--- /dev/null
+/* quickhull, Copyright (c) 2016 Karim Naaji, karim.naaji@gmail.com
+ https://github.com/karimnaaji/3d-quickhull
+
+ LICENCE:
+ The MIT License (MIT)
+
+ Copyright (c) 2016 Karim Naaji, karim.naaji@gmail.com
+
+ Permission is hereby granted, free of charge, to any person obtaining a copy
+ of this software and associated documentation files (the "Software"), to deal
+ in the Software without restriction, including without limitation the rights
+ to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+ copies of the Software, and to permit persons to whom the Software is
+ furnished to do so, subject to the following conditions:
+
+ The above copyright notice and this permission notice shall be included in
+ all copies or substantial portions of the Software.
+
+ THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+ IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+ FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+ AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+ LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+ OUT OF OR IN CONNECTION WITH THE
+
+ REFERENCES:
+ [1] http://box2d.org/files/GDC2014/DirkGregorius_ImplementingQuickHull.pdf
+ [2] http://www.cs.smith.edu/~orourke/books/compgeom.html
+ [3] http://www.flipcode.com/archives/The_Half-Edge_Data_Structure.shtml
+ [4] http://doc.cgal.org/latest/HalfedgeDS/index.html
+ [5] http://thomasdiewald.com/blog/?p=1888
+ [6] https://fgiesen.wordpress.com/2012/02/21/half-edge-based-mesh-representations-theory/
+
+ HOWTO:
+ #define QUICKHULL_DEBUG // Only if assertions need to be checked
+ #include "quickhull.h"
+
+ HISTORY:
+ - 25-Feb-2018: jwz: adapted for xscreensaver
+ - 1.0.1 (2016-11-01): Various improvements over epsilon issues and
+ degenerate faces
+ Debug functionalities to test final results dynamically
+ API to export hull meshes in OBJ files
+ - 1.0 (2016-09-10): Initial
+
+ TODO:
+ - use float* from public interface
+ - reduce memory usage
+*/
+
+#ifdef HAVE_CONFIG_H
+# include "config.h"
+#endif /* HAVE_CONFIG_H */
+
+#include "quickhull.h"
+
+#include <math.h> /* sqrt & fabs */
+#include <stdio.h> /* FILE */
+#include <string.h> /* memcpy */
+
+/* Quickhull helpers, define your own if needed */
+#ifndef QUICKHULL_HELPERS
+#include <stdlib.h> /* malloc, free, realloc */
+#define QUICKHULL_HELPERS 1
+#define QH_MALLOC(T, N) ((T*) malloc(N * sizeof(T)))
+#define QH_REALLOC(T, P, N) ((T*)realloc(P, sizeof(T) * N))
+#define QH_FREE(T) free(T)
+#define QH_SWAP(T, A, B) { T tmp = B; B = A; A = tmp; }
+#ifdef QUICKHULL_DEBUG
+#define QH_ASSERT(STMT) if (!(STMT)) { *(int *)0 = 0; }
+#define QH_LOG(FMT, ...) printf(FMT, ## __VA_ARGS__)
+#else
+#define QH_ASSERT(STMT)
+#define QH_LOG(FMT, ...)
+#endif /* QUICKHULL_DEBUG */
+#endif /* QUICKHULL_HELPERS */
+
+#ifndef QH_FLT_MAX
+#define QH_FLT_MAX 1e+37F
+#endif
+
+#ifndef QH_FLT_EPS
+#define QH_FLT_EPS 1E-5F
+#endif
+
+#ifndef QH_VERTEX_SET_SIZE
+#define QH_VERTEX_SET_SIZE 128
+#endif
+
+typedef long qh_index_t;
+
+typedef struct qh_half_edge {
+ qh_index_t opposite_he; /* index of the opposite half edge */
+ qh_index_t next_he; /* index of the next half edge */
+ qh_index_t previous_he; /* index of the previous half edge */
+ qh_index_t he; /* index of the current half edge */
+ qh_index_t to_vertex; /* index of the next vertex */
+ qh_index_t adjacent_face; /* index of the ajacent face */
+} qh_half_edge_t;
+
+typedef struct qh_index_set {
+ qh_index_t* indices;
+ unsigned int size;
+ unsigned int capacity;
+} qh_index_set_t;
+
+typedef struct qh_face {
+ qh_index_set_t iset;
+ qh_vec3_t normal;
+ qh_vertex_t centroid;
+ qh_index_t edges[3];
+ qh_index_t face;
+ double sdist;
+ int visitededges;
+} qh_face_t;
+
+typedef struct qh_index_stack {
+ qh_index_t* begin;
+ unsigned int size;
+} qh_index_stack_t;
+
+typedef struct qh_context {
+ qh_face_t* faces;
+ qh_half_edge_t* edges;
+ qh_vertex_t* vertices;
+ qh_vertex_t centroid;
+ qh_index_stack_t facestack;
