/** \file * Render a hidden wireframe version of an STL file. * */ #include #include #include #include #include #include #include #include #include "v3.h" #include "camera.h" #ifndef M_PI #define M_PI 3.1415926535897932384 #endif static int debug = 1; typedef struct { char header[80]; uint32_t num_triangles; } __attribute__((__packed__)) stl_header_t; typedef struct { v3_t normal; v3_t p[3]; uint16_t attr; } __attribute__((__packed__)) 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( const char * color, const float * p1, const float * p2, float thick ) { printf("\n", p1[0], p1[1], p2[0], p2[1], color, thick ); } static inline int v2_eq( const float p0[], const float p1[], const float eps ) { const float dx = p0[0] - p1[0]; const float dy = p0[1] - p1[1]; // are the points within epsilon of each other? if (-eps < dx && dx < eps && -eps < dy && dy < eps) return 1; // nope, not equal return 0; } static inline int v2_dist( const float p0[], const float p1[] ) { const float dx = p0[0] - p1[0]; const float dy = p0[1] - p1[1]; return sqrt(dx*dx + dy*dy); } /** 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; *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] ); } 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 */ 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; } /* * 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; 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, 0.5) && v2_eq(s->src[1].p, t->p[1].p, 0.5)) continue; if (v2_eq(s->src[0].p, t->p[1].p, 0.5) && v2_eq(s->src[1].p, t->p[2].p, 0.5)) continue; if (v2_eq(s->src[0].p, t->p[2].p, 0.5) && v2_eq(s->src[1].p, t->p[0].p, 0.5)) continue; if (v2_eq(s->src[0].p, t->p[1].p, 0.5) && v2_eq(s->src[1].p, t->p[0].p, 0.5)) continue; if (v2_eq(s->src[0].p, t->p[2].p, 0.5) && v2_eq(s->src[1].p, t->p[1].p, 0.5)) continue; if (v2_eq(s->src[0].p, t->p[0].p, 0.5) && v2_eq(s->src[1].p, t->p[2].p, 0.5)) continue; //fprintf(stderr, "triangle "); tri_print(t); #if 0 // do a quick test of does this segment even comes // close to this triangle if (p0x < t->min[0] && p1x < t->min[0] && p0y < t->min[1] && p1y < t->min[1]) continue; if (p0x > t->max[0] && p1x > t->max[0] && p0y > t->max[2] && p1y > t->max[2]) continue; if (p0x < t->min[0] && p1x < t->min[0] && p0y > t->max[2] && p1y > t->max[2]) continue; if (p0x > t->max[0] && p1x > t->max[0] && p0y < t->min[1] && p1y < t->min[1]) continue; // make sure this isn't the same actual line if (v3_eq(&s->src[0], &t->p[0]) || v3_eq(&s->src[1], &t->p[1])) continue; if (v3_eq(&s->src[0], &t->p[1]) || v3_eq(&s->src[1], &t->p[2])) continue; if (v3_eq(&s->src[0], &t->p[2]) || v3_eq(&s->src[1], &t->p[0])) continue; #endif 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) continue; if (s->p[1].p[2] <= z1) continue; //svg_line("#0000FF", s->p[0].p, s->p[1].p, 0); //svg_line("#00FF00", t->p[0].p, t->p[1].p, 0); //svg_line("#00FF00", t->p[1].p, t->p[2].p, 0); //svg_line("#00FF00", t->p[2].p, t->p[0].p, 0); if(0) { fprintf(stderr, "BOTH INSIDE\n"); tri_print(t); seg_print(s); } //svg_line("#00FF00", s->p[0].p, s->p[1].p, 10); //svg_line("#0000FF", t->p[0].p, t->p[1].p, 2); //svg_line("#0000FF", t->p[1].p, t->p[2].p, 2); //svg_line("#0000FF", t->p[2].p, t->p[0].p, 2); 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; // deal with corner cases where the segment // exactly lines up with the triangle edge // we do not treat this as an intersection /* if (-EPS < ratio && ratio < EPS) { inside0 = 0; } else if (1-EPS < ratio && ratio < 1+EPS) { inside1 = 0; } else { // this is a real intersection intersections++; } */ intersections++; } // if none of them intersect, we keep looking if (intersections == 0) continue; //fprintf(stderr, "split %d %d inter %d\n", inside0 , inside1, intersections); if (intersections == 3) { // this likely means that the triangle is very, very // small, so let's just throw away this line segment /* fprintf(stderr, "uh, three intersections?\n"); seg_print(s); tri_print(t); svg_line("#00FF00", s->p[0].p, s->p[1].p, 10); */ 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]); //fprintf(stderr, "two intersections %.0f %.0f\n", d00, d01); // 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]; } /* fprintf(stderr, "old segment:" ); seg_print(s); fprintf(stderr, "%d new segment:", recursive++ ); seg_print(news); */ // recursively start splitting the new segment // starting at the next triangle down the z-depth tri_seg_intersect(zlist->next, news, slist_visible); //fprintf(stderr, "%d -----\n", --recursive); // 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; } /* // due to floating point issues, one of these might // be closer to the edge. re-check