Tessellating Algebraic Curves and Surfaces Using A-Patches

Spline;Surface;A-Patch;Computer Science

Luk, Curtis

University of Waterloo

关键词: Spline;    Surface;    A-Patch;    Computer Science;   

Others  :  https://uwspace.uwaterloo.ca/bitstream/10012/3693/1/uw-ethesis.pdf

瑞士|英语

来源: UWSPACE Waterloo Institutional Repository

【 摘 要 】

This work approaches the problem of triangulating algebraic curves/surfaces with a subdivision-style algorithm using A-Patches.An implicit algebraic curve is converted from the monomial basis to the bivariate Bernstein-Bezier basis while implicit algebraic surfaces are converted to the trivariate Bernstein basis.The basis is then used to determine the scalar coefficients of the A-patch, which are used to find whether or not the patch contains a separation layer of coefficients.Those that have such a separation have only a single sheet of the surface passing through the domain while one that has all positive or negative coefficients does not contain a zero-set of the surface.Ambiguous cases are resolved by subdividing the structure into a set of smaller patches and repeating the algorithm.Using A-patches to generate a tessellation of the surface has potential advantages by reducing the amount of subdivision required compared to other subdivision algorithms and guarantees a single-sheeted surface passing through it.This revelation allows the tessellation of surfaces with acute features and perturbed features in greater accuracy.