A Generalization of Algebraic Surface Drawing
ACM Transactions on Graphics (TOG)
Numerical Methods, Software and Analysis
Numerical Methods, Software and Analysis
Computational Geometry for Design and Manufacture
Computational Geometry for Design and Manufacture
Ray tracing algebraic surfaces
SIGGRAPH '83 Proceedings of the 10th annual conference on Computer graphics and interactive techniques
Ray tracing parametric patches
SIGGRAPH '82 Proceedings of the 9th annual conference on Computer graphics and interactive techniques
Implicit and parametric curves and surfaces for computer aided geometric design
Implicit and parametric curves and surfaces for computer aided geometric design
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
SIGGRAPH '86 Proceedings of the 13th annual conference on Computer graphics and interactive techniques
Ray tracing on a connection machine
ICS '88 Proceedings of the 2nd international conference on Supercomputing
An updated cross-indexed guide to the ray-tracing literature
ACM SIGGRAPH Computer Graphics
Creation and smooth-shading of Steiner patch tessellations
ACM '86 Proceedings of 1986 ACM Fall joint computer conference
On ray tracing parametric surfaces
SIGGRAPH '85 Proceedings of the 12th annual conference on Computer graphics and interactive techniques
Direct ray tracing of phong tessellation
EGSR'11 Proceedings of the Twenty-second Eurographics conference on Rendering
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Steiner patches are triangular surface patches for which the Cartesian coordinates of points on the patch are defined parametrically by quadratic polynomial functions of two variables. It has recently been shown that it is possible to express a Steiner patch in an implicit equation which is a degree four polynomial in x,y,z. Furthermore, the parameters of a point known to be on the surface can be computed as rational polynomial functions of x,y,z. These findings lead to a straightforward algorithm for ray tracing Steiner patches in which the ray intersection equation is a degree four polynomial in the parameter of the ray. The algorithm presented represents a major simplification over existing techniques for ray tracing free-form surface patches.