SIGGRAPH '86 Proceedings of the 13th annual conference on Computer graphics and interactive techniques
Adaptive forward differencing for rendering curves and surfaces
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Scan line methods for displaying parametrically defined surfaces
Communications of the ACM
Smoothly shaded renderings of polyhedral objects on raster displays
SIGGRAPH '79 Proceedings of the 6th annual conference on Computer graphics and interactive techniques
SURFACES FOR COMPUTER-AIDED DESIGN OF SPACE FORMS
SURFACES FOR COMPUTER-AIDED DESIGN OF SPACE FORMS
Adaptive forward differencing for rendering curves and surfaces
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
Rendering cubic curves and surfaces with integer adaptive forward differencing
SIGGRAPH '89 Proceedings of the 16th annual conference on Computer graphics and interactive techniques
Interactive display of large-scale NURBS models
I3D '95 Proceedings of the 1995 symposium on Interactive 3D graphics
Adaptive isocurve-based rendering for freeform surfaces
ACM Transactions on Graphics (TOG)
Accelerated walkthrough of large spline models
Proceedings of the 1997 symposium on Interactive 3D graphics
Texture mapping 3D models of real-world scenes
ACM Computing Surveys (CSUR)
Quadratic Bezier triangles as drawing primitives
HWWS '98 Proceedings of the ACM SIGGRAPH/EUROGRAPHICS workshop on Graphics hardware
Rendering trimmed NURBS with adaptive forward differencing
SIGGRAPH '88 Proceedings of the 15th annual conference on Computer graphics and interactive techniques
Interactive Display of Large NURBS Models
IEEE Transactions on Visualization and Computer Graphics
New 3d graphics rendering engine architecture for direct tessellation of spline surfaces
ICCS'05 Proceedings of the 5th international conference on Computational Science - Volume Part II
Extensions for 3d graphics rendering engine used for direct tessellation of spline surfaces
ICCS'06 Proceedings of the 6th international conference on Computational Science - Volume Part II
EGGH'90 Proceedings of the Fifth Eurographics conference on Advances in Computer Graphics Hardware: rendering, ray tracing and visualization systems
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We present several techniques for implementing Phong shading in hardware for bicubic patches. Patches are shaded, not by subdividing into polygons, but by drawing many curves close together leaving no pixel gaps. Each curve is drawn using an adaptive forward difference algorithm which generates the coordinates as well as the shading parameters as cubic functions incrementally evaluated along the curve. The forward difference step size is adaptively adjusted so that it generates approximately one pixel along the curve per forward difference step. The hardware implements Phong shading directly with a surprisingly simple configuration built from general purpose compute units and look-up tables. Two new methods are presented for deriving bicubic approximations to the shading parameters over a bicubic patch. One method uses two Coons patches to approximate the unnormalized N·L, and N·H, and a third Coons patch for N·N, where N is the surface normal, L is the light direction, and H is the direction of maximum highlight. In this case the hardware performs the normalization per pixel. The second method uses two Coons patches to approximate the normalized dot products N·L, and N·H. The method is suitable for both hardware and software implementations.