Abstract: A method, device, and computer-readable storage medium for retrieving a stored triangulation of a polygonal mesh. The method includes: receiving an input polygonal mesh that is a computer representation of a three-dimensional (3D) object; identifying one or more faces of the input polygonal mesh that have more than three edges; retrieving for each face of the one or more faces, integer counts of a number of triangles that are incident to each vertex of the face stored in face-vertex properties of the face, wherein a specific triangulation of the face is represented by the number of triangles that are incident to each vertex of the face; and generating a triangulated polygonal mesh corresponding to the input polygonal mesh by triangulating, for each face of the one or more faces, the face based on the integer counts of the number of triangles that are incident to each vertex of the face.

Abstract: A method, device, and computer-readable storage medium for generating a proxy mesh. The method includes: receiving an input polygonal mesh that includes multiple sub-meshes, each of which is a polygonal mesh, where the input polygonal mesh is a computer representation of a three-dimensional (3D) object; generating a voxel volume representing the input polygonal mesh, wherein the voxel volume comprises voxels that approximates a shape of the 3D object, wherein a first set of voxels of the voxel volume includes voxels that are identified as boundary voxels that correspond to positions of polygons of the multiple sub-meshes of the input polygonal mesh; determining a grouping of two or more sub-meshes that together enclose one or more voxels of the voxel volume other than the voxels in the first set of voxels; and generating a proxy mesh corresponding to the input polygonal mesh based on the grouping of two or more sub-meshes.

Abstract: A method, device, and computer-readable storage medium for generating a proxy mesh. The method includes: receiving an input polygonal mesh that includes multiple sub-meshes, each of which is a polygonal mesh, where the input polygonal mesh is a computer representation of a three-dimensional (3D) object; generating a voxel volume representing the input polygonal mesh, wherein the voxel volume comprises voxels that approximates a shape of the 3D object, wherein a first set of voxels of the voxel volume includes voxels that are identified as boundary voxels that correspond to positions of polygons of the multiple sub-meshes of the input polygonal mesh; determining a grouping of two or more sub-meshes that together enclose one or more voxels of the voxel volume other than the voxels in the first set of voxels; and generating a proxy mesh corresponding to the input polygonal mesh based on the grouping of two or more sub-meshes.

Abstract: Apparatuses and methods pertaining to computer handling of three-dimensional volumes are disclosed. One such method comprises obtaining data representing an input set of one or more three-dimensional volumes; selecting a first three-dimensional volume from among the input set of three-dimensional volumes; identifying a concavity in the first three-dimensional volume, the concavity having a region of deepest concavity; splitting the first three-dimensional volume along a split plane or intersection loop contacting or intersecting the region of deepest concavity, such as to provide plural three-dimensional volumes; and providing data representing an output set of two or more three-dimensional volumes.

Abstract: A method, device, and computer-readable storage medium for generating a proxy mesh are disclosed. The method includes: receiving a reference mesh comprising a polygonal mesh that is a computer representation of a three-dimensional object; receiving a smoothed mesh corresponding to the reference mesh; selecting a given vertex in the smoothed mesh; identifying neighbor vertices of the given vertex in the smoothed mesh; for each neighbor vertex of the given vertex, determining a nearest location on the reference mesh overlaid on the smoothed mesh; determining an average position of the nearest locations on the reference mesh for the neighbor vertices of the given vertex; setting a new location of a vertex in a smoothed output polygonal mesh corresponding to the given vertex to the average position; and outputting the smoothed output polygonal mesh as a proxy mesh for the reference mesh.

Abstract: Apparatuses and methods pertaining to computer handling of three-dimensional volumes are disclosed. One such method comprises obtaining data representing an input set of one or more three-dimensional volumes; selecting a first three-dimensional volume from among the input set of three-dimensional volumes; identifying a concavity in the first three-dimensional volume, the concavity having a region of deepest concavity; splitting the first three-dimensional volume along a split plane or intersection loop contacting or intersecting the region of deepest concavity, such as to provide plural three-dimensional volumes; and providing data representing an output set of two or more three-dimensional volumes.

