UBC Theses and Dissertations
Developable surface processing methods for three-dimensional meshes Julius, Dan Natan
Developable surfaces are of great significance in computer graphics as they play a key role in many applications involving planar surface parameterization. Industries where 3D objects are constructed from sheets of material such as fabric or metal typically employ these surfaces throughout their design processes. This work introduces a new descriptor for developable mesh surfaces, which provides the means for creating simple and robust tools for detecting, measuring, and approximating developable surface charts in meshes. Based on this descriptor two novel algorithms are proposed. D-Charts, an algorithm for mesh segmentation into (nearly) developable charts, and DCS approximation, an algorithm for approximation of meshes with developable surfaces. D-Charts uses the proposed descriptor to segment meshes into nearly developable charts for texture atlas generation. By bounding the distortion directly during the segmentation stage, the generated atlases exhibit less distortion for the same number of charts compared to those created using state-of-the-art techniques. In addition to texture atlases, we demonstrate the practicality of this method for industrial applications using the patterns produced by the algorithm to make fabric and paper copies of popular computer graphics models. The DCS approximation method increases surface developability by modifying the geometry, while at the same time keeping the deformed surface as close as possible to the input surface. The method was developed in the context of virtual fabric design, and was combined with a sketching interface to provide a novel design system. The algorithm modifies non-developable meshes generated from sketches into piecewise developable surfaces. These allow straightforward computation of distortion-free texture mapping and automatic generation of 2D patterns for sewing real replicas of the designed garments.
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