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UBC Theses and Dissertations

Modeling developable surfaces from arbitrary boundary curves Rose, Kenneth Lloyd Patrick

Abstract

Developable surfaces are surfaces that can be unfolded into the plane with no distortion. Although ubiquitous in our everyday surroundings, there is currently no easy way to model them on a computer. This thesis fills this void by presenting a general method for creating developable geometry that utilizes the connection between developable surfaces and the convex hulls of their boundaries. Given an arbitrary, user-specified 3D polyline boundary, our system generates a smooth discrete developable surface that interpolates this boundary. We identify desirable properties of such surfaces, present a practical algorithm to compute them, and extend it to handle.darts and internal singular points. We demonstrate the effectiveness of our method through a series of examples, from architectural design to garments, using a sketch-based interface to quickly create the boundaries.

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