Robust interval algorithm for curve intersections

Topological and Geometric Properties of Interval Solid Models

“…Pick points We shall see in the next section that such a solid can be constructed using interval surface intersection algorithms [14,15]. Preliminary to this construction is the following set of conditions on B and V (see Fig.…”

“…The required curve and surface intersection algorithms using interval arithmetic were presented in [14,15]. However, topological issues involved in interval solid modeling were not studied in these papers [10,11,14,15]. As an interval boundary model defines a family of infinitely many boundaries, maintaining topological invariance of such boundaries is, by no means, a trivial problem.…”

“…Hu et al [10,11] introduced a method for robust solid modeling using interval arithmetic and developed a data structure and Boolean operations for manifold and nonmanifold interval boundary models. The required curve and surface intersection algorithms using interval arithmetic were presented in [14,15]. However, topological issues involved in interval solid modeling were not studied in these papers [10,11,14,15].…”

Topologically Reliable Approximation of Trimmed Polynomial Surface Patches

“…These systems will frequently fail as a result of the limited precision of geometrically crucial computations, which is inherent to the internal representation of floating point numbers. In our approach, we employ a new representation scheme based on interval parametric curves and surfaces [20][21][22][23]28] implemented in rounded interval arithmetic (RIA) [1,30] which ensures numerical robustness and provides results with verifiable numeric certainty. For example, we have developed a robust interval Delaunay test [9] to overcome serious problems such as degeneracy, nonconformance, and topologically invalid triangulations in the conventional Bowyer-Watson algorithm operating in FPA.…”

Problem Reduction to Parameter Space

“…A subdivision based approach, using the Berstein-B ezier basis functions, has been used in implementing the examples shown in this paper 5,6,12]. The basic approach is similar to conventional techniques in computing the solutions of multivariate equations 17,21,25] …”