Complex-valued contour meshing
Chris Weigle, David C. Banks · 1996
An isovalue contour of a function of two complex variables defines a surface in four-space. We present a robust technique for creating polygonal contours of complex-valued functions. The technique, Contour Meshing, generalizes well to larger dimensions. CR Descriptors: G.1.5 [Numerical Analysis] Roots of Nonlinear Equations; G.1.6 [Numerical Analysis] Optimization; G.2.1 [Discrete Mathematics] Combinatorics; I.3.5 [Computer Graphics] Computational Geometry and Object Modeling; I.3.6 [Computer Graphics]: Methodology and Techniques; J.2 [Physical Sciences and Engineering] Mathematics and Statistics. 1 Introduction This paper describes a recursive technique to construct a triangle mesh on an implicit surface (also called a variety or contour) in 4-space. The technique readily extends to large dimensions. We explore the resulting family of surfaces with an interactive 4D viewer in order to inspect the behavior of a complex curve as it sweeps through a singularity. The k-dimensional anal...