+ qh_index_stack_t scratch;
+ qh_index_stack_t horizonedges;
+ qh_index_stack_t newhorizonedges;
+ char* valid;
+ unsigned int nedges;
+ unsigned int nvertices;
+ unsigned int nfaces;
+
+ #ifdef QUICKHULL_DEBUG
+ unsigned int maxfaces;
+ unsigned int maxedges;
+ #endif
+} qh_context_t;
+
+static void
+qh__find_6eps(qh_vertex_t* vertices, unsigned int nvertices, qh_index_t* eps)
+{
+ qh_vertex_t* ptr = vertices;
+
+ double minxy = +QH_FLT_MAX;
+ double minxz = +QH_FLT_MAX;
+ double minyz = +QH_FLT_MAX;
+
+ double maxxy = -QH_FLT_MAX;
+ double maxxz = -QH_FLT_MAX;
+ double maxyz = -QH_FLT_MAX;
+
+ int i = 0;
+ for (i = 0; i < 6; ++i) {
+ eps[i] = 0;
+ }
+
+ for (i = 0; i < nvertices; ++i) {
+ if (ptr->z < minxy) {
+ eps[0] = i;
+ minxy = ptr->z;
+ }
+ if (ptr->y < minxz) {
+ eps[1] = i;
+ minxz = ptr->y;
+ }
+ if (ptr->x < minyz) {
+ eps[2] = i;
+ minyz = ptr->x;
+ }
+ if (ptr->z > maxxy) {
+ eps[3] = i;
+ maxxy = ptr->z;
+ }
+ if (ptr->y > maxxz) {
+ eps[4] = i;
+ maxxz = ptr->y;
+ }
+ if (ptr->x > maxyz) {
+ eps[5] = i;
+ maxyz = ptr->x;
+ }
+ ptr++;
+ }
+}
+
+static double
+qh__vertex_segment_length2(qh_vertex_t* p, qh_vertex_t* a, qh_vertex_t* b)
+{
+ double dx = b->x - a->x;
+ double dy = b->y - a->y;
+ double dz = b->z - a->z;
+
+ double d = dx * dx + dy * dy + dz * dz;
+
+ double x = a->x;
+ double y = a->y;
+ double z = a->z;
+
+ if (d != 0) {
+ double t = ((p->x - a->x) * dx +
+ (p->y - a->y) * dy +
+ (p->z - a->z) * dz) / d;
+
+ if (t > 1) {
+ x = b->x;
+ y = b->y;
+ z = b->z;
+ } else if (t > 0) {
+ x += dx * t;
+ y += dy * t;
+ z += dz * t;
+ }
+ }
+
+ dx = p->x - x;
+ dy = p->y - y;
+ dz = p->z - z;
+
+ return dx * dx + dy * dy + dz * dz;
+}
+
+static void
+qh__vec3_sub(qh_vec3_t* a, qh_vec3_t* b)
+{
+ a->x -= b->x;
+ a->y -= b->y;
+ a->z -= b->z;
+}
+
+static void
+qh__vec3_add(qh_vec3_t* a, qh_vec3_t* b)
+{
+ a->x += b->x;
+ a->y += b->y;
+ a->z += b->z;
+}
+
+static void
+qh__vec3_multiply(qh_vec3_t* a, double v)
+{
+ a->x *= v;
+ a->y *= v;
+ a->z *= v;
+}
+
+static int
+qh__vertex_equals_epsilon(qh_vertex_t* a, qh_vertex_t* b, double epsilon)
+{
+ return fabs(a->x - b->x) <= epsilon &&
+ fabs(a->y - b->y) <= epsilon &&
+ fabs(a->z - b->z) <= epsilon;
+}
+
+static double
+qh__vec3_length2(qh_vec3_t* v)
+{
+ return v->x * v->x + v->y * v->y + v->z * v->z;
+}
+
+static double
+qh__vec3_dot(qh_vec3_t* v1, qh_vec3_t* v2)
+{
+ return v1->x * v2->x + v1->y * v2->y + v1->z * v2->z;
+}
+
+static void
+qh__vec3_normalize(qh_vec3_t* v)
+{
+ qh__vec3_multiply(v, 1.f / sqrt(qh__vec3_length2(v)));
+}
+
+static void
+qh__find_2dps_6eps(qh_vertex_t* vertices, qh_index_t* eps,
+ int* ii, int* jj)
+{
+ int i, j;
+ double max = -QH_FLT_MAX;
+
+ for (i = 0; i < 6; ++i) {
+ for (j = 0; j < 6; ++j) {
+ qh_vertex_t d;
+ double d2;
+
+ if (i == j) {
+ continue;
+ }
+
+ d = vertices[eps[i]];
+ qh__vec3_sub(&d, &vertices[eps[j]]);
+ d2 = qh__vec3_length2(&d);
+
+ if (d2 > max) {
+ *ii = i;
+ *jj = j;
+ max = d2;
+ }
+ }
+ }
+}
+
+static qh_vec3_t
+qh__vec3_cross(qh_vec3_t* v1, qh_vec3_t* v2)
+{
+ qh_vec3_t cross;
+
+ cross.x = v1->y * v2->z - v1->z * v2->y;
+ cross.y = v1->z * v2->x - v1->x * v2->z;
+ cross.z = v1->x * v2->y - v1->y * v2->x;
+
+ return cross;
+}
+
+static qh_vertex_t
+qh__face_centroid(qh_index_t vertices[3], qh_context_t* context)
+{
+ qh_vertex_t centroid;
+ int i;
+
+ centroid.x = centroid.y = centroid.z = 0.0;
+ for (i = 0; i < 3; ++i) {
+ qh__vec3_add(¢roid, context->vertices + vertices[i]);
+ }
+
+ qh__vec3_multiply(¢roid, 1.0 / 3.0);
+
+ return centroid;
+}
+
+static double
+qh__dist_point_plane(qh_vertex_t* v, qh_vec3_t* normal, double sdist)
+{
+ return fabs(qh__vec3_dot(v, normal) - sdist);
+}
+
+static void
+qh__init_half_edge(qh_half_edge_t* half_edge) {
+ half_edge->adjacent_face = -1;
+ half_edge->he = -1;
+ half_edge->next_he = -1;
+ half_edge->opposite_he = -1;
+ half_edge->to_vertex = -1;
+ half_edge->previous_he = -1;
+}
+
+static qh_half_edge_t*