the barycentric // coordinates for "close enough" inside0 = bary[0].p[0] > -EPS && bary[0].p[1] > -EPS && bary[0].p[2] > -EPS; inside1 = bary[1].p[0] > -EPS && bary[1].p[1] > -EPS && bary[1].p[2] > -EPS; */ // segment is behind the triangle, so it needs to be // cut into pieces /* if (v2_eq(s->p[0].p, is[0].p, 0.01) || v2_eq(s->p[1].p, is[0].p, 0.01)) { // we're touching on one side, ignore it continue; } else */ if (inside0) { // shorten it on the 0 side s->p[0] = is[0]; //fprintf(stderr, "short seg 0: "); seg_print(s); continue; } else if (inside1) { // shorten it on the 1 side s->p[1] = is[0]; //fprintf(stderr, "short seg 1: "); seg_print(s); 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); //svg_line("#00FF00", s->p[0].p, s->p[1].p, 10); //fprintf(stderr, "%d -----\n", --recursive); // continue splitting our current segment continue; /* fprintf(stderr, "**** uh, both outside but one intersection? %.3f,%.3f\n", is[0].p[0], is[0].p[1] ); seg_print(s); tri_print(t); fprintf(stderr, "bary0 %f,%f,%f\n", bary[0].p[0], bary[0].p[1], bary[0].p[2]); fprintf(stderr, "bary1 %f,%f,%f\n", bary[1].p[0], bary[1].p[1], bary[1].p[2]); svg_line("#00FF00", s->p[0].p, s->p[1].p, 10); continue; */ } } } // if we've reached here the segment is visible // and should be added to the visible list if(0) fprintf(stderr, "good: %.0f,%.0f,%.0f-> %.0f,%.0f,%.0f\n", s->p[0].p[0], s->p[0].p[1], s->p[0].p[2], s->p[1].p[0], s->p[1].p[1], s->p[1].p[2] ); s->next = *slist_visible; *slist_visible = s; recursive--; } int main( int argc, char ** argv ) { const size_t max_len = 32 << 20; uint8_t * const buf = calloc(max_len, 1); float phi = argc > 1 ? atof(argv[1]) * M_PI/180 : 0; float theta = argc > 2 ? atof(argv[2]) * M_PI/180 : 0; float psi = argc > 3 ? atof(argv[3]) * M_PI/180 : 0; ssize_t rc = read(0, buf, max_len); if (rc == -1) return EXIT_FAILURE; const stl_header_t * const hdr = (const void*) buf; const stl_face_t * const stl_faces = (const void*)(hdr+1); const int num_triangles = hdr->num_triangles; int backface = 1; int coplanar = 1; int hidden = 1; float coplanar_eps = 0.001; if(debug) { fprintf(stderr, "header: '%s'\n", hdr->header); fprintf(stderr, "num: %d\n", num_triangles); } // looking at (0,0,0) v3_t eye = { { 0, 0, 400 } }; const camera_t * const cam = camera_new(eye, phi, theta, psi); printf("\n"); float off_x = 500; float off_y = 500; printf("\n", off_x, off_y); int rejected = 0; tri_t * zlist = NULL; seg_t * slist = NULL; seg_t * slist_visible = NULL; int retained = 0; // transform the stl by the camera projection and generate // a z-sorted list of triangles for (int i = 0 ; i < num_triangles ; i++) { const stl_face_t * const stl = &stl_faces[i]; v3_t s[3]; for(int j = 0 ; j < 3 ; j++) camera_project(cam, &stl->p[j], &s[j]); if(0)fprintf(stderr, "%.3f,%.3f,%.3f -> %.0f,%.0f\n", stl->p[0].p[0], stl->p[0].p[1], stl->p[0].p[2], s[0].p[0], s[0].p[1] ); tri_t * const tri = tri_new(s, stl->p); // reject this face if any of the vertices are behind us if (tri->min[2] < 0) goto reject; // do a back-face cull to determine if this triangle // is not facing us. we have to determine the orientation // from the winding of the new projection if (backface && tri->normal.p[2] <= 0) goto reject; retained++; // it passes the first tests, so insert the triangle // into the list and the three line segments tri_insert(&zlist, tri); continue; reject: tri_delete(tri); rejected++; } if (debug) fprintf(stderr, "Retained %d, rejected %d triangles\n", retained, rejected); // generate a list of segments, dropping any coplanar ones rejected = 0; for(tri_t * t = zlist ; t ; t = t->next) { unsigned matches = 0; tri_print(t); if(coplanar) for(tri_t * t2 = zlist ; t2 ; t2 = t2->next) { if (t == t2) continue; const int edge = tri_coplanar(t, t2, coplanar_eps); if (edge < 0) continue; matches |= 1 << edge; } for(int j = 0 ; j < 3 ; j++) { // drop any that are coplanar if (matches & (1 << j)) { rejected++; continue; } seg_t * s = seg_new(t->p[j], t->p[(j+1) % 3]); s->next = slist; slist = s; } } if (debug) fprintf(stderr, "Rejected %d coplanar segments\n", rejected); // we now have a z-sorted list of triangles rejected = 0; if(hidden) { // work on each segment, intersecting it with all of the triangles while(slist) { seg_t * s = slist; slist = s->next; tri_seg_intersect(zlist, s, &slist_visible); } } else { // don't do any intersection tests slist_visible = slist; slist = NULL; } // display all of the visible segments for(seg_t * s = slist_visible ; s ; s = s->next) { svg_line("#FF0000", s->p[0].p, s->p[1].p, 1); } if (debug) fprintf(stderr, "Occluded %d triangles\n", rejected); printf("\n"); printf("\n"); return 0; }