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split triangle and segment into separate headers

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This commit is contained in:
Trammell hudson 2018-03-01 23:00:01 -05:00
parent 38fd7d66ff
commit e04a5c9f37
Failed to extract signature
4 changed files with 736 additions and 635 deletions
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664
hiddenwire.c
View File

@ -4,6 +4,8 @@
*/
// ./hiddenwire --no-hidden --prune 1 -v < nyc-50000.stl --camera 400,60,-600 --lookat 450,0,-800 --up 0,1,0 --fov 20 > test3.svg
static int debug = 0;
#include <stdio.h>
#include <stdlib.h>
#include <stdint.h>
@ -14,6 +16,7 @@
#include <assert.h>
#include <getopt.h>
#include "v3.h"
#include "tri.h"
#include "camera.h"
@ -55,7 +58,6 @@ static const struct option long_options[] = {
#define M_PI 3.1415926535897932384
#endif
static int debug = 0;
typedef struct
{
@ -74,27 +76,6 @@ typedef struct
stl_face_t;
typedef struct _tri_t tri_t;
struct _tri_t
{
v3_t p[3]; // camera space
v3_t normal; // camera space
v3_t normal_xyz; // original xyz space
float min[3]; // camera space
float max[3]; // camera space
tri_t * next;
tri_t ** prev;
};
typedef struct _seg_t seg_t;
struct _seg_t {
v3_t p[2];
v3_t src[2];
seg_t * next;
};
void
svg_line(
@ -136,620 +117,37 @@ v2_eq(
}
/** 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;
}
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);
}
seg_t *
seg_new(
const v3_t p0,
const v3_t p1
)
{
seg_t * const s = calloc(1, sizeof(*s));
if (!s)
return NULL;
s->p[0] = p0;
s->p[1] = p1;
s->src[0] = p0;
s->src[1] = p1;
s->next = NULL;
return s;
}
void
seg_print(
const seg_t * const s
)
{
fprintf(stderr, "%.0f,%.0f -> %.0f,%.0f (was %.0f,%.0f -> %.0f,%.0f\n",
s->p[0].p[0],
s->p[0].p[1],
s->p[1].p[0],
s->p[1].p[1],
s->src[0].p[0],
s->src[0].p[1],
s->src[1].p[0],
s->src[1].p[1]
);
}
// Compute the length of a line in screen space, ignoring Z
float
v3_dist_2d(
const v3_t * p0,
const v3_t * p1
)
{
const float dx = p1->p[0] - p0->p[0];
const float dy = p1->p[1] - p0->p[1];
return sqrt(dx*dx + dy*dy);
}
// 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
* Determine if a segment is part of a triangle edge
*/
int
tri_find_z(
const tri_t * const t,
const v3_t * const p,
float * const zout
parallel(
const v3_t * const p00,
const v3_t * const p01,
const v3_t * const p10,
const v3_t * const p11
)
{
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];
//v3_t v = v3_sub(*p11, *p10);
v3_t v0 = v3_sub(*p01, *p00);
v3_t v1 = v3_sub(*p11, *p10);
v3_t vx = v3_cross(v0, v1);
const float a = (px * t2y - py * t2x) / (t1x * t2y - t2x * t1y);
const float b = (px * t1y - py * t1x) / (t2x * t1y - t1x * t2y);
float angle = v3_mag2(vx);
const float z = t->p[0].p[2] + a * t1z + b * t2z;
if (zout)
*zout = z;
return 0 <= a && 0 <= b && a + b <= 1;
}
/*
* 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);
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;
// 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;
float z0, z1;
int inside0 = tri_find_z(t, &s->p[0], &z0);
int inside1 = tri_find_z(t, &s->p[1], &z1);
// 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;
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;
intersections++;
}
// if none of them intersect, we keep looking
if (intersections == 0)
continue;
if (intersections == 3)
{
// this likely means that the triangle is very, very
// small, so let's just throw away this line segment
recursive--;
return;
}
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]);
// 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;
}
}
}
// 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)
// if the angle is far from zero, definitely not parallel
if (angle < -EPS || EPS < angle)
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;
// they might be parallel, figure out if they are the same
return 1;
}
int v3_parse(v3_t * out, const char * str)
{
int rc = sscanf(str, "%f,%f,%f",
@ -774,12 +172,6 @@ int onscreen(
/*
if (p->p[1] < -height/2 || height/2 < p->p[1])
return 0;
*/
/*
if (p->p[0] < 0 || width < p->p[0])
return 0;
if (p->p[1] < 0 || height < p->p[1])
return 0;
*/
return 1;
}
@ -911,6 +303,7 @@ int main(
goto reject_early;
}
// scale to the image size
s[j].p[0] *= width;
s[j].p[1] *= width;
s[j].p[2] *= width;
@ -919,7 +312,7 @@ int main(
if(debug >= 2)
for(int j = 0 ; j < 3 ; j++)
{
fprintf(stderr, "%.3f %.3f %.3f -> %.3f %.3f %.3f\n",
fprintf(stderr, "%+8.1f %+8.1f %+8.1f -> %+8.1f %+8.1f %+8.1f\n",
stl->p[j].p[0],
stl->p[j].p[1],
stl->p[j].p[2],
@ -1054,13 +447,23 @@ reject_early:
// we now have a z-sorted list of triangles
rejected = 0;
// compute how many we actuall have remaining
int remaining = 0;
if (debug)
{
for(seg_t * s = slist ; s ; s = s->next)
remaining++;
fprintf(stderr, "%d segments remain to process\n", remaining);
}
if(do_hidden)
{
// work on each segment, intersecting it with all of the triangles
int processed = 0;
while(slist)
{
if (++processed % 100 == 0)
if (debug && ++processed % 1 == 0)
fprintf(stderr, "Hidden %d\n", processed);
seg_t * s = slist;
@ -1080,9 +483,6 @@ reject_early:
svg_line("#FF0000", s->p[0].p, s->p[1].p, 1);
}
if (debug)
fprintf(stderr, "Occluded %d triangles\n", rejected);
printf("</g>\n");
printf("</svg>\n");