+qh__next_edge(qh_context_t* context)
+{
+ qh_half_edge_t* edge = context->edges + context->nedges;
+ qh__init_half_edge(edge);
+
+ edge->he = context->nedges;
+ context->nedges++;
+
+ QH_ASSERT(context->nedges < context->maxedges);
+
+ return edge;
+}
+
+static qh_face_t*
+qh__next_face(qh_context_t* context)
+{
+ qh_face_t* face = context->faces + context->nfaces;
+
+ face->face = context->nfaces;
+ face->iset.indices = NULL;
+ context->valid[context->nfaces] = 1;
+ context->nfaces++;
+
+ QH_ASSERT(context->nfaces < context->maxfaces);
+
+ return face;
+}
+
+static qh_vec3_t
+qh__edge_vec3(qh_half_edge_t* edge, qh_context_t* context)
+{
+ qh_half_edge_t prevhe = context->edges[edge->previous_he];
+ qh_vec3_t v0, v1;
+
+ v0 = context->vertices[prevhe.to_vertex];
+ v1 = context->vertices[edge->to_vertex];
+
+ qh__vec3_sub(&v1, &v0);
+ qh__vec3_normalize(&v1);
+
+ return v1;
+}
+
+static void
+qh__face_init(qh_face_t* face, qh_index_t vertices[3],
+ qh_context_t* context)
+{
+ qh_half_edge_t* e0 = qh__next_edge(context);
+ qh_half_edge_t* e1 = qh__next_edge(context);
+ qh_half_edge_t* e2 = qh__next_edge(context);
+ qh_vec3_t v0, v1;
+ qh_vertex_t centroid, normal;
+
+ e2->to_vertex = vertices[0];
+ e0->to_vertex = vertices[1];
+ e1->to_vertex = vertices[2];
+
+ e0->next_he = e1->he;
+ e2->previous_he = e1->he;
+ face->edges[1] = e1->he;
+
+ e1->next_he = e2->he;
+ e0->previous_he = e2->he;
+ face->edges[2] = e2->he;
+ v1 = qh__edge_vec3(e2, context);
+
+ e2->next_he = e0->he;
+ e1->previous_he = e0->he;
+ face->edges[0] = e0->he;
+ v0 = qh__edge_vec3(e0, context);
+
+ e2->adjacent_face = face->face;
+ e1->adjacent_face = face->face;
+ e0->adjacent_face = face->face;
+
+ qh__vec3_multiply(&v1, -1.f);
+ normal = qh__vec3_cross(&v0, &v1);
+
+ qh__vec3_normalize(&normal);
+ centroid = qh__face_centroid(vertices, context);
+ face->centroid = centroid;
+ face->sdist = qh__vec3_dot(&normal, ¢roid);
+ face->normal = normal;
+ face->iset.indices = QH_MALLOC(qh_index_t, QH_VERTEX_SET_SIZE);
+ face->iset.capacity = QH_VERTEX_SET_SIZE;
+ face->iset.size = 0;
+ face->visitededges = 0;
+}
+
+static void
+qh__tetrahedron_basis(qh_context_t* context, qh_index_t vertices[3])
+{
+ qh_index_t eps[6];
+ int i, j = 0, k = 0, l = 0;
+ double max = -QH_FLT_MAX;
+
+ qh__find_6eps(context->vertices, context->nvertices, eps);
+ qh__find_2dps_6eps(context->vertices, eps, &j, &k);
+
+ for (i = 0; i < 6; ++i) {
+ double d2;
+
+ if (i == j || i == k) {
+ continue;
+ }
+
+ d2 = qh__vertex_segment_length2(context->vertices + eps[i],
+ context->vertices + eps[j],
+ context->vertices + eps[k]);
+
+ if (d2 > max) {
+ max = d2;
+ l = i;
+ }
+ }
+
+ vertices[0] = eps[j];
+ vertices[1] = eps[k];
+ vertices[2] = eps[l];
+}
+
+static void
+qh__push_stack(qh_index_stack_t* stack, qh_index_t index)
+{
+ stack->begin[stack->size] = index;
+ stack->size++;
+}
+
+static qh_index_t
+qh__pop_stack(qh_index_stack_t* stack)
+{
+ qh_index_t top = -1;
+
+ if (stack->size > 0) {
+ top = stack->begin[stack->size - 1];
+ stack->size--;
+ }
+
+ return top;
+}
+
+static qh_index_t
+qh__furthest_point_from_plane(qh_context_t* context,
+ qh_index_t* indices,
+ int nindices,
+ qh_vec3_t* normal,
+ double sdist)
+{
+ int i, j = -1;
+ double max = -QH_FLT_MAX;
+
+ for (i = 0; i < nindices; ++i) {
+ qh_index_t index = indices ? *(indices + i) : i;
+ double dist = qh__dist_point_plane(context->vertices + index,
+ normal, sdist);
+
+ if (dist > max) {
+ j = i;
+ max = dist;
+ }
+ }
+
+ return j;
+}
+
+static int
+qh__face_can_see_vertex(qh_face_t* face, qh_vertex_t* v)
+{
+ qh_vec3_t tov = *v;
+
+ qh__vec3_sub(&tov, &face->centroid);
+ return qh__vec3_dot(&tov, &face->normal) > 0;
+}
+
+static int
+qh__face_can_see_vertex_epsilon(qh_context_t* context, qh_face_t* face,
+ qh_vertex_t* v, double epsilon)
+{
+ double dot;
+ qh_vec3_t tov = *v;
+
+ qh__vec3_sub(&tov, &face->centroid);
+ dot = qh__vec3_dot(&tov, &face->normal);
+
+ if (dot > epsilon) {
+ return 1;
