Add convex hull operator (bmesh operator and wm operator.)

Image-heavy user documentation:
http://wiki.blender.org/index.php/User:Nicholasbishop/Convex_Hull

Thanks to Campbell for providing code review:
http://codereview.appspot.com/6114060

8 files changed, 883 insertions, 9 deletions

diff --git a/source/blender/bmesh/CMakeLists.txt b/source/blender/bmesh/CMakeLists.txt
index a23f1935ae0..730b741fa38 100644
--- a/source/blender/bmesh/CMakeLists.txt
+++ b/source/blender/bmesh/CMakeLists.txt
@@ -41,6 +41,7 @@ set(SRC
 	operators/bmo_dupe.c
 	operators/bmo_edgesplit.c
 	operators/bmo_extrude.c
+	operators/bmo_hull.c
 	operators/bmo_inset.c
 	operators/bmo_join_triangles.c
 	operators/bmo_mesh_conv.c
diff --git a/source/blender/bmesh/intern/bmesh_error.h b/source/blender/bmesh/intern/bmesh_error.h
index 84065fe88f6..606e9eeb23b 100644
--- a/source/blender/bmesh/intern/bmesh_error.h
+++ b/source/blender/bmesh/intern/bmesh_error.h
@@ -69,6 +69,7 @@ void BMO_error_clear(BMesh *bm);
 #define BMERR_NONMANIFOLD				8
 #define BMERR_INVALID_SELECTION			9
 #define BMERR_MESH_ERROR				10
+#define BMERR_CONVEX_HULL_FAILED		11
 
 /* BMESH_ASSERT */
 #ifdef WITH_ASSERT_ABORT
diff --git a/source/blender/bmesh/intern/bmesh_opdefines.c b/source/blender/bmesh/intern/bmesh_opdefines.c
index af083fc30a6..2ff28aee191 100644
--- a/source/blender/bmesh/intern/bmesh_opdefines.c
+++ b/source/blender/bmesh/intern/bmesh_opdefines.c
@@ -1144,6 +1144,35 @@ static BMOpDefine bmo_vertex_slide_def = {
 	BMO_OP_FLAG_UNTAN_MULTIRES
 };
 
+/*
+ * Convex Hull
+ *
+ * Builds a convex hull from the vertices in 'input'.
+ *
+ * If 'use_existing_faces' is true, the hull will not output triangles
+ * that are covered by a pre-existing face.
+ *
+ * All hull vertices, faces, and edges are added to 'geomout'. Any
+ * input elements that end up inside the hull (i.e. are not used by an
+ * output face) are added to the 'interior_geom' slot. The
+ * 'unused_geom' slot will contain all interior geometry that is
+ * completely unused. Lastly, 'holes_geom' contains edges and faces
+ * that were in the input and are part of the hull.
+*/
+static BMOpDefine bmo_convex_hull_def = {
+	"convex_hull",
+	{{BMO_OP_SLOT_ELEMENT_BUF, "input"},
+	 {BMO_OP_SLOT_BOOL, "use_existing_faces"},
+
+	 /* Outputs */
+	 {BMO_OP_SLOT_ELEMENT_BUF, "geomout"},
+	 {BMO_OP_SLOT_ELEMENT_BUF, "interior_geom"},
+	 {BMO_OP_SLOT_ELEMENT_BUF, "unused_geom"},
+	 {BMO_OP_SLOT_ELEMENT_BUF, "holes_geom"},
+	 {0} /* null-terminating sentinel */},
+	bmo_convex_hull_exec,
+	0
+};
 
 BMOpDefine *opdefines[] = {
 	&bmo_split_def,
@@ -1214,6 +1243,7 @@ BMOpDefine *opdefines[] = {
 	&bmo_inset_def,
 	&bmo_wireframe_def,
 	&bmo_vertex_slide_def,
+	&bmo_convex_hull_def,
 };
 
 int bmesh_total_ops = (sizeof(opdefines) / sizeof(void *));
diff --git a/source/blender/bmesh/intern/bmesh_operators_private.h b/source/blender/bmesh/intern/bmesh_operators_private.h
index e222c3422c0..df48ec8468f 100644
--- a/source/blender/bmesh/intern/bmesh_operators_private.h
+++ b/source/blender/bmesh/intern/bmesh_operators_private.h
@@ -101,5 +101,6 @@ void bmo_bridge_loops_exec(BMesh *bm, BMOperator *op);
 void bmo_solidify_face_region_exec(BMesh *bm, BMOperator *op);
 void bmo_inset_exec(BMesh *bm, BMOperator *op);
 void bmo_wireframe_exec(BMesh *bm, BMOperator *op);
+void bmo_convex_hull_exec(BMesh *bm, BMOperator *op);
 
