Decimating a three-dimensional mesh via successive self-parameterization

A system comprising:

• at least one computer memory comprising an initial three-dimensional mesh;
• and
• one or more servers configured to cause the system to:
• determine a surface mapping between a plurality of vertices in the initial three-dimensional mesh and corresponding vertices in a two-dimensional surface mapping space;
• successively self-parameterizing the initial three-dimensional mesh for each decimation iteration of a plurality of decimation iterations by:
• collapsing edges in the initial three-dimensional mesh by combining selected vertices of the plurality of vertices that form the edges to generate new vertices in the initial three-dimensional mesh;
• and
• collapsing corresponding edges in the two-dimensional surface mapping space by combining selected vertices of the corresponding vertices that form the corresponding edges to generate new corresponding vertices in the two-dimensional surface mapping space, wherein collapsing the edges in the initial three-dimensional mesh and the corresponding edges in the two-dimensional surface mapping space results in bijective maps for between first points in local geometries of the edges in the initial three-dimensional mesh before collapsing the edges and second points in new local geometries after collapsing the edges;
• and
• generate, in response to the plurality of decimation iterations, a decimated three-dimensional mesh associated with a final bijective map that maps the decimated three-dimensional mesh to the initial three-dimensional mesh via composition of one or more additional bijective maps associated with one or more intermediate three-dimensional meshes.

A computer-implemented method comprising:

• determining, by at least one processor, a surface mapping between a plurality of vertices in local geometries associated with edges in a three-dimensional mesh and a corresponding local geometries associated with corresponding edges in a two-dimensional surface mapping space;
• performing a step for collapsing the edges in the three-dimensional mesh and the corresponding edges in the two-dimensional surface mapping space to provide a bijective map for the local geometries;
• and
• generating, by the at least one processor and across a plurality of decimation iterations of the three-dimensional mesh, a final decimated three-dimensional mesh associated with a final bijective map determined via composition of a plurality of bijective maps corresponding to the plurality of decimation iterations.