+ } else {
+ dot = fabs(dot);
+
+ if (dot <= epsilon && dot >= 0) {
+ qh_vec3_t n = face->normal;
+
+ /* allow epsilon degeneration along the face normal */
+ qh__vec3_multiply(&n, epsilon);
+ qh__vec3_add(v, &n);
+
+ return 1;
+ }
+ }
+
+ return 0;
+}
+
+static inline void
+qh__assert_half_edge(qh_half_edge_t* edge, qh_context_t* context)
+{
+ QH_ASSERT(edge->opposite_he != -1);
+ QH_ASSERT(edge->he != -1);
+ QH_ASSERT(edge->adjacent_face != -1);
+ QH_ASSERT(edge->next_he != -1);
+ QH_ASSERT(edge->previous_he != -1);
+ QH_ASSERT(edge->to_vertex != -1);
+ QH_ASSERT(context->edges[edge->opposite_he].to_vertex != edge->to_vertex);
+}
+
+static inline void
+qh__assert_face(qh_face_t* face, qh_context_t* context)
+{
+ int i;
+
+ for (i = 0; i < 3; ++i) {
+ qh__assert_half_edge(context->edges + face->edges[i], context);
+ }
+
+ QH_ASSERT(context->valid[face->face]);
+}
+
+#ifdef QUICKHULL_DEBUG
+
+void
+qh__log_face(qh_context_t* context, qh_face_t const* face) {
+ QH_LOG("Face %ld:\n", face->face);
+ for (int i = 0; i < 3; ++i) {
+ qh_half_edge_t edge = context->edges[face->edges[i]];
+ QH_LOG("\te%d %ld\n", i, edge.he);
+ QH_LOG("\t\te%d.opposite_he %ld\n", i, edge.opposite_he);
+ QH_LOG("\t\te%d.next_he %ld\n", i, edge.next_he);
+ QH_LOG("\t\te%d.previous_he %ld\n", i, edge.previous_he);
+ QH_LOG("\t\te%d.to_vertex %ld\n", i, edge.to_vertex);
+ QH_LOG("\t\te%d.adjacent_face %ld\n", i, edge.adjacent_face);
+ }
+ QH_LOG("\tnormal %f %f %f\n", face->normal.x, face->normal.y,
+ face->normal.z);
+ QH_LOG("\tsdist %f\n", face->sdist);
+ QH_LOG("\tcentroid %f %f %f\n", face->centroid.x, face->centroid.y,
+ face->centroid.z);
+}
+
+static int
+qh__test_hull(qh_context_t* context, double epsilon, int testiset)
+{
+ unsigned int i, j, k;
+
+ for (i = 0; i < context->nvertices; ++i) {
+ qh_index_t vindex = i;
+ char valid = 1;
+
+ for (j = 0; j < context->nfaces; ++j) {
+ if (!context->valid[j]) {
+ continue;
+ }
+ qh_face_t* face = context->faces + j;
+
+ qh_half_edge_t* e0 = context->edges + face->edges[0];
+ qh_half_edge_t* e1 = context->edges + face->edges[1];
+ qh_half_edge_t* e2 = context->edges + face->edges[2];
+
+ if (e0->to_vertex == vindex ||
+ e1->to_vertex == vindex ||
+ e2->to_vertex == vindex) {
+ valid = 0;
+ break;
+ }
+
+ if (testiset) {
+ for (k = 0; k < face->iset.size; ++k) {
+ if (vindex == face->iset.indices[k]) {
+ valid = 0;
+ }
+ }
+ }
+ }
+
+ if (!valid) {
+ continue;
+ }
+
+ for (j = 0; j < context->nfaces; ++j) {
+ if (!context->valid[j]) {
+ continue;
+ }
+ qh_face_t* face = context->faces + j;
+
+ qh_vertex_t vertex = context->vertices[vindex];
+ qh__vec3_sub(&vertex, &face->centroid);
+ if (qh__vec3_dot(&face->normal, &vertex) > epsilon) {
+ #ifdef QUICKHULL_DEBUG
+ qh__log_face(context, face);
+ #endif
+ return 0;
+ }
+ }
+ }
+
+ return 1;
+}
+#endif /* QUICKHULL_DEBUG */
+
+
+static void
+#ifdef QUICKHULL_DEBUG
+qh__build_hull(qh_context_t* context, double epsilon, unsigned int step,
+ unsigned int* failurestep)
+#else
+qh__build_hull(qh_context_t* context, double epsilon)
+#endif
+{
+ qh_index_t topface = qh__pop_stack(&context->facestack);
+ int i, j, k;
+
+ #ifdef QUICKHULL_DEBUG
+ unsigned int iteration = 0;
+ #endif
+
+ while (topface != -1) {
+ qh_face_t* face = context->faces + topface;
+ qh_index_t fvi, apex;
+ qh_vertex_t* fv;
+ int reversed = 0;
+
+ #ifdef QUICKHULL_DEBUG
+ if (!context->valid[topface] || face->iset.size == 0 || iteration == step)
+ #else
+ if (!context->valid[topface] || face->iset.size == 0)
+ #endif
+ {
+ topface = qh__pop_stack(&context->facestack);
+ continue;
+ }
+
+ #ifdef QUICKHULL_DEBUG
+ if (failurestep != NULL && !qh__test_hull(context, epsilon, 1)) {
+ if (*failurestep == 0) {
+ *failurestep = iteration;
+ break;
+ }
+ }
+
+ iteration++;
+ #endif
+
+ fvi = qh__furthest_point_from_plane(context, face->iset.indices,
+ face->iset.size, &face->normal, face->sdist);
+ fv = context->vertices + *(face->iset.indices + fvi);
+