 #endif /* __BMESH_OPERATORS_PRIVATE_H__ */
diff --git a/source/blender/bmesh/operators/bmo_hull.c b/source/blender/bmesh/operators/bmo_hull.c
new file mode 100644
index 00000000000..ddc744550b2
--- /dev/null
+++ b/source/blender/bmesh/operators/bmo_hull.c
@@ -0,0 +1,742 @@
+/*
+ * ***** BEGIN GPL LICENSE BLOCK *****
+ *
+ * This program is free software; you can redistribute it and/or
+ * modify it under the terms of the GNU General Public License
+ * as published by the Free Software Foundation; either version 2
+ * of the License, or (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software Foundation,
+ * Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ *
+ * Contributor(s): Nicholas Bishop
+ *
+ * ***** END GPL LICENSE BLOCK *****
+ */
+
+/** \file blender/bmesh/operators/bmo_hull.c
+ *  \ingroup bmesh
+ */
+
+#include "MEM_guardedalloc.h"
+
+#include "BLI_ghash.h"
+#include "BLI_listbase.h"
+#include "BLI_math.h"
+#include "BLI_utildefines.h"
+
+/* XXX: using 128 for totelem and pchunk of mempool, no idea what good
+   values would be though */
+#include "BLI_mempool.h"
+
+#include "bmesh.h"
+
+/* Internal operator flags */
+typedef enum {
+	HULL_FLAG_INPUT =			(1 << 0),
+	HULL_FLAG_TETRA_VERT =		(1 << 1),
+	
+	HULL_FLAG_INTERIOR_ELE = 	(1 << 2),
+	HULL_FLAG_OUTPUT_GEOM =		(1 << 3),
+	
+	HULL_FLAG_DEL =				(1 << 4),
+	HULL_FLAG_HOLE =			(1 << 5)
+} HullFlags;
+
+/* Store hull triangles seperate from BMesh faces until the end; this
+   way we don't have to worry about cleaning up extraneous edges or
+   incorrectly deleting existing geometry. */
+typedef struct HullTriangle {
+	BMVert *v[3];
+	float no[3];
+	int skip;
+} HullTriangle;
+
+/* These edges define the hole created in the hull by deleting faces
+   that can "see" a new vertex (the boundary edges then form the edge
+   of a new triangle fan that has the new vertex as its center) */
+typedef struct HullBoundaryEdge {
+	struct HullBoundaryEdge *next, *prev;
+	BMVert *v[2];
+} HullBoundaryEdge;
+
+
+
+/*************************** Boundary Edges ***************************/
+
+static int edge_match(BMVert *e1_0, BMVert *e1_1, BMVert *e2[2])
+{
+	return (e1_0 == e2[0] && e1_1 == e2[1]) ||
+	       (e1_0 == e2[1] && e1_1 == e2[0]);
+}
+
+/* Returns true if the edge (e1, e2) is already in edges; that edge is
+   deleted here as well. if not found just returns 0 */
+static int check_for_dup(ListBase *edges, BLI_mempool *pool,
+						 BMVert *e1, BMVert *e2)
+{
+	HullBoundaryEdge *e, *next;
+
+	for (e = edges->first; e; e = next) {
+		next = e->next;
+
+		if (edge_match(e1, e2, e->v)) {
+			/* remove the interior edge */
+			BLI_remlink(edges, e);
+			BLI_mempool_free(pool, e);
+			return 1;
+		}
+	}
+
+	return 0;
+}
+
+static void expand_boundary_edges(ListBase *edges, BLI_mempool *edge_pool,
+								  const HullTriangle *t)
+{
+	HullBoundaryEdge *new;
+	int i;
+
+	/* Insert each triangle edge into the boundary list; if any of
+	   its edges are already in there, remove the edge entirely */
+	for (i = 0; i < 3; i++) {
+		if (!check_for_dup(edges, edge_pool, t->v[i], t->v[(i + 1) % 3])) {
+			new = BLI_mempool_calloc(edge_pool);
+			new->v[0] = t->v[i];
+			new->v[1] = t->v[(i + 1) % 3];
+			BLI_addtail(edges, new);
+		}
+	}
+}
+
+
+
+/*************************** Hull Triangles ***************************/
+
+static void hull_add_triangle(GHash *hull_triangles, BLI_mempool *pool,
+							  BMVert *v1, BMVert *v2, BMVert *v3)
+{
+	HullTriangle *t;
+
+	t = BLI_mempool_calloc(pool);
+	t->v[0] = v1;
+	t->v[1] = v2;
+	t->v[2] = v3;
+
+	BLI_ghash_insert(hull_triangles, t, NULL);
+	normal_tri_v3(t->no, v1->co, v2->co, v3->co);
+}
+
+static int hull_point_tri_side(const HullTriangle *t, const float co[3])
+{
+	float p[3], d;
+	sub_v3_v3v3(p, co, t->v[0]->co);
+	d = dot_v3v3(t->no, p);
+	if (d < 0) return -1;
+	else if (d > 0) return 1;
+	else return 0;
+}
+
+/* Get all hull triangles that vertex 'v' is outside of */
+static GHash *hull_triangles_v_outside(GHash *hull_triangles, const BMVert *v)
+{
+	GHash *outside;
+	GHashIterator iter;
