UBC Theses and Dissertations

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UBC Theses and Dissertations

Design-driven quadrangulation of closed 3D curves Wang, Caoyu


This work presents a novel, design-driven quadrangulating method for closed 3D curves. While the quadrangulation of existing surfaces has been well studied for a long time, there are few works that can successfully construct a quad-mesh relying solely on 3D curves, as the shape of the surface interior is not uniquely defined. I observe that, in most cases, viewers can complete the intended shape by envisioning a dense network of smooth, gradually changing flow-lines across a pair of input curve segments with similar orientation and shape. The method proposed here mimics this behavior. This algorithm begins by segmenting the input closed curves into pairs of matching segments. I interpolate the input curves by a network of quadrilateral cycles whose iso-lines define the desired flow line network. I proceed to interpolate these networks with all-quad meshes that convey designer intents. I evaluate my results by showing convincing quadrangulations of complex and diverse curve networks with concave, non-planar cycles, and validate my approach by comparing my results to artist generated interpolating meshes. My algorithm is suitable for use in sketch-based modeling systems as well as in other applications where artist curves can be created.

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Attribution-NonCommercial-NoDerivatives 4.0 International