Abstract: Apparatuses and methods pertaining to computer handling of three dimensional volumes are disclosed. One such method comprises obtaining data representing an input set of one or more three-dimensional volumes; selecting a first three-dimensional volume from among the input set of three-dimensional volumes; identifying a concavity in the first three-dimensional volume, the concavity having a region of deepest concavity; splitting the first three-dimensional volume along a split plane or intersection loop contacting or intersecting the region of deepest concavity, such as to provide plural three-dimensional volumes; and providing data representing an output set of two or more three-dimensional volumes.

Abstract: Apparatuses and methods pertaining to computer handling of three dimensional volumes are disclosed. One such method comprises obtaining data representing an input set of one or more three-dimensional volumes; selecting a first three-dimensional volume from among the input set of three-dimensional volumes; identifying a concavity in the first three-dimensional volume, the concavity having a region of deepest concavity; splitting the first three-dimensional volume along a split plane or intersection loop contacting or intersecting the region of deepest concavity, such as to provide plural three-dimensional volumes; and providing data representing an output set of two or more three-dimensional volumes.

Abstract: A computer implemented method for determining a silhouette volume of a 3D object, e.g. for mesh simplification, comprises: receiving a computer representation of a 3D object; determining a silhouette volume of the object, wherein the silhouette volume is the maximal volume of space having a silhouette from every viewing direction which is identical to the silhouette of the object from the same viewing direction, and wherein points of the object which lie on the boundary of the silhouette volume also lie on the boundary of the object's projected silhouette from at least one viewing direction; determining, based on the silhouette volume, the extent to which features of the object are silhouette features; determining, for a plurality of planes and for a plurality of different axes, at least one intersection loop, wherein each intersection loop corresponds to a planar cross-section of the boundary of the object in its respective plane; and determining the convex hull of each intersection loop.

Abstract: A computer implemented method of handling polygons is disclosed, including polygons which are complex and include degeneracies. The method includes receiving an input polygon with at least one boundary, the at least one boundary having at least one vertex joining edges of the polygon boundary; determining an edge direction for each of the edges; determining a signed exterior or interior angle of each vertex angle wherein, if the exterior angle between the edges is ?pi or pi to within a predetermined threshold, determining the signed angle of the vertex angle including assigning a sign based on the winding of the edges of the polygon boundary, a sequence of angles of polygon vertices which can be directly computed or retrieved from a memory, the geometrical property that all exterior angles of the polygon sum to ?2pi or 2pi, and the known sign of the polygon area.

Abstract: A computer implemented method of handling polygons is disclosed, including polygons which are complex and include degeneracies. The method includes receiving an input polygon with at least one boundary, the at least one boundary having at least one vertex joining edges of the polygon boundary; determining an edge direction for each of the edges; determining a signed exterior or interior angle of each vertex angle wherein, if the exterior angle between the edges is pi or pi to within a predetermined threshold, determining the signed angle of the vertex angle including assigning a sign based on the winding of the edges of the polygon boundary, a sequence of angles of polygon vertices which can be directly computed or retrieved from a memory, the geometrical property that all exterior angles of the polygon sum to ?2 pi or 2 pi, and the known sign of the polygon area.

Abstract: A computer implemented method for determining a silhouette volume of a 3D object, e.g. for mesh simplification, comprises: receiving a computer representation of a 3D object; determining a silhouette volume of the object, wherein the silhouette volume is the maximal volume of space having a silhouette from every viewing direction which is identical to the silhouette of the object from the same viewing direction, and wherein points of the object which lie on the boundary of the silhouette volume also lie on the boundary of the object's projected silhouette from at least one viewing direction; determining, based on the silhouette volume, the extent to which features of the object are silhouette features; determining, for a plurality of planes and for a plurality of different axes, at least one intersection loop, wherein each intersection loop corresponds to a planar cross-section of the boundary of the object in its respective plane; and determining the convex hull of each intersection loop.