+
+	outside = BLI_ghash_new(BLI_ghashutil_ptrhash,
+							BLI_ghashutil_ptrcmp,
+							"outside");
+
+	GHASH_ITER (iter, hull_triangles) {
+		HullTriangle *t = BLI_ghashIterator_getKey(&iter);
+		
+		if (hull_point_tri_side(t, v->co) >= 0)
+			BLI_ghash_insert(outside, t, NULL);
+	}
+
+	return outside;
+}
+
+/* Similar to above, but just get true/false rather than triangles */
+static int hull_test_v_outside(GHash *hull_triangles, const BMVert *v)
+{
+	GHashIterator iter;
+
+	GHASH_ITER (iter, hull_triangles) {
+		HullTriangle *t = BLI_ghashIterator_getKey(&iter);
+		
+		if (hull_point_tri_side(t, v->co) >= 0)
+			return TRUE;
+	}
+
+	return FALSE;
+}
+
+
+/* For vertex 'v', find which triangles must be deleted to extend the
+   hull; find the boundary edges of that hole so that it can be filled
+   with connections to the new vertex, and update the hull_triangles
+   to delete the marked triangles */
+static void add_point(GHash *hull_triangles, BLI_mempool *hull_pool,
+					  BLI_mempool *edge_pool, GHash *outside, BMVert *v)
+{
+	ListBase edges = {NULL, NULL};
+	HullBoundaryEdge *e, *next;
+	GHashIterator iter;
+
+	GHASH_ITER (iter, outside) {
+		HullTriangle *t = BLI_ghashIterator_getKey(&iter);
+		expand_boundary_edges(&edges, edge_pool, t);
+		
+		/* Delete the triangle */
+		BLI_ghash_remove(hull_triangles, t, NULL, NULL);
+		BLI_mempool_free(hull_pool, t);
+	}
+
+	/* Fill hole boundary with triangles to new point */
+	for (e = edges.first; e; e = next) {
+		next = e->next;
+		hull_add_triangle(hull_triangles, hull_pool, e->v[0], e->v[1], v);
+		BLI_mempool_free(edge_pool, e);
+	}
+}
+
+static BMFace *hull_find_example_face(BMesh *bm, BMEdge *e)
+{
+	BMIter iter;
+	BMFace *f;
+
+	BM_ITER_ELEM (f, &iter, e, BM_FACES_OF_EDGE) {
+		if (BMO_elem_flag_test(bm, f, HULL_FLAG_INPUT) ||
+			!BMO_elem_flag_test(bm, f, HULL_FLAG_OUTPUT_GEOM))
+			return f;
+	}
+
+	return NULL;
+}
+
+static void hull_output_triangles(BMesh *bm, GHash *hull_triangles)
+{
+	GHashIterator iter;
+	
+	GHASH_ITER (iter, hull_triangles) {
+		HullTriangle *t = BLI_ghashIterator_getKey(&iter);
+
+		if (!t->skip) {
+			BMEdge *edges[3] = {
+				BM_edge_create(bm, t->v[0], t->v[1], NULL, TRUE),
+				BM_edge_create(bm, t->v[1], t->v[2], NULL, TRUE),
+				BM_edge_create(bm, t->v[2], t->v[0], NULL, TRUE)
+			};
+			BMFace *f, *example = NULL;
+			int i;
+
+			/* Look for an adjacent face that existed before the hull */
+			for (i = 0; i < 3; i++) {
+				if (!example)
+					example = hull_find_example_face(bm, edges[i]);
+			}
+
+			f = BM_face_create_quad_tri_v(bm, t->v, 3, example, FALSE);
+			BM_face_copy_shared(bm, f);
+
+			/* Mark face/verts/edges for 'geomout' slot and select */
+			BMO_elem_flag_enable(bm, f, HULL_FLAG_OUTPUT_GEOM);
+			BM_face_select_set(bm, f, TRUE);
+			for (i = 0; i < 3; i++) {
+				BMO_elem_flag_enable(bm, t->v[i], HULL_FLAG_OUTPUT_GEOM);
+				BMO_elem_flag_enable(bm, edges[i], HULL_FLAG_OUTPUT_GEOM);
+			}
+		}
+	}
+}
+
+
+
+/***************************** Final Edges ****************************/
+
+typedef struct {
+	GHash *edges;
+	BLI_mempool *base_pool, *link_pool;
+} HullFinalEdges;
+
+static LinkData *final_edges_find_link(ListBase *adj, BMVert *v)
+{
+	LinkData *link;
+
+	for (link = adj->first; link; link = link->next) {
+		if (link->data == v)
+			return link;
+	}
+
+	return NULL;
+}
+
+static int hull_final_edges_lookup(HullFinalEdges *final_edges,
+								   BMVert *v1, BMVert *v2)
+{
+	ListBase *adj;
+
+	/* Use lower vertex pointer for hash key */
+	if (v1 > v2)
+		SWAP(BMVert*, v1, v2);
+
+	adj = BLI_ghash_lookup(final_edges->edges, v1);
+	if (!adj)
+		return FALSE;
+
+	return !!final_edges_find_link(adj, v2);
+}
+
+/* Used for checking whether a pre-existing edge lies on the hull */
+static HullFinalEdges *hull_final_edges(GHash *hull_triangles)
+{
+	HullFinalEdges *final_edges;
+	GHashIterator iter;
+	
+	final_edges = MEM_callocN(sizeof(HullFinalEdges), "HullFinalEdges");
+	final_edges->edges = BLI_ghash_new(BLI_ghashutil_ptrhash,
+									   BLI_ghashutil_ptrcmp,