+ qh__assert_face(face, context);
+
+ /* Reset visited flag for faces */
+ {
+ for (i = 0; i < context->nfaces; ++i) {
+ context->faces[i].visitededges = 0;
+ }
+ }
+
+ /* Find horizon edge */
+ {
+ qh_index_t tovisit = topface;
+ qh_face_t* facetovisit = context->faces + tovisit;
+
+ /* Release scratch */
+ context->scratch.size = 0;
+
+ while (tovisit != -1) {
+ if (facetovisit->visitededges >= 3) {
+ context->valid[tovisit] = 0;
+ tovisit = qh__pop_stack(&context->scratch);
+ facetovisit = context->faces + tovisit;
+ } else {
+ qh_index_t edgeindex = facetovisit->edges[facetovisit->visitededges];
+ qh_half_edge_t* edge;
+ qh_half_edge_t* oppedge;
+ qh_face_t* adjface;
+
+ facetovisit->visitededges++;
+
+ edge = context->edges + edgeindex;
+ oppedge = context->edges + edge->opposite_he;
+ adjface = context->faces + oppedge->adjacent_face;
+
+ if (!context->valid[oppedge->adjacent_face]) { continue; }
+
+ qh__assert_half_edge(oppedge, context);
+ qh__assert_half_edge(edge, context);
+ qh__assert_face(adjface, context);
+
+ if (!qh__face_can_see_vertex(adjface, fv)) {
+ qh__push_stack(&context->horizonedges, edge->he);
+ } else {
+ context->valid[tovisit] = 0;
+ qh__push_stack(&context->scratch, adjface->face);
+ }
+ }
+ }
+ }
+
+ apex = face->iset.indices[fvi];
+
+ /* Sort horizon edges in CCW order */
+ {
+ qh_vertex_t triangle[3];
+ int vindex = 0;
+ qh_vec3_t v0, v1, toapex;
+ qh_vertex_t n;
+
+ for (i = 0; i < context->horizonedges.size; ++i) {
+ qh_index_t he0 = context->horizonedges.begin[i];
+ qh_index_t he0vert = context->edges[he0].to_vertex;
+ qh_index_t phe0 = context->edges[he0].previous_he;
+ qh_index_t phe0vert = context->edges[phe0].to_vertex;
+
+ for (j = i + 2; j < context->horizonedges.size; ++j) {
+ qh_index_t he1 = context->horizonedges.begin[j];
+ qh_index_t he1vert = context->edges[he1].to_vertex;
+ qh_index_t phe1 = context->edges[he1].previous_he;
+ qh_index_t phe1vert = context->edges[phe1].to_vertex;
+
+ if (phe1vert == he0vert || phe0vert == he1vert) {
+ QH_SWAP(qh_index_t, context->horizonedges.begin[j],
+ context->horizonedges.begin[i + 1]);
+ break;
+ }
+ }
+
+ if (vindex < 3) {
+ triangle[vindex++] =
+ context->vertices[context->edges[he0].to_vertex];
+ }
+ }
+
+ if (vindex == 3) {
+ /* Detect first triangle face ordering */
+ v0 = triangle[0];
+ v1 = triangle[2];
+
+ qh__vec3_sub(&v0, &triangle[1]);
+ qh__vec3_sub(&v1, &triangle[1]);
+
+ n = qh__vec3_cross(&v0, &v1);
+
+ /* Get the vector to the apex */
+ toapex = triangle[0];
+
+ qh__vec3_sub(&toapex, context->vertices + apex);
+
+ reversed = qh__vec3_dot(&n, &toapex) < 0.f;
+ }
+ }
+
+ /* Create new faces */
+ {
+ qh_index_t top = qh__pop_stack(&context->horizonedges);
+ qh_index_t last = qh__pop_stack(&context->horizonedges);
+ qh_index_t first = top;
+ int looped = 0;
+
+ QH_ASSERT(context->newhorizonedges.size == 0);
+
+ /* Release scratch */
+ context->scratch.size = 0;
+
+ while (!looped) {
+ qh_half_edge_t* prevhe;
+ qh_half_edge_t* nexthe;
+ qh_half_edge_t* oppedge;
+ /* qh_vec3_t normal; */
+ /* qh_vertex_t fcentroid; */
+ qh_index_t verts[3];
+ qh_face_t* newface;
+
+ if (last == -1) {
+ looped = 1;
+ last = first;
+ }
+
+ prevhe = context->edges + last;
+ nexthe = context->edges + top;
+
+ if (reversed) {
+ QH_SWAP(qh_half_edge_t*, prevhe, nexthe);
+ }
+
+ verts[0] = prevhe->to_vertex;
+ verts[1] = nexthe->to_vertex;
+ verts[2] = apex;
+
+ context->valid[nexthe->adjacent_face] = 0;
+
+ oppedge = context->edges + nexthe->opposite_he;
+ newface = qh__next_face(context);
+
+ qh__face_init(newface, verts, context);
+
+ oppedge->opposite_he = context->edges[newface->edges[0]].he;
+ context->edges[newface->edges[0]].opposite_he = oppedge->he;
+
+ qh__push_stack(&context->scratch, newface->face);
+ qh__push_stack(&context->newhorizonedges, newface->edges[0]);
+
+ top = last;
+ last = qh__pop_stack(&context->horizonedges);
+ }
+ }
+
+ /* Attach point sets to newly created faces */
+ {
+ for (k = 0; k < context->nfaces; ++k) {
