Triangular Berstein-Be´zier patches
Computer Aided Geometric Design
Conversion from Be´zier rectangles to Be´zier triangles
Computer-Aided Design
Computer graphics: principles and practice (2nd ed.)
Computer graphics: principles and practice (2nd ed.)
Ray tracing trimmed rational surface patches
SIGGRAPH '90 Proceedings of the 17th annual conference on Computer graphics and interactive techniques
OBBTree: a hierarchical structure for rapid interference detection
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
An efficient surface intersection algorithm based on lower-dimensional formulation
ACM Transactions on Graphics (TOG)
On ray tracing parametric surfaces
SIGGRAPH '85 Proceedings of the 12th annual conference on Computer graphics and interactive techniques
Strip trees: a hierarchical representation for curves
Communications of the ACM
Curves and Surfaces for Computer-Aided Geometric Design: A Practical Code
Curves and Surfaces for Computer-Aided Geometric Design: A Practical Code
Parallel Boxing in B-Spline Intersection
IEEE Computer Graphics and Applications
New techniques for ray tracing procedurally defined objects
SIGGRAPH '83 Proceedings of the 10th annual conference on Computer graphics and interactive techniques
A 3-dimensional representation for fast rendering of complex scenes
SIGGRAPH '80 Proceedings of the 7th annual conference on Computer graphics and interactive techniques
A new method for speeding up ray tracing NURBS surfaces
Computers and Graphics
I3D '99 Proceedings of the 1999 symposium on Interactive 3D graphics
Pixel-shader-based curved triangles
ACM SIGGRAPH 2006 Research posters
SIGGRAPH '05 ACM SIGGRAPH 2005 Courses
A tracing method for parametric Bezier triangular surface/plane intersection
International Journal of Computer Applications in Technology
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This paper presents a new approach to rendering triangular algebraic free-form surfaces. A hierarchical subdivision of the surface with associated tight bounding volumes provides for quick identification of the surface regions likely to be hit by a ray. For each leaf of the hierarchy, an approximation to the corresponding surface region is stored. The approximation is used to compute a good starting point for the iteration, which ensures rapid convergence. Trimming curves are described by a tree of trimming primitives, such as squares, circles, polygons, and free-form curves, combined with Boolean operations. For trimmed surfaces, an irregular adaptive subdivision is constructed to quickly eliminate all parts outside the trimming curve from consideration during rendering. Cost heuristics are introduced to optimize the rendering time further.