+									   "final edges ghash");
+	final_edges->base_pool = BLI_mempool_create(sizeof(ListBase), 128, 128, 0);
+	final_edges->link_pool = BLI_mempool_create(sizeof(LinkData), 128, 128, 0);
+
+	GHASH_ITER (iter, hull_triangles) {
+		LinkData *link;
+		int i;
+		
+		for (i = 0; i < 3; i++) {
+			HullTriangle *t = BLI_ghashIterator_getKey(&iter);
+			BMVert *v1 = t->v[i];
+			BMVert *v2 = t->v[(i + 1) % 3];
+			ListBase *adj;
+
+			/* Use lower vertex pointer for hash key */
+			if (v1 > v2)
+				SWAP(BMVert*, v1, v2);
+
+			adj = BLI_ghash_lookup(final_edges->edges, v1);
+			if (!adj) {
+				adj = BLI_mempool_calloc(final_edges->base_pool);
+				BLI_ghash_insert(final_edges->edges, v1, adj);
+			}
+
+			if (!final_edges_find_link(adj, v2)) {
+				link = BLI_mempool_calloc(final_edges->link_pool);
+				link->data = v2;
+				BLI_addtail(adj, link);
+			}
+		}
+	}
+
+	return final_edges;
+}
+
+static void hull_final_edges_free(HullFinalEdges *final_edges)
+{
+	BLI_ghash_free(final_edges->edges, NULL, NULL);
+	BLI_mempool_destroy(final_edges->base_pool);
+	BLI_mempool_destroy(final_edges->link_pool);
+	MEM_freeN(final_edges);
+}
+
+
+
+/************************* Initial Tetrahedron ************************/
+
+static void hull_add_tetrahedron(GHash *hull_triangles, BLI_mempool *pool,
+								 BMVert *tetra[4])
+{
+	float center[3];
+	int i, indices[4][3] = {
+		{0, 1, 2},
+		{0, 2, 3},
+		{1, 0, 3},
+		{2, 1, 3}};
+
+	/* Calculate center */
+	zero_v3(center);
+	for (i = 0; i < 4; i++)
+		add_v3_v3(center, tetra[i]->co);
+	mul_v3_fl(center, 0.25f);
+
+	for (i = 0; i < 4; i++) {
+		BMVert *v1 = tetra[indices[i][0]];
+		BMVert *v2 = tetra[indices[i][1]];
+		BMVert *v3 = tetra[indices[i][2]];
+		float no[3], d[3];
+
+		normal_tri_v3(no, v1->co, v2->co, v3->co);
+		sub_v3_v3v3(d, center, v1->co);
+		if (dot_v3v3(no, d) > 0)
+			SWAP(BMVert*, v1, v3);
+
+		hull_add_triangle(hull_triangles, pool, v1, v2, v3);
+	}
+}
+
+/* For each axis, get the minimum and maximum input vertices */
+static void hull_get_min_max(BMesh *bm, BMOperator *op,
+							 BMVert *min[3], BMVert *max[3])
+{
+	BMOIter oiter;
+	BMVert *v;
+
+	min[0] = min[1] = min[2] = NULL;
+	max[0] = max[1] = max[2] = NULL;
+
+	BMO_ITER (v, &oiter, bm, op, "input", BM_VERT) {
+		int i;
+		
+		for (i = 0; i < 3; i++) {
+			if (!min[i] || v->co[i] < min[i]->co[i])
+				min[i] = v;
+			if (!max[i] || v->co[i] > max[i]->co[i])
+				max[i] = v;
+		}
+	}
+}
+
+/* Returns true if input is coplanar */
+static int hull_find_large_tetrahedron(BMesh *bm, BMOperator *op,
+									   BMVert *tetra[4])
+{
+	BMVert *min[3], *max[3], *v;
+	BMOIter oiter;
+	float widest_axis_len, largest_dist, plane_normal[3];
+	int i, j, widest_axis;
+	
+	hull_get_min_max(bm, op, min, max);
+
+	/* Check for flat axis */
+	for (i = 0; i < 3; i++) {
+		if (min[i] == max[i]) {
+			return TRUE;
+		}
+	}
+
+	/* Find widest axis */
+	widest_axis_len = 0;
+	for (i = 0; i < 3; i++) {
+		float len = (max[i]->co[i] - min[i]->co[i]);
+		if (len >= widest_axis_len) {
+			widest_axis_len = len;
+			widest_axis = i;
+		}
+	}
+
+	/* Use widest axis for first two points */
+	tetra[0] = min[widest_axis];
+	tetra[1] = max[widest_axis];
+	BMO_elem_flag_enable(bm, tetra[0], HULL_FLAG_TETRA_VERT);
+	BMO_elem_flag_enable(bm, tetra[1], HULL_FLAG_TETRA_VERT);
+
+	/* Choose third vertex farthest from existing line segment */
+	largest_dist = 0;
+	for (i = 0; i < 3; i++) {
+		BMVert *v;
+		float dist;
+
+		if (i == widest_axis)
+			continue;
+
+		v = min[i];
+		for (j = 0; j < 2; j++) {
+			dist = dist_to_line_segment_v3(v->co, tetra[0]->co, tetra[1]->co);
+			if (dist > largest_dist) {
+				largest_dist = dist;
+				tetra[2] = v;
+			}
+
+			v = max[i];
+		}
+	}
+
+	BMO_elem_flag_enable(bm, tetra[2], HULL_FLAG_TETRA_VERT);
+	/* Check for colinear vertices */
+	if (largest_dist < 0.0001)
+		return TRUE;
+
+	/* Choose fourth point farthest from existing plane */
+	largest_dist = 0;
+	normal_tri_v3(plane_normal, tetra[0]->co, tetra[1]->co, tetra[2]->co);
+	BMO_ITER (v, &oiter, bm, op, "input", BM_VERT) {
