Generalized implicit functions for computer graphics

Dynamic Implicit Models for Computer Graphics

This paper presents a survey of the work done in implicit modeling, physics-based modeling, and haptic interaction. Implicit models characterized by the zero-set of polynomial-based algebraic equations and other commonly used analytic equations are extremely powerful in graphics, geometric design, and visualization. We first review the commonly-used techniques in geometric modeling and examine ...

Generalized Sampling in Computer Graphics

Analysis and reconstruction filters are crucial in graphics. The signal processing community has recently developed new filtering strategies based on a generalization of the traditional sampling pipeline. The main idea is to select simple basis functions such as B-splines but to effectively reshape these kernels by adding a discrete transformation filter. This approach is not widely known to gr...

A Generalized Surface Appearance Representation for Computer Graphics

(Under the direction of Anselmo Lastra) For image synthesis in computer graphics, two major approaches for representing a surface's appearance are texture mapping, which provides spatial detail, such as wallpaper, or wood grain; and the 4D bi-directional reflectance distribution function (BRDF) which provides angular detail, telling how light reflects off surfaces. I combine these two modes of ...

Asymptotics of Implicit Functions and Computer Algebra

We describe several algorithms for the asymptotic inversion of functions, from the computer algebra viewpoint. We start with some classical results, such as the inversion theorem of Lagrange. We next consider functions which can only be expanded in more complicated as-ymptotic scales. Finally, we brieey discuss the problem of nding the asymptotic behaviour of implicit functions.

Generalized Barycentric Coordinates in Computer Graphics and Computational Mechanics