Scan line methods for displaying parametrically defined surfaces
Communications of the ACM
Models of light reflection for computer synthesized pictures
SIGGRAPH '77 Proceedings of the 4th annual conference on Computer graphics and interactive techniques
A subdivision algorithm for computer display of curved surfaces.
A subdivision algorithm for computer display of curved surfaces.
Computer display of curved surfaces.
Computer display of curved surfaces.
Accurate triangulations of deformed, intersecting surfaces
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Geometric collisions for time-dependent parametric surfaces
SIGGRAPH '90 Proceedings of the 17th annual conference on Computer graphics and interactive techniques
Drawing antialiased cubic spline curves
ACM Transactions on Graphics (TOG)
Integer forward differencing of cubic polynomials: analysis and algorithms
ACM Transactions on Graphics (TOG)
Rendering curves and surfaces with hybrid subdivision and forward differencing
ACM Transactions on Graphics (TOG)
Interactive manipulation and display of surfaces in four dimensions
I3D '92 Proceedings of the 1992 symposium on Interactive 3D graphics
Spatial partitioning of solids for solid freeform fabrication
SMA '97 Proceedings of the fourth ACM symposium on Solid modeling and applications
Semi-uniform, 2-different tessellation of triangular parametric surfaces
ISVC'10 Proceedings of the 6th international conference on Advances in visual computing - Volume Part I
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A scanline algorