Procedural elements for computer graphics
Procedural elements for computer graphics
ARTSccelerated ray-tracing system
IEEE Computer Graphics and Applications
Ray tracing parametric surface patches utilizing numerical techniques and ray coherence
SIGGRAPH '86 Proceedings of the 13th annual conference on Computer graphics and interactive techniques
Fast ray tracing by ray classification
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Ray tracing complex models containing surface tessellations
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Real-time rendering of trimmed surfaces
SIGGRAPH '89 Proceedings of the 16th annual conference on Computer graphics and interactive techniques
Curves and surfaces for computer aided geometric design
Curves and surfaces for computer aided geometric design
Ray tracing parametric surfaces by subdivision in viewing plane
Theory and practice of geometric modeling
Ray tracing trimmed rational surface patches
SIGGRAPH '90 Proceedings of the 17th annual conference on Computer graphics and interactive techniques
Curve intersection using Be´zier clipping
Computer-Aided Design - Special Issue: Be´zier Techniques
On ray tracing parametric surfaces
SIGGRAPH '85 Proceedings of the 12th annual conference on Computer graphics and interactive techniques
An improved illumination model for shaded display
Communications of the ACM
IEEE Computer Graphics and Applications
IEEE Computer Graphics and Applications
Ray tracing parametric patches
SIGGRAPH '82 Proceedings of the 9th annual conference on Computer graphics and interactive techniques
Color image quantization for frame buffer display
SIGGRAPH '82 Proceedings of the 9th annual conference on Computer graphics and interactive techniques
Ray Tracing Free-Form B-Spline Surfaces
IEEE Computer Graphics and Applications
Rational B-Splines for Curve and Surface Representation
IEEE Computer Graphics and Applications
Ray-Tracing Triangular Trimmed Free-Form Surfaces
IEEE Transactions on Visualization and Computer Graphics
Robust and numerically stable Bézier clipping method for ray tracing NURBS surfaces
Proceedings of the 21st spring conference on Computer graphics
Finite Elements in Analysis and Design
A second order geometric method for ray/parametric surface intersection
Computer Aided Geometric Design
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In this paper, a new method for computing the intersection of a ray and a NURBS surface is presented. The method is based on Newton iteration for a system of nonlinear equations, but its convergence is accelerated by using the polynomial extrapolation. Additionally, a ray is defined to be the intersection of two planes, which are usually non-orthogonal, so that theoperations are significantly reduced. A trapezoid prism is adopted for the bounding box enclosing the patch as tightly as possible. It can be used both for getting a good start point for the Newton iteration and for efficiently detecting whether a ray intersects a patch. The method proposed for speeding up ray tracing NURBS surfaces can reduce both the iteration steps and arithmetic operations, thus much CPU time is saved. The new method is faster than the previous methods for which published performance data allow reliable comparison. The acceleration techniques with extrapolation presented for solution to a system of nonlinear equations can also be used to speed up tracing the intersection of two parametric surfaces as well as others that need Newton iteration.