+		if (!BMO_elem_flag_test(bm, v, HULL_FLAG_TETRA_VERT)) {
+			float dist = dist_to_plane_v3(v->co, tetra[0]->co, plane_normal);
+			if (dist > largest_dist) {
+				largest_dist = dist;
+				tetra[3] = v;
+			}
+		}
+	}
+
+	BMO_elem_flag_enable(bm, tetra[3], HULL_FLAG_TETRA_VERT);
+	if (largest_dist < 0.0001)
+		return TRUE;
+
+	return FALSE;
+}
+
+
+
+/**************************** Final Output ****************************/
+
+static void hull_remove_overlapping(BMesh *bm, GHash *hull_triangles,
+									HullFinalEdges *final_edges)
+{
+	GHashIterator hull_iter;
+
+	GHASH_ITER (hull_iter, hull_triangles) {
+		HullTriangle *t = BLI_ghashIterator_getKey(&hull_iter);
+		BMIter bm_iter1, bm_iter2;
+		BMFace *f;
+		int f_on_hull;
+
+		BM_ITER_ELEM (f, &bm_iter1, t->v[0], BM_FACES_OF_VERT) {
+			BMEdge *e;
+
+			/* Check that all the face's edges are on the hull,
+			   otherwise can't reuse it */
+			f_on_hull = TRUE;
+			BM_ITER_ELEM (e, &bm_iter2, f, BM_EDGES_OF_FACE) {
+				if (!hull_final_edges_lookup(final_edges, e->v1, e->v2)) {
+					f_on_hull = FALSE;
+					break;
+				}
+			}
+			
+			/* Note: can't change ghash while iterating, so mark
+			   with 'skip' flag rather than deleting triangles */
+			if (BM_vert_in_face(f, t->v[1]) &&
+				BM_vert_in_face(f, t->v[2]) && f_on_hull) {
+				t->skip = TRUE;
+				BMO_elem_flag_disable(bm, f, HULL_FLAG_INTERIOR_ELE);
+				BMO_elem_flag_enable(bm, f, HULL_FLAG_HOLE);
+			}
+		}
+	}
+}
+
+static void hull_mark_interior_elements(BMesh *bm, BMOperator *op,
+										GHash *hull_triangles,
+										HullFinalEdges *final_edges)
+{
+	BMVert *v;
+	BMEdge *e;
+	BMFace *f;
+	BMOIter oiter;
+
+	/* Check all input vertices again to see if they are actually part
+	   of the hull */
+	BMO_ITER (v, &oiter, bm, op, "input", BM_VERT) {
+		if (!hull_test_v_outside(hull_triangles, v)) {
+			/* Mark for 'interior_verts' slot */
+			BMO_elem_flag_enable(bm, v, HULL_FLAG_INTERIOR_ELE);
+		}
+	}
+
+	/* Check for interior edges too */
+	BMO_ITER (e, &oiter, bm, op, "input", BM_EDGE) {
+		if (!hull_final_edges_lookup(final_edges, e->v1, e->v2))
+			BMO_elem_flag_enable(bm, e, HULL_FLAG_INTERIOR_ELE);
+	}
+
+	/* Mark all input faces as interior, some may be unmarked in
+	   hull_remove_overlapping() */
+	BMO_ITER (f, &oiter, bm, op, "input", BM_FACE) {
+		BMO_elem_flag_enable(bm, f, HULL_FLAG_INTERIOR_ELE);
+	}
+}
+
+static void hull_tag_unused(BMesh *bm, BMOperator *op)
+{
+	BMIter iter;
+	BMOIter oiter;
+	BMVert *v;
+	BMEdge *e;
+	BMFace *f;
+
+	/* Mark vertices, edges, and faces that are already marked
+	   interior (i.e. were already part of the input, but not part of
+	   the hull), but that aren't also used by elements outside the
+	   input set */
+	BMO_ITER (v, &oiter, bm, op, "input", BM_VERT) {
+		if (BMO_elem_flag_test(bm, v, HULL_FLAG_INTERIOR_ELE)) {
+			int del = TRUE;
+		
+			BM_ITER_ELEM(e, &iter, v, BM_EDGES_OF_VERT) {
+				if (!BMO_elem_flag_test(bm, e, HULL_FLAG_INPUT)) {
+					del = FALSE;
+					break;
+				}
+			}
+
+			BM_ITER_ELEM(f, &iter, v, BM_FACES_OF_VERT) {
+				if (!BMO_elem_flag_test(bm, f, HULL_FLAG_INPUT)) {
+					del = FALSE;
+					break;
+				}
+			}
+
+			if (del)
+				BMO_elem_flag_enable(bm, v, HULL_FLAG_DEL);
+		}
+	}
+
+	BMO_ITER (e, &oiter, bm, op, "input", BM_EDGE) {
+		if (BMO_elem_flag_test(bm, e, HULL_FLAG_INTERIOR_ELE)) {
+			int del = TRUE;
+
+			BM_ITER_ELEM(f, &iter, e, BM_FACES_OF_EDGE) {
+				if (!BMO_elem_flag_test(bm, f, HULL_FLAG_INPUT)) {
+					del = FALSE;
+					break;
+				}
+			}
+
+			if (del)
+				BMO_elem_flag_enable(bm, e, HULL_FLAG_DEL);
+		}
+	}
+
+	BMO_ITER (f, &oiter, bm, op, "input", BM_FACE) {
+		if (BMO_elem_flag_test(bm, f, HULL_FLAG_INTERIOR_ELE))
+			BMO_elem_flag_enable(bm, f, HULL_FLAG_DEL);
+	}
+}
+
+void hull_tag_holes(BMesh *bm, BMOperator *op)
+{
+	BMIter iter;
+	BMOIter oiter;
+	BMFace *f;
+	BMEdge *e;
+
+	/* Unmark any hole faces if they are isolated or part of a
+	   border */
+	BMO_ITER (f, &oiter, bm, op, "input", BM_FACE) {
+		if (BMO_elem_flag_test(bm, f, HULL_FLAG_HOLE)) {
