Fundamentals of computer aided geometric design
Fundamentals of computer aided geometric design
A new approach to the surface intersection problem
Computer Aided Geometric Design
Differential geometry of intersection curves of two surfaces
Computer Aided Geometric Design
Topological and geometric properties of interval solid models
Graphical Models
Perspectives on Enclosure Methods
Perspectives on Enclosure Methods
Shape Interrogation for Computer Aided Design and Manufacturing
Shape Interrogation for Computer Aided Design and Manufacturing
Computing rigorous bounds on the solution of an initial value problem for an ordinary differential equation
Analysis of validated error bounds of surface-to-surface intersection
Computer-Aided Design
Computer Aided Geometric Design
Proceedings of the 14th ACM Symposium on Solid and Physical Modeling
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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.