Abstract: Tetrahedra can be used as primitives to represent volumetric shells because of their ease of performing geometric tests such as intersection with other geometric primitives. Each triangular face of a triangulated surface mesh can be extruded or otherwise formed into a prism, and that prism can be filled with tets (tetrahedra). An edge of a tet can be deemed to be rising if, going counterlockwise around the face, the corresponding tet-edge that splits the extruded face proceeds from the inset surface to the offset surface. To determine a valid tet orientation, each directed edge of the surface mesh is labeled as Rising or Falling (R, F). In various embodiments, one or more simple rules are used for determining whether an edge is rising or falling. In one aspect, a partial ordering of the connectivity of a surface is used in the tet generation process.

Abstract: A method allowing for quick manipulation of weight values associated with points on a polygonal mesh that is to be deformed. A point on the polygonal mesh may be selected by the user. Then, a solution space of possible positions for the selected point may be calculated by solving a deformation model for a range of weight values. A graphical representation of the solution space may be provided, such as a locus of possible positions for the selected point, where each point on the locus corresponds to a particular weight value. Manipulation of these weight values, and hence, the deformation of the polygonal mesh, may be achieved simply by selecting a position on the locus. The mesh may be updated to reflect the weight corresponding to the selected position.