+ qh_face_t* f = context->faces + k;
+
+ if (context->valid[k] || f->iset.size == 0) {
+ continue;
+ }
+
+ if (f->visitededges == 3) {
+ context->valid[k] = 0;
+ }
+
+ for (i = 0; i < f->iset.size; ++i) {
+ qh_index_t vertex = f->iset.indices[i];
+ /* qh_vertex_t* v = context->vertices + vertex; */
+ qh_face_t* dface = NULL;
+
+ for (j = 0; j < context->scratch.size; ++j) {
+ qh_face_t* newface = context->faces + context->scratch.begin[j];
+ qh_half_edge_t* e0 = context->edges + newface->edges[0];
+ qh_half_edge_t* e1 = context->edges + newface->edges[1];
+ qh_half_edge_t* e2 = context->edges + newface->edges[2];
+ /* qh_vertex_t cv; */
+
+ if (e0->to_vertex == vertex ||
+ e1->to_vertex == vertex ||
+ e2->to_vertex == vertex) {
+ continue;
+ }
+
+ if (qh__face_can_see_vertex_epsilon(context, newface,
+ context->vertices + vertex,
+ epsilon)) {
+ dface = newface;
+ break;
+ }
+ }
+
+ if (dface) {
+ if (dface->iset.size + 1 >= dface->iset.capacity) {
+ dface->iset.capacity *= 2;
+ dface->iset.indices = QH_REALLOC(qh_index_t,
+ dface->iset.indices, dface->iset.capacity);
+ }
+
+ dface->iset.indices[dface->iset.size++] = vertex;
+ }
+ }
+
+ f->iset.size = 0;
+ }
+ }
+
+ /* Link new faces together */
+ {
+ for (i = 0; i < context->newhorizonedges.size; ++i) {
+ qh_index_t phe0, nhe1;
+ qh_half_edge_t* he0;
+ qh_half_edge_t* he1;
+ int ii;
+
+ if (reversed) {
+ ii = (i == 0) ? context->newhorizonedges.size - 1 : (i-1);
+ } else {
+ ii = (i+1) % context->newhorizonedges.size;
+ }
+
+ phe0 = context->edges[context->newhorizonedges.begin[i]].previous_he;
+ nhe1 = context->edges[context->newhorizonedges.begin[ii]].next_he;
+
+ he0 = context->edges + phe0;
+ he1 = context->edges + nhe1;
+
+ QH_ASSERT(he1->to_vertex == apex);
+ QH_ASSERT(he0->opposite_he == -1);
+ QH_ASSERT(he1->opposite_he == -1);
+
+ he0->opposite_he = he1->he;
+ he1->opposite_he = he0->he;
+ }
+
+ context->newhorizonedges.size = 0;
+ }
+
+ /* Push new face to stack */
+ {
+ for (i = 0; i < context->scratch.size; ++i) {
+ qh_face_t* face = context->faces + context->scratch.begin[i];
+
+ if (face->iset.size > 0) {
+ qh__push_stack(&context->facestack, face->face);
+ }
+ }
+
+ /* Release scratch */
+ context->scratch.size = 0;
+ }
+
+ topface = qh__pop_stack(&context->facestack);
+
+ /* TODO: push all non-valid faces for reuse in face stack memory pool */
+ }
+}
+
+#ifdef QUICKHULL_FILES
+void
+qh_mesh_export(qh_mesh_t const* mesh, char const* filename)
+{
+ FILE* objfile = fopen(filename, "wt");
+ fprintf(objfile, "o\n");
+
+ for (int i = 0; i < mesh->nvertices; ++i) {
+ qh_vertex_t v = mesh->vertices[i];
+ fprintf(objfile, "v %f %f %f\n", v.x, v.y, v.z);
+ }
+
+ for (int i = 0; i < mesh->nnormals; ++i) {
+ qh_vec3_t n = mesh->normals[i];
+ fprintf(objfile, "vn %f %f %f\n", n.x, n.y, n.z);
+ }
+
+ for (int i = 0, j = 0; i < mesh->nindices; i += 3, j++) {
+ fprintf(objfile, "f %u/%u %u/%u %u/%u\n",
+ mesh->indices[i+0] + 1, mesh->normalindices[j] + 1,
+ mesh->indices[i+1] + 1, mesh->normalindices[j] + 1,
+ mesh->indices[i+2] + 1, mesh->normalindices[j] + 1);
+ }
+
+ fclose(objfile);
+}
+#endif /* QUICKHULL_FILES */
+
+static qh_face_t*
+qh__build_tetrahedron(qh_context_t* context, double epsilon)
+{
+ int i, j;
+ qh_index_t vertices[3];
+ qh_index_t apex;
+ qh_face_t* faces;
+ qh_vertex_t normal, centroid, vapex, tcentroid;
+
+ /* Get the initial tetrahedron basis (first face) */
+ qh__tetrahedron_basis(context, &vertices[0]);
+
+ /* Find apex from the tetrahedron basis */
+ {
+ double sdist;
+ qh_vec3_t v0, v1;
+
+ v0 = context->vertices[vertices[1]];
+ v1 = context->vertices[vertices[2]];
+
+ qh__vec3_sub(&v0, context->vertices + vertices[0]);
+ qh__vec3_sub(&v1, context->vertices + vertices[0]);
+
+ normal = qh__vec3_cross(&v0, &v1);
+ qh__vec3_normalize(&normal);
+
+ centroid = qh__face_centroid(vertices, context);
+ sdist = qh__vec3_dot(&normal, ¢roid);
+
+ apex = qh__furthest_point_from_plane(context, NULL,
