Solid Modeling

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Tracing Surface Intersection with a Validated ODE System Solver
(The Eurographics Association, 2004) Mukundan, H.; Ko, K. H.; Maekawa, T.; Sakkalis, T.; Patrikalakis, N. M.; Gershon Elber and Nicholas Patrikalakis and Pere Brunet
This paper presents a robust method for tracing intersection curve segments between continuous rational parametric surfaces, typically rational polynomial parametric surface patches. The tracing procedure is based on a validated ordinary differential equation (ODE) system solver which can be applied, without substantial overhead, for transversal as well as tangential intersections. Application of the validated ODE solver in the context of eliminating the phenomenon of straying and looping is discussed. In addition, we develop a method to fulfill the condition of a continuous gap-free boundary with a definite numerically verified upper bound for the intersection curve error in parameter space and is further mapped to an upper bound for the intersection curve error in 3D model space, which assists in defining well-formed boundary representation models of complex 3D solids.