CSG Operations of Arbitrary Primitives with Interval Arithmetic and Real-Time Ray Casting

We apply Knoll et al.'s algorithm [9] to interactively ray-cast constructive solid geometry (CSG) objects of arbitrary primitives represented as implicit functions. Whereas modeling globally with implicit surfaces suffers from a lack of control, implicits are well-suited for arbitrary primitives and can be combined through various operations. The conventional way to represent union and intersection with interval arithmetic (IA) is simply using min and max but other operations such as the product of two forms can be useful in modeling joints between multiple objects. Typical primitives are objects of simple shape, e.g. cubes, cylinders, spheres, etc. Our method handles arbitrary primitives, e.g. superquadrics or non-algebraic implicits. Subdivision and interval arithmetic guarantee robustness whereas GPU ray casting allows for fast and aesthetic rendering. Indeed, ray casting parallelizes efficiently and trivially and thus takes advantage of the continuous increasing computational...

• Type: Conference
• Year: 2010
• Where: DAGSTUHL
• Authors: Younis Hijazi, Aaron Knoll, Mathias Schott, Andrew Kensler, Charles D. Hansen
• Keywords: Arbitrary Primitives, Constructive Solid Geometry, DAGSTUHL 2010, Interval Arithmetic, Software Engineering