+ context->nvertices, &normal, sdist);
+ vapex = context->vertices[apex];
+
+ qh__vec3_sub(&vapex, ¢roid);
+
+ /* Whether the face is looking towards the apex */
+ if (qh__vec3_dot(&vapex, &normal) > 0) {
+ QH_SWAP(qh_index_t, vertices[1], vertices[2]);
+ }
+ }
+
+ faces = qh__next_face(context);
+ qh__face_init(&faces[0], vertices, context);
+
+ /* Build faces from the tetrahedron basis to the apex */
+ {
+ qh_index_t facevertices[3];
+ for (i = 0; i < 3; ++i) {
+ qh_half_edge_t* edge = context->edges + faces[0].edges[i];
+ qh_half_edge_t prevedge = context->edges[edge->previous_he];
+ qh_face_t* face = faces+i+1;
+ qh_half_edge_t* e0;
+
+ facevertices[0] = edge->to_vertex;
+ facevertices[1] = prevedge.to_vertex;
+ facevertices[2] = apex;
+
+ qh__next_face(context);
+ qh__face_init(face, facevertices, context);
+
+ e0 = context->edges + faces[i+1].edges[0];
+ edge->opposite_he = e0->he;
+ e0->opposite_he = edge->he;
+ }
+ }
+
+ /* Attach half edges to faces tied to the apex */
+ {
+ for (i = 0; i < 3; ++i) {
+ qh_face_t* face;
+ qh_face_t* nextface;
+ qh_half_edge_t* e1;
+ qh_half_edge_t* e2;
+
+ j = (i+2) % 3;
+
+ face = faces+i+1;
+ nextface = faces+j+1;
+
+ e1 = context->edges + face->edges[1];
+ e2 = context->edges + nextface->edges[2];
+
+ QH_ASSERT(e1->opposite_he == -1);
+ QH_ASSERT(e2->opposite_he == -1);
+
+ e1->opposite_he = e2->he;
+ e2->opposite_he = e1->he;
+
+ qh__assert_half_edge(e1, context);
+ qh__assert_half_edge(e2, context);
+ }
+ }
+
+ /* Create initial point set; every point is */
+ /* attached to the first face it can see */
+ {
+ for (i = 0; i < context->nvertices; ++i) {
+ /* qh_vertex_t* v; */
+ qh_face_t* dface = NULL;
+
+ if (vertices[0] == i || vertices[1] == i || vertices[2] == i) {
+ continue;
+ }
+
+ for (j = 0; j < 4; ++j) {
+ if (qh__face_can_see_vertex_epsilon(context, context->faces + j,
+ context->vertices + i, epsilon)) {
+ dface = context->faces + j;
+ break;
+ }
+ }
+
+ if (dface) {
+ int valid = 1;
+ int j;
+
+ for (j = 0; j < 3; ++j) {
+ qh_half_edge_t* e = context->edges + dface->edges[j];
+ if (i == e->to_vertex) {
+ valid = 0;
+ break;
+ }
+ }
+
+ if (!valid) { continue; }
+
+ if (dface->iset.size + 1 >= dface->iset.capacity) {
+ dface->iset.capacity *= 2;
+ dface->iset.indices = QH_REALLOC(qh_index_t,
+ dface->iset.indices, dface->iset.capacity);
+ }
+
+ dface->iset.indices[dface->iset.size++] = i;
+ }
+ }
+ }
+
+ /* Add initial tetrahedron faces to the face stack */
+ tcentroid.x = tcentroid.y = tcentroid.z = 0.0;
+ for (i = 0; i < 4; ++i) {
+ context->valid[i] = 1;
+ qh__assert_face(context->faces + i, context);
+ qh__push_stack(&context->facestack, i);
+ qh__vec3_add(&tcentroid, &context->faces[i].centroid);
+ }
+
+ /* Assign the tetrahedron centroid */
+ qh__vec3_multiply(&tcentroid, 0.25);
+ context->centroid = tcentroid;
+
+ QH_ASSERT(context->nedges == context->nfaces * 3);
+ QH_ASSERT(context->nfaces == 4);
+ QH_ASSERT(context->facestack.size == 4);
+
+ return faces;
+}
+
+static void
+qh__remove_vertex_duplicates(qh_context_t* context, double epsilon)
+{
+ int i, j, k;
+ for (i = 0; i < context->nvertices; ++i) {
+ qh_vertex_t* v = context->vertices + i;
+ if (v->x == 0) v->x = 0;
+ if (v->y == 0) v->y = 0;
+ if (v->z == 0) v->z = 0;
+ for (j = i + 1; j < context->nvertices; ++j) {
+ if (qh__vertex_equals_epsilon(context->vertices + i,
+ context->vertices + j, epsilon))
+ {
+ for (k = j; k < context->nvertices - 1; ++k) {
+ context->vertices[k] = context->vertices[k+1];
+ }
+ context->nvertices--;
+ }
+ }
+ }
+}
+
+static void
+qh__init_context(qh_context_t* context, qh_vertex_t const* vertices,
+ unsigned int nvertices)
+{
+ /* TODO: */
+ /* size_t nedges = 3 * nvertices - 6; */
+ /* size_t nfaces = 2 * nvertices - 4; */
+ unsigned int nfaces = nvertices * (nvertices - 1);
+ unsigned int nedges = nfaces * 3;
+
+ context->edges = QH_MALLOC(qh_half_edge_t, nedges);
+ context->faces = QH_MALLOC(qh_face_t, nfaces);
