Warren, Joe2013-09-162013-09-162013-09-162013-09-162013-052013-09-16May 2013Feng, Powei. "Functional representation and manipulation of shapes with applications in surface and solid modeling." (2013) Diss., Rice University. <a href="https://hdl.handle.net/1911/71952">https://hdl.handle.net/1911/71952</a>.https://hdl.handle.net/1911/71952Real-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.application/pdfengCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.Geometric modelingB-splineGraphicsComputer graphicsThesis2013-09-16123456789/ETD-2013-05-448