Abstract: A mesh that includes a polychord with edges may be received. A first mesh simplification operation may be performed with the mesh to remove the edges of the polychord and to generate a first simplified mesh. Guide planes may be generated based on the first simplified mesh. Furthermore, a second mesh simplification operation may be performed with a combination of the mesh with the guide planes to remove the edges of the polychord based on the guide planes and to generate a second simplified mesh.

Abstract: A polygonal mesh is received and the edges and vertices of the polygonal mesh are analyzed. A positive (e.g., convex or protruding) feature may be identified where the positive feature is bound by a non-concave edge (e.g., a convex edge or a planar edge). A negative (e.g., concave or receding) feature may also be identified where the negative feature is bound by a non-convex edge (e.g., a concave edge or a planar edge).

Abstract: An example method of transforming polygonal meshes by sub-polychord collapse may include identifying, among a plurality of sub-polychords of a given size, a seed sub-polychord having an optimal value of a metric associated with collapsing the respective sub-polychord. The example method may further include identifying a first test value of the metric for a first test sub-polychord comprising the seed sub-polychord and a first adjacent edge, and further identifying a second test value of the metric for a second test sub-polychord comprising the seed sub-polychord and a second adjacent edge. The example method may further include, responsive to determining a minimum of the first test value of the metric and the second test value of the metrics is less than a base value of the metric for the seed sub-polychord, transforming the seed sub-polychord by adding an adjacent edge that produces a test sub-polychord having the minimum test value.

Abstract: An example method of transforming polygonal meshes by sub-polychord collapse may include identifying, among a plurality of sub-polychords of a given size, a seed sub-polychord having an optimal value of a metric associated with collapsing the respective sub-polychord. The example method may further include identifying a first test value of the metric for a first test sub-polychord comprising the seed sub-polychord and a first adjacent edge, and further identifying a second test value of the metric for a second test sub-polychord comprising the seed sub-polychord and a second adjacent edge. The example method may further include, responsive to determining a minimum of the first test value of the metric and the second test value of the metrics is less than a base value of the metric for the seed sub-polychord, transforming the seed sub-polychord by adding an adjacent edge that produces a test sub-polychord having the minimum test value.

Abstract: A mesh that includes a polychord with edges may be received. A first mesh simplification operation may be performed with the mesh to remove the edges of the polychord and to generate a first simplified mesh. Guide planes may be generated based on the first simplified mesh. Furthermore, a second mesh simplification operation may be performed with a combination of the mesh with the guide planes to remove the edges of the polychord based on the guide planes and to generate a second simplified mesh.

Abstract: A polygonal mesh is received and the edges and vertices of the polygonal mesh are analyzed. A positive (e.g., convex or protruding) feature may be identified where the positive feature is bound by a non-concave edge (e.g., a convex edge or a planar edge). A negative (e.g., concave or receding) feature may also be identified where the negative feature is bound by a non-convex edge (e.g., a concave edge or a planar edge).

Abstract: A polygonal mesh is received and the edges and vertices of the polygonal mesh are analyzed. A positive (e.g., convex or protruding) feature may be identified where the positive feature is bound by a non-concave edge (e.g., a convex edge or a planar edge). A negative (e.g., concave or receding) feature may also be identified where the negative feature is bound by a non-convex edge (e.g., a concave edge or a planar edge).

Abstract: A polygonal mesh is received and the edges and vertices of the polygonal mesh are analyzed. A positive (e.g., convex or protruding) feature may be identified where the positive feature is bound by a non-concave edge (e.g., a convex edge or a planar edge). A negative (e.g., concave or receding) feature may also be identified where the negative feature is bound by a non-convex edge (e.g., a concave edge or a planar edge).