Thickening freeform surfaces for solid fabrication

Given an intersection-free mesh surface S, the paper introduces a method to thicken S into a solid H located at one side of S. By such a surface-to-solid conversion operation, industrial users are able to fabricate a designed (or reconstructed) surface by rapid prototyping.

The paper first investigates an implicit representation of the thickened solid H according to an extension of signed distance function. After that, a partial surface reconstruction algorithm is proposed to generate the boundary surface of H, which retains the given surface S on the resultant surface.

Experimental tests show that the thickening results generated by the method give nearly uniform thickness and meanwhile do not present shape approximation error at the region of input surface S. These two good properties are important to the industrial applications of solid fabrication.

The input polygonal model is assumed to be intersection-free, where models containing self-intersection will lead to invalid thickening results.

A novel robust operation is to convert a freeform open surface into a solid by introducing no shape approximation error. A new implicit function gives a compact mathematical representation, which can easily handle the topological change on the thickened solids. A new polygonization algorithm generates faces for the boundary of thickened solid meanwhile retaining faces on the input open mesh.