Geometric Illumination of Implicit Surfaces
For computer graphics researchers, this provides a novel approach to illuminate implicit surfaces without polygonal meshes, though limited to polynomial surfaces of moderate degree.
The paper presents a geometric method for illuminating implicit surfaces using projections and algebraic algorithms, enabling illumination of polynomial surfaces up to degree eight.
Illumination of scenes is usually generated in computer graphics using polygonal meshes. In this paper, we present a geometric method using projections. Starting from an implicit polynomial equation of a surface in 3-D or a curve in 2-D, we provide a semi-algebraic representation of each part of the construction. To solve polynomial condition systems and find constrained regions, we apply algebraic computational algorithms for computing the Gr{\" o}bner basis and cylindrical algebraic decomposition. The final selection of illuminated and self-shaded components for polynomial surfaces of a degree higher than three is discussed. The text is accompanied by visualizations of illumination of surfaces up to degree eight.