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Ray Casting Algebraic Surfaces using the Frustum Form
Author(s) -
Reimers Martin,
Seland Johan
Publication year - 2008
Publication title -
computer graphics forum
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.578
H-Index - 120
eISSN - 1467-8659
pISSN - 0167-7055
DOI - 10.1111/j.1467-8659.2008.01133.x
Subject(s) - frustum , computer science , simple (philosophy) , algorithm , tetrahedron , algebraic number , point (geometry) , mathematics , geometry , mathematical analysis , philosophy , epistemology
We propose an algorithm for interactive ray‐casting of algebraic surfaces of high degree. A key point of our approach is a polynomial form adapted to the view frustum. This so called frustum form yields simple expressions for the Bernstein form of the ray equations, which can be computed efficiently using matrix products and pre‐computed quantities. Numerical root‐finding is performed using B‐spline and Bézier techniques, and we compare the performances of recent and classical algorithms. Furthermore, we propose a simple and fairly efficient anti‐aliasing scheme, based on a combination of screen space and object space techniques. We show how our algorithms can be implemented on streaming architectures with single precision, and demonstrate interactive frame‐rates for degrees up to 16.