Interval and Affine Arithmetic for Surface Location of Power— and Bernstein—Form Polynomials

Abstract

This paper describes a problem of interest in CSG modelling, namely the location of implicit polynomial surfaces in space. It is common for surfaces defined by implicits to be located using interval arithmetic. However, the method only gives conservative bounds for the values of the function inside a region of interest. This paper gives two possible ways of producing tighter bounds. One involves using a Bernstein–form representation of the implicit polynomials used as input to the method. The other fine–tunes the method itself by employing careful use of affine arithmetic—a more sophisticated version of interval arithmetic. As both methods contribute significant improvements, we speculate about combining the two into a fast and accurate method for surface location.