[0];
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const float t2y = t->p[2].p[1] - t->p[0].p[1];
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const float t2z = t->p[2].p[2] - t->p[0].p[2];
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const float px = p->p[0] - t->p[0].p[0];
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const float py = p->p[1] - t->p[0].p[1];
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const float a = (px * t2y - py * t2x) / (t1x * t2y - t2x * t1y);
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const float b = (px * t1y - py * t1x) / (t2x * t1y - t1x * t2y);
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const float z = t->p[0].p[2] + a * t1z + b * t2z;
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if (zout)
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*zout = z;
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return 0 <= a && 0 <= b && a + b <= 1;
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}
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/** Compute the points of intersection for two segments in 2d, and z points.
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*
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* This is a specialized ray intersection algorithm for the
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* hidden wire-frame removal code that computes the intersection
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* points for two rays (in 2D, "orthographic") and then computes
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* the Z depth for the intersections along each of the segments.
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*
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* Returns -1 for non-intersecting, otherwise a ratio of how far
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* along the intersection is on the l0.
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*/
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float
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hidden_intersect(
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const v3_t * const p0,
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const v3_t * const p1,
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const v3_t * const p2,
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const v3_t * const p3,
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v3_t * const l0_int,
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v3_t * const l1_int
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)
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{
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const float p0_x = p0->p[0];
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const float p0_y = p0->p[1];
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const float p0_z = p0->p[2];
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const float p1_x = p1->p[0];
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const float p1_y = p1->p[1];
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const float p1_z = p1->p[2];
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const float p2_x = p2->p[0];
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const float p2_y = p2->p[1];
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const float p2_z = p2->p[2];
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const float p3_x = p3->p[0];
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const float p3_y = p3->p[1];
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const float p3_z = p3->p[2];
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const float s1_x = p1_x - p0_x;
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const float s1_y = p1_y - p0_y;
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const float s2_x = p3_x - p2_x;
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const float s2_y = p3_y - p2_y;
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// compute r x s
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const float d = -s2_x * s1_y + s1_x * s2_y;
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// if they are close to parallel, then we do not need to check
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// for intersection (we define that as "non-intersecting")
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if (-EPS < d && d < EPS)
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return -1;
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// Compute how far along each line they would interesect
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const float r0 = ( s2_x * (p0_y - p2_y) - s2_y * (p0_x - p2_x)) / d;
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const float r1 = (-s1_y * (p0_x - p2_x) + s1_x * (p0_y - p2_y)) / d;
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// if they are not within the ratio (0,1), then the intersecton occurs
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// outside of the segments and is not of concern
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if (r0 < 0 || r0 > 1)
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return -1;
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if (r1 < 0 || r1 > 1)
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return -1;
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// Collision detected with the segments
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if(0) fprintf(stderr, "collision: %.0f,%.0f,%.0f->%.0f,%.0f,%.0f %.0f,%.0f,%.0f->%.0f,%.0f,%.0f == %.3f,%.3f\n",
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p0_x, p0_y, p0_z,
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p1_x, p1_y, p1_z,
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p2_x, p2_y, p2_z,
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p3_x, p3_y, p2_z,
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r0,
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r1
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);
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const float ix = p0_x + (r0 * s1_x);
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const float iy = p0_y + (r0 * s1_y);
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// compute the z intercept for each on the two different coordinates
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if(l0_int)
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{
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*l0_int = (v3_t){{
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ix,
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iy,
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p0_z + r0 * (p1_z - p0_z)
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}};
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}
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if(l1_int)
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{
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*l1_int = (v3_t){{
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ix,
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iy,
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p2_z + r1 * (p3_z - p2_z)
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}};
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}
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return r0;
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}
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/*
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* Recursive algorithm:
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* Given a line segment and a list of triangles,
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* find if the line segment crosses any triangle.
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* If it crosses a triangle the segment will be shortened
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* and an additional one might be created.
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* Recusively try intersecting the new segment (starting at the same triangle)
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* and then continue trying the shortened segment.
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*/
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void
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tri_seg_intersect(
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const tri_t * zlist,
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seg_t * s,
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seg_t ** slist_visible
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)
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{
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const float p0z = s->p[0].p[2];
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const float p1z = s->p[1].p[2];
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const float seg_max_z = max(p0z, p1z);
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// avoid processing empty segments
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const float seg_len = v3_len(&s->p[0], &s->p[1]);
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if (seg_len < EPS)
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return;
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static int recursive;
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recursive++;
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//fprintf(stderr, "%d: processing segment ", recursive); seg_print(s);
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fprintf(stderr, "--- recursive %d\n", recursive);
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seg_print(s);
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for( const tri_t * t = zlist ; t ; t = t->next )
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{
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// if the segment is closer than the triangle,
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// then we no longer have to check any further into
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// the zlist (it is sorted by depth).