+			BM_ITER_ELEM(e, &iter, f, BM_EDGES_OF_FACE) {
+				if (BM_edge_face_count(e) == 1) {
+					BMO_elem_flag_disable(bm, f, HULL_FLAG_HOLE);
+					break;
+				}
+			}
+		}
+	}
+
+	/* Mark edges too if all adjacent faces are holes */
+	BMO_ITER (e, &oiter, bm, op, "input", BM_EDGE) {
+		int hole = TRUE;
+		
+		BM_ITER_ELEM(f, &iter, e, BM_FACES_OF_EDGE) {
+			if (!BMO_elem_flag_test(bm, f, HULL_FLAG_HOLE)) {
+				hole = FALSE;
+				break;
+			}
+		}
+
+		if (hole)
+			BMO_elem_flag_enable(bm, e, HULL_FLAG_HOLE);
+	}
+}
+
+void bmo_convex_hull_exec(BMesh *bm, BMOperator *op)
+{
+	HullFinalEdges *final_edges;
+	BLI_mempool *hull_pool, *edge_pool;
+	BMVert *v, *tetra[4];
+	BMElemF *ele;
+	BMOIter oiter;
+	GHash *hull_triangles;
+
+	/* Verify that at least four verts in the input */
+	if (BMO_slot_get(op, "input")->len < 4) {
+		BMO_error_raise(bm, op, BMERR_CONVEX_HULL_FAILED,
+						"Requires at least four vertices");
+		return;
+	}
+
+	/* Initialize the convex hull by building a tetrahedron. A
+	   degenerate tetrahedron can cause problems, so report error and
+	   fail if the result is coplanar */
+	if (hull_find_large_tetrahedron(bm, op, tetra)) {
+		BMO_error_raise(bm, op, BMERR_CONVEX_HULL_FAILED,
+						"Input vertices are coplanar");
+		return;
+	}
+
+	/* Tag input elements */
+	BMO_ITER (ele, &oiter, bm, op, "input", BM_ALL)
+		BMO_elem_flag_enable(bm, ele, HULL_FLAG_INPUT);
+
+	edge_pool = BLI_mempool_create(sizeof(HullBoundaryEdge), 128, 128, 0);
+	hull_pool = BLI_mempool_create(sizeof(HullTriangle), 128, 128, 0);
+	hull_triangles = BLI_ghash_new(BLI_ghashutil_ptrhash,
+								   BLI_ghashutil_ptrcmp,
+								   "hull_triangles");
+
+	/* Add tetrahedron triangles */
+	hull_add_tetrahedron(hull_triangles, hull_pool, tetra);
+
+	/* Expand hull to cover new vertices outside the existing hull */
+	BMO_ITER (v, &oiter, bm, op, "input", BM_VERT) {
+		if (!BMO_elem_flag_test(bm, v, HULL_FLAG_TETRA_VERT)) {
+			GHash *outside = hull_triangles_v_outside(hull_triangles, v);
+			if (BLI_ghash_size(outside)) {
+				/* Expand hull and delete interior triangles */
+				add_point(hull_triangles, hull_pool, edge_pool, outside, v);
+			}
+			BLI_ghash_free(outside, NULL, NULL);
+		}
+	}
+
+	BLI_mempool_destroy(edge_pool);
+	final_edges = hull_final_edges(hull_triangles);
+	
+	hull_mark_interior_elements(bm, op, hull_triangles, final_edges);
+
+	/* Remove hull triangles covered by an existing face */
+	if (BMO_slot_bool_get(op, "use_existing_faces")) {
+		hull_remove_overlapping(bm, hull_triangles, final_edges);
+
+		hull_tag_holes(bm, op);
+	}
+
+	/* Done with edges */
+	hull_final_edges_free(final_edges);
+
+	/* Convert hull triangles to BMesh faces */
+	hull_output_triangles(bm, hull_triangles);
+	BLI_mempool_destroy(hull_pool);
+
+	BLI_ghash_free(hull_triangles, NULL, NULL);
+
+	hull_tag_unused(bm, op);
+
+	/* Output slot of input elements that ended up inside the hull
+	   rather than part of it */
+	BMO_slot_buffer_from_enabled_flag(bm, op, "interior_geom", BM_ALL,
+									  HULL_FLAG_INTERIOR_ELE);
+
+	/* Output slot of input elements that ended up inside the hull and
+	 * are are unused by other geometry. */
+	BMO_slot_buffer_from_enabled_flag(bm, op, "unused_geom", BM_ALL,
+									  HULL_FLAG_DEL);
+
+	/* Output slot of faces and edges that were in the input and on
+	   the hull (useful for cases like bridging where you want to
+	   delete some input geometry) */
+	BMO_slot_buffer_from_enabled_flag(bm, op, "holes_geom", BM_ALL,
+									  HULL_FLAG_HOLE);
+
+	/* Output slot of all hull vertices, faces, and edges */
+	BMO_slot_buffer_from_enabled_flag(bm, op, "geomout", BM_ALL,
+									  HULL_FLAG_OUTPUT_GEOM);
+}
diff --git a/source/blender/editors/mesh/editmesh_tools.c b/source/blender/editors/mesh/editmesh_tools.c
index b650a361369..898e82c0660 100644
--- a/source/blender/editors/mesh/editmesh_tools.c
+++ b/source/blender/editors/mesh/editmesh_tools.c
@@ -3123,10 +3123,22 @@ static int edbm_tris_convert_to_quads_exec(bContext *C, wmOperator *op)
 	return OPERATOR_FINISHED;
 }
 
