Abstract: Methods and systems improve quality of a hex-mesh by: performing a first iterative procedure which starts with the input hex-mesh and which outputs an output hex-mesh having improved quality. Performing the first iterative procedure comprises: initializing a current hex-mesh to be equal to the input hex mesh; for each iteration of the first iterative procedure: performing an optimization of an energy function over a plurality of directed-edges in the current hex-mesh to determine updated vertex positions for vertices in the current hex-mesh, wherein for each directed edge, the energy function comprises a term that expresses a preference for the directed edge to be aligned with normal vectors of base triangles of an edge-cone corresponding to the directed edge; and updating the current hex-mesh with the updated vertex positions; and after one or more iterations, setting the output hex-mesh to be equal to the current hex-mesh.

Abstract: A method for generating a polycube segmentation of an input object comprises: providing an input mesh of the object comprising a plurality of surface faces; generating an initial polycube labeling for the faces by assigning, to each face, a label which is one of six directions (±X,±Y,±Z) aligned with a set of Cartesian axes, the initial polycube labeling defining a plurality of charts, and generating the initial polycube labeling comprising effecting a tradeoff between competing objectives of: making the initial polycube labeling relatively compact; and making the initial polycube labeling relatively faithful to the input object. The method further comprises generating an updated polycube segmentation by changing the label assigned to each of one or more surface faces and thereby modifying one or more of the charts to provide the charts with monotonic boundaries.

Abstract: Methods and systems improve quality of a hex-mesh by: performing a first iterative procedure which starts with the input hex-mesh and which outputs an output hex-mesh having improved quality. Performing the first iterative procedure comprises: initializing a current hex-mesh to be equal to the input hex mesh; for each iteration of the first iterative procedure: performing an optimization of an energy function over a plurality of directed-edges in the current hex-mesh to determine updated vertex positions for vertices in the current hex-mesh, wherein for each directed edge, the energy function comprises a term that expresses a preference for the directed edge to be aligned with normal vectors of base triangles of an edge-cone corresponding to the directed edge; and updating the current hex-mesh with the updated vertex positions; and after one or more iterations, setting the output hex-mesh to be equal to the current hex-mesh.

Abstract: A method for generating a polycube segmentation of an input object comprises: providing an input mesh of the object comprising a plurality of surface faces; generating an initial polycube labeling for the faces by assigning, to each face, a label which is one of six directions (±X,±Y,±Z) aligned with a set of Cartesian axes, the initial polycube labeling defining a plurality of charts, and generating the initial polycube labeling comprising effecting a tradeoff between competing objectives of: making the initial polycube labeling relatively compact; and making the initial polycube labeling relatively faithful to the input object. The method further comprises generating an updated polycube segmentation by changing the label assigned to each of one or more surface faces and thereby modifying one or more of the charts to provide the charts with monotonic boundaries.