Topological design of sculptured surfaces

Topology is primal geometry. Our design philosophy embodies this principle. We report on a new surface &sign perspective based on a “marked” polygon for each object. The marked polygon captures the topology of the object surface. We construct multiply periodic mappings from polygon to sculptured surface. The mappings arise naturally from the topology and other design considerations. Hence we give a single domain global parameteriration for surfaces with handles. Examples demonstrate the design of sculptured objects and their ntanufimture.