-void MESH_OT_tris_convert_to_quads(wmOperatorType *ot)
+static void join_triangle_props(wmOperatorType *ot)
 {
 	PropertyRNA *prop;
 
+	prop = RNA_def_float_rotation(ot->srna, "limit", 0, NULL, 0.0f, DEG2RADF(180.0f),
+	                              "Max Angle", "Angle Limit", 0.0f, DEG2RADF(180.0f));
+	RNA_def_property_float_default(prop, DEG2RADF(40.0f));
+
+	RNA_def_boolean(ot->srna, "uvs", 0, "Compare UVs", "");
+	RNA_def_boolean(ot->srna, "vcols", 0, "Compare VCols", "");
+	RNA_def_boolean(ot->srna, "sharp", 0, "Compare Sharp", "");
+	RNA_def_boolean(ot->srna, "materials", 0, "Compare Materials", "");
+}
+
+void MESH_OT_tris_convert_to_quads(wmOperatorType *ot)
+{
 	/* identifiers */
 	ot->name = "Tris to Quads";
 	ot->idname = "MESH_OT_tris_convert_to_quads";
@@ -3139,14 +3151,7 @@ void MESH_OT_tris_convert_to_quads(wmOperatorType *ot)
 	/* flags */
 	ot->flag = OPTYPE_REGISTER | OPTYPE_UNDO;
 