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if (seg_max_z <= t->min[2])
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break;
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#if 0
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// make sure that we're not comparing to our own triangle
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// or one that shares an edge with us (which might be in
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// a different order)
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if (v2_eq(s->src[0].p, t->p[0].p, 0.0005)
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&& v2_eq(s->src[1].p, t->p[1].p, 0.0005))
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continue;
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if (v2_eq(s->src[0].p, t->p[1].p, 0.0005)
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&& v2_eq(s->src[1].p, t->p[2].p, 0.0005))
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continue;
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if (v2_eq(s->src[0].p, t->p[2].p, 0.0005)
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&& v2_eq(s->src[1].p, t->p[0].p, 0.0005))
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continue;
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if (v2_eq(s->src[0].p, t->p[1].p, 0.0005)
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&& v2_eq(s->src[1].p, t->p[0].p, 0.0005))
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continue;
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if (v2_eq(s->src[0].p, t->p[2].p, 0.0005)
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&& v2_eq(s->src[1].p, t->p[1].p, 0.0005))
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continue;
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if (v2_eq(s->src[0].p, t->p[0].p, 0.0005)
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&& v2_eq(s->src[1].p, t->p[2].p, 0.0005))
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continue;
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#endif
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if (debug >= 2)
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tri_print(t);
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/*
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// if the segment is co-linear to any of the
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// triangle edges, include it
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for(int i = 0 ; i < 3 ; i++)
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{
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if (parallel(
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&s->p[0], &s->p[1],
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&t->p[i], &t->p[(i+1)%3]
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))
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goto next_segment;
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}
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*/
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float z0, z1;
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int inside0 = tri_find_z(t, &s->p[0], &z0);
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int inside1 = tri_find_z(t, &s->p[1], &z1);
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if (debug >= 2 && (inside0 || inside1))
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{
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fprintf(stderr, "inside %d %d\n", inside0, inside1);
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}
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// if both are inside but the segment is infront of the
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// triangle, then we retain the segment.
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// otherwies we discard the segment
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if (inside0 && inside1)
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{
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if (s->p[0].p[2] <= z0
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&& s->p[1].p[2] <= z1)
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continue;
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if (debug >= 2)
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fprintf(stderr, "BOTH INSIDE\n");
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recursive--;
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return;
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}
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// split the segment for each intersection with the
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// triangle segments and add it to the work queue.
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int intersections = 0;
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v3_t is[3] = {}; // 3d point of segment intercept
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v3_t it[3] = {}; // 3d point of triangle intercept
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for(int j = 0 ; j < 3 ; j++)
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{
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float ratio = hidden_intersect(
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&s->p[0], &s->p[1],
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&t->p[j], &t->p[(j+1)%3],
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&is[intersections],
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&it[intersections]
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);
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if (ratio < 0)
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continue;
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if (debug >= 2)
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fprintf(stderr, "%d ratio=%.2f\n", j, ratio);
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intersections++;
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}
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|
|
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// if none of them intersect, we keep looking
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if (intersections == 0)
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continue;
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if (debug >= 2)
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fprintf(stderr, "%d intersections\n", intersections);
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if (intersections == 3)
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{
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// this likely means that the triangle is very, very
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// small, so let's just ignore this triangle
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if (debug >= 2)
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fprintf(stderr, "Three intersections\n");
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continue;
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}
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|
|
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if (intersections == 2)
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{
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// figure out how far it is to each of the intersections
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const float d00 = v3_len(&s->p[0], &is[0]);
|
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const float d01 = v3_len(&s->p[0], &is[1]);
|
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const float d10 = v3_len(&s->p[1], &is[0]);
|
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const float d11 = v3_len(&s->p[1], &is[1]);
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|
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if (debug >= 2)
|
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fprintf(stderr, "Two intersections\n");
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// discard segments that have two interesections that match
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// the segment exactly (distance from segment ends to
|
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// intersection point close enough to zero).
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if (d00 < EPS && d11 < EPS)
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{
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recursive--;
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return;
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}
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if (d01 < EPS && d10 < EPS)
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{
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recursive--;
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return;
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}
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|
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// if the segment intersection is closer than the triangle,
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// then we do nothing. degenerate cases are not handled
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if (d00 <= d01
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&& is[0].p[2] <= it[0].p[2]
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&& is[1].p[2] <= it[1].p[2])
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continue;
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if (d00 > d01
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&& is[1].p[2] <= it[0].p[2]
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&& is[0].p[2] <= it[1].p[2])
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continue;
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|
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// segment is behind the triangle,
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// we have to create a new segment
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// and shorten the existing segment
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// find the two intersections that we have
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// update the src field
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|
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// we need to create a new segment
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seg_t * news;
|
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if (d00 < d01)
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{
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// split from p0 to ix0
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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;
|
|
}
|
|
|
|
#endif
|