50
seg.h Normal file
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@ -0,0 +1,50 @@
#ifndef _seg_h_
#define _seg_h_
#include "v3.h"
typedef struct _seg_t seg_t;
struct _seg_t {
v3_t p[2];
v3_t src[2];
seg_t * next;
};
seg_t *
seg_new(
const v3_t p0,
const v3_t p1
)
{
seg_t * const s = calloc(1, sizeof(*s));
if (!s)
return NULL;
s->p[0] = p0;
s->p[1] = p1;
s->src[0] = p0;
s->src[1] = p1;
s->next = NULL;
return s;
}
void
seg_print(
const seg_t * const s
)
{
fprintf(stderr, "%.0f,%.0f -> %.0f,%.0f (was %.0f,%.0f -> %.0f,%.0f)\n",
s->p[0].p[0],
s->p[0].p[1],
s->p[1].p[0],
s->p[1].p[1],
s->src[0].p[0],
s->src[0].p[1],
s->src[1].p[0],
s->src[1].p[1]
);
}
#endif

628
tri.h Normal file
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@ -0,0 +1,628 @@
/*
* Triangle manipulations
*/
#ifndef _tri_h_
#define _tri_h_
#include "v3.h"
#include "seg.h"
typedef struct _tri_t tri_t;
struct _tri_t
{
v3_t p[3]; // camera space
v3_t normal; // camera space
v3_t normal_xyz; // original xyz space
float min[3]; // camera space
float max[3]; // camera space
tri_t * next;
tri_t ** prev;
};
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 (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.
*/
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

29
v3.h
View File

@ -6,7 +6,7 @@
#include <math.h>
#define EPS 0.0001
#define EPS 0.001
#ifndef M_PI
#define M_PI 3.1415926535897932384
@ -82,7 +82,7 @@ v3_len(
}
static inline double
v3_mag(
v3_mag2(
const v3_t v0
)
{
@ -90,7 +90,15 @@ v3_mag(
float dy = v0.p[1];
float dz = v0.p[2];
return sqrt(dx*dx + dy*dy + dz*dz);
return dx*dx + dy*dy + dz*dz;
}
static inline double
v3_mag(
const v3_t v0
)
{
return sqrt(v3_mag2(v0));
}
@ -199,4 +207,19 @@ v3_cross(
return c;
}
// Compute the length of a line in screen space, ignoring Z
static inline float
v3_dist_2d(
const v3_t * p0,
const v3_t * p1
)
{
const float dx = p1->p[0] - p0->p[0];
const float dy = p1->p[1] - p0->p[1];
return sqrt(dx*dx + dy*dy);
}
#endif