-	prop = RNA_def_float_rotation(ot->srna, "limit", 0, NULL, 0.0f, DEG2RADF(180.0f),
-	                              "Max Angle", "Angle Limit", 0.0f, DEG2RADF(180.0f));
-	RNA_def_property_float_default(prop, DEG2RADF(40.0f));
-
-	RNA_def_boolean(ot->srna, "uvs", 0, "Compare UVs", "");
-	RNA_def_boolean(ot->srna, "vcols", 0, "Compare VCols", "");
-	RNA_def_boolean(ot->srna, "sharp", 0, "Compare Sharp", "");
-	RNA_def_boolean(ot->srna, "materials", 0, "Compare Materials", "");
+	join_triangle_props(ot);
 }
 
 static int edbm_dissolve_exec(bContext *C, wmOperator *op)
@@ -4335,3 +4340,93 @@ void MESH_OT_wireframe(wmOperatorType *ot)
 	RNA_def_boolean(ot->srna, "use_replace",         TRUE, "Replace", "Remove original faces");
 }
 
+static int edbm_convex_hull_exec(bContext *C, wmOperator *op)
+{
+	Object *obedit = CTX_data_edit_object(C);
+	BMEditMesh *em = BMEdit_FromObject(obedit);
+	BMOperator bmop;
+		
+	EDBM_op_init(em, &bmop, op, "convex_hull input=%hvef "
+				 "use_existing_faces=%b",
+				 BM_ELEM_SELECT,
+				 RNA_boolean_get(op->ptr, "use_existing_faces"));
+	BMO_op_exec(em->bm, &bmop);
+
+	/* Hull fails if input is coplanar */
+	if (BMO_error_occurred(em->bm)) {
+		EDBM_op_finish(em, &bmop, op, TRUE);
+		return OPERATOR_CANCELLED;
+	}
+
+	
+	/* Delete unused vertices, edges, and faces */
+	if (RNA_boolean_get(op->ptr, "delete_unused")) {
+		if(!EDBM_op_callf(em, op, "del geom=%s context=%i",
+						  &bmop, "unused_geom", DEL_ONLYTAGGED)) {
+			EDBM_op_finish(em, &bmop, op, TRUE);
+			return OPERATOR_CANCELLED;
+		}
+	}
+
+	/* Delete hole edges/faces */
+	if (RNA_boolean_get(op->ptr, "make_holes")) {
+		if(!EDBM_op_callf(em, op, "del geom=%s context=%i",
+						  &bmop, "holes_geom", DEL_ONLYTAGGED)) {
+			EDBM_op_finish(em, &bmop, op, TRUE);
+			return OPERATOR_CANCELLED;
+		}
+	}
+
+	/* Merge adjacent triangles */
+	if (RNA_boolean_get(op->ptr, "join_triangles")) {
+		if(!EDBM_op_callf(em, op, "join_triangles faces=%s limit=%f",
+						  &bmop, "geomout",
+						  RNA_float_get(op->ptr, "limit"))) {
+			EDBM_op_finish(em, &bmop, op, TRUE);
+			return OPERATOR_CANCELLED;
+		}
+	}
+
+	if (!EDBM_op_finish(em, &bmop, op, TRUE)) {
+		return OPERATOR_CANCELLED;
+	}
+	else {
+		EDBM_update_generic(C, em, TRUE);
+		EDBM_selectmode_flush(em);
+		return OPERATOR_FINISHED;
+	}
+}
+
+void MESH_OT_convex_hull(wmOperatorType *ot)
+{
+	/* identifiers */
+	ot->name = "Convex Hull";
+	ot->description = "Enclose selected vertices in a convex polyhedron";
+	ot->idname = "MESH_OT_convex_hull";
+
+	/* api callbacks */
+	ot->exec = edbm_convex_hull_exec;
+	ot->poll = EM_view3d_poll;
+
+	/* flags */
+	ot->flag = OPTYPE_REGISTER | OPTYPE_UNDO;
+
+	/* props */
+	RNA_def_boolean(ot->srna, "delete_unused", TRUE,
+					"Delete Unused",
+					"Delete selected elements that are not used by the hull");
+
+	RNA_def_boolean(ot->srna, "use_existing_faces", TRUE,
+					"Use Existing Faces",
+					"Skip hull triangles that are covered by a pre-existing face");
+
+	RNA_def_boolean(ot->srna, "make_holes", FALSE,
+					"Make Holes",
+					"Delete selected faces that are used by the hull");
+
+	RNA_def_boolean(ot->srna, "join_triangles", TRUE,
+					"Join Triangles",
+					"Merge adjacent triangles into quads");
+
+	join_triangle_props(ot);
+}
diff --git a/source/blender/editors/mesh/mesh_intern.h b/source/blender/editors/mesh/mesh_intern.h
index ca989a25ccd..31c130d20c9 100644
--- a/source/blender/editors/mesh/mesh_intern.h
+++ b/source/blender/editors/mesh/mesh_intern.h
@@ -214,6 +214,8 @@ void MESH_OT_inset(struct wmOperatorType *ot);
 void MESH_OT_wireframe(struct wmOperatorType *ot);
 void MESH_OT_vert_slide(struct wmOperatorType *ot);
 
+void MESH_OT_convex_hull(struct wmOperatorType *ot);
+
 /* ******************* mesh_navmesh.c */
 void MESH_OT_navmesh_make(struct wmOperatorType *ot);
 void MESH_OT_navmesh_face_copy(struct wmOperatorType *ot);
diff --git a/source/blender/editors/mesh/mesh_ops.c b/source/blender/editors/mesh/mesh_ops.c
index 0b2a6d2bd66..1b87e7813db 100644
--- a/source/blender/editors/mesh/mesh_ops.c
+++ b/source/blender/editors/mesh/mesh_ops.c
@@ -167,6 +167,8 @@ void ED_operatortypes_mesh(void)
 	WM_operatortype_append(MESH_OT_wireframe);
 	WM_operatortype_append(MESH_OT_edge_split);
 
+	WM_operatortype_append(MESH_OT_convex_hull);
+
 #ifdef WITH_GAMEENGINE
 	WM_operatortype_append(MESH_OT_navmesh_make);
 	WM_operatortype_append(MESH_OT_navmesh_face_copy);