+ context->facestack.begin = QH_MALLOC(qh_index_t, nfaces);
+ context->scratch.begin = QH_MALLOC(qh_index_t, nfaces);
+ context->horizonedges.begin = QH_MALLOC(qh_index_t, nedges);
+ context->newhorizonedges.begin = QH_MALLOC(qh_index_t, nedges);
+ context->valid = QH_MALLOC(char, nfaces);
+
+ context->vertices = QH_MALLOC(qh_vertex_t, nvertices);
+ memcpy(context->vertices, vertices, sizeof(qh_vertex_t) * nvertices);
+
+ context->nvertices = nvertices;
+ context->nedges = 0;
+ context->nfaces = 0;
+ context->facestack.size = 0;
+ context->scratch.size = 0;
+ context->horizonedges.size = 0;
+ context->newhorizonedges.size = 0;
+
+ #ifdef QUICKHULL_DEBUG
+ context->maxfaces = nfaces;
+ context->maxedges = nedges;
+ #endif
+}
+
+static void
+qh__free_context(qh_context_t* context)
+{
+ int i;
+
+ for (i = 0; i < context->nfaces; ++i) {
+ QH_FREE(context->faces[i].iset.indices);
+ context->faces[i].iset.size = 0;
+ }
+
+ context->nvertices = 0;
+ context->nfaces = 0;
+
+ QH_FREE(context->edges);
+
+ QH_FREE(context->faces);
+ QH_FREE(context->facestack.begin);
+ QH_FREE(context->scratch.begin);
+ QH_FREE(context->horizonedges.begin);
+ QH_FREE(context->newhorizonedges.begin);
+ QH_FREE(context->vertices);
+ QH_FREE(context->valid);
+}
+
+void
+qh_free_mesh(qh_mesh_t mesh)
+{
+ QH_FREE(mesh.vertices);
+ QH_FREE(mesh.indices);
+ QH_FREE(mesh.normalindices);
+ QH_FREE(mesh.normals);
+}
+
+static double
+qh__compute_epsilon(qh_vertex_t const* vertices, unsigned int nvertices)
+{
+ double epsilon;
+ unsigned int i;
+
+ double maxxi = -QH_FLT_MAX;
+ double maxyi = -QH_FLT_MAX;
+
+ for (i = 0; i < nvertices; ++i) {
+ double fxi = fabs(vertices[i].x);
+ double fyi = fabs(vertices[i].y);
+
+ if (fxi > maxxi) {
+ maxxi = fxi;
+ }
+ if (fyi > maxyi) {
+ maxyi = fyi;
+ }
+ }
+
+ epsilon = 2 * (maxxi + maxyi) * QH_FLT_EPS;
+
+ return epsilon;
+}
+
+qh_mesh_t
+qh_quickhull3d(qh_vertex_t const* vertices, unsigned int nvertices)
+{
+ qh_mesh_t m;
+ qh_context_t context;
+ /* unsigned int* indices; */
+ unsigned int nfaces = 0, i, index, nindices;
+ double epsilon;
+
+ epsilon = qh__compute_epsilon(vertices, nvertices);
+
+ qh__init_context(&context, vertices, nvertices);
+
+ qh__remove_vertex_duplicates(&context, epsilon);
+
+ /* Build the initial tetrahedron */
+ qh__build_tetrahedron(&context, epsilon);
+
+ /* Build the convex hull */
+ #ifdef QUICKHULL_DEBUG
+ qh__build_hull(&context, epsilon, -1, NULL);
+ #else
+ qh__build_hull(&context, epsilon);
+ #endif
+
+ /* QH_ASSERT(qh__test_hull(&context, epsilon)); */
+
+ for (i = 0; i < context.nfaces; ++i) {
+ if (context.valid[i]) { nfaces++; }
+ }
+
+ nindices = nfaces * 3;
+
+ m.normals = QH_MALLOC(qh_vertex_t, nfaces);
+ m.normalindices = QH_MALLOC(unsigned int, nfaces);
+ m.vertices = QH_MALLOC(qh_vertex_t, nindices);
+ m.indices = QH_MALLOC(unsigned int, nindices);
+ m.nindices = nindices;
+ m.nnormals = nfaces;
+ m.nvertices = 0;
+
+ {
+ index = 0;
+ for (i = 0; i < context.nfaces; ++i) {
+ if (!context.valid[i]) { continue; }
+ m.normals[index] = context.faces[i].normal;
+ index++;
+ }
+
+ index = 0;
+ for (i = 0; i < context.nfaces; ++i) {
+ if (!context.valid[i]) { continue; }
+ m.normalindices[index] = index;
+ index++;
+ }
+
+ index = 0;
+ for (i = 0; i < context.nfaces; ++i) {
+ if (!context.valid[i]) { continue; }
+ m.indices[index+0] = index+0;
+ m.indices[index+1] = index+1;
+ m.indices[index+2] = index+2;
+ index += 3;
+ }
+
+ for (i = 0; i < context.nfaces; ++i) {
+ if (!context.valid[i]) { continue; }
+ qh_half_edge_t e0 = context.edges[context.faces[i].edges[0]];
+ qh_half_edge_t e1 = context.edges[context.faces[i].edges[1]];
+ qh_half_edge_t e2 = context.edges[context.faces[i].edges[2]];
+
+ m.vertices[m.nvertices++] = context.vertices[e0.to_vertex];
+ m.vertices[m.nvertices++] = context.vertices[e1.to_vertex];
+ m.vertices[m.nvertices++] = context.vertices[e2.to_vertex];
+ }
+ }
+
+ qh__free_context(&context);
+
+ return m;
+}
projects / xscreensaver / blobdiff