Surface algorithms using bounds on derivatives

✍ Scribed by Daniel Filip; Robert Magedson; Robert Markot

• Publisher: Elsevier Science
• Year: 1986
• Tongue: English
• Weight: 1016 KB
• Volume: 3
• Category: Article
• ISSN: 0167-8396
• DOI: 10.1016/0167-8396(86)90005-1

✦ Synopsis

This paper generalizes three very important algorithms for surfaces which previously only worked well with polynomials. The algorithms are calculation of piecewise linear approximations, min-max boxes, and surface/surface intersections. The class of surfaces that can be handled are all parametric C 2 surfaces. All the algorithms are related by theorems from approximation theory which give information about the maximum deviation an approximation to a surface can have if bounds on partial derivatives are known. We generalize these theorems to work with parametric geometry, and we also show how to obtain the necessary bounds.