Real-valued functions have wide applications in various areas within computer graphics. In this work, we examine three representation of shapes using functions. In particular, we study the classical B-spline representation of piece-wise polynomials in the univariate domain. We provide a generalization of B-spline to the bivariate domain using intuition gained from the univariate construction. We also study the popular scheme of representing 3D density distribution using a uniform, rectilinear grid, where we provide a novel contouring scheme that culls occluded inner geometries. Lastly, we examine a ray-based representation for 3D indicator functions called ray-rep, for which we present a novel meshing scheme with multi-material extensions.
| Identifer | oai:union.ndltd.org:RICE/oai:scholarship.rice.edu:1911/71952 |
| Date | 16 September 2013 |
| Creators | Feng, Po-Wei |
| Contributors | Warren, Joe |
| Source Sets | Rice University |
| Language | English |
| Detected Language | English |
| Type | thesis, text |
| Format | application/pdf |
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