Generalized scanning technique for display of parametrically defined surfaces
IEEE Computer Graphics and Applications
Surface algorithms using bounds on derivatives
Computer Aided Geometric Design
Real-time rendering of trimmed surfaces
SIGGRAPH '89 Proceedings of the 16th annual conference on Computer graphics and interactive techniques
Ray tracing trimmed rational surface patches
SIGGRAPH '90 Proceedings of the 17th annual conference on Computer graphics and interactive techniques
Curves and surfaces for computer aided geometric design (3rd ed.): a practical guide
Curves and surfaces for computer aided geometric design (3rd ed.): a practical guide
Tessellation of trimmed NURB surfaces
Computer Aided Geometric Design
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A trimmed parametric surface is mainly composed of a surface together with trimming curves lying in D, the parametric space of the surface. By investigating the interrelation between surface tessellation and trimming curve approximation, we point out some problems on trimming curve approximation in existing trimmed surface tessellation algorithms. Counter examples are presented to show that a valid approximation of trimming curves in D together with the refinement imposed by surface tessellation does not necessarily generate a valid linear approximation in 3D space. To assure the 3D derivation tolerance, we propose two novel step-length estimation methods such that a piecewise linear interpolant of the trimming curve based on the proposed step lengths will result in a valid linear approximation in 3D space. The first method exploits the triangle inequality and takes the derivation tolerance in 3D space into account to compute the effective step length. Our second method is based on segmenting the trimming curve into subcurves first and then approximates each subcurve according to the derivation tolerance in 3D space. Moreover, several empirical tests are given to demonstrate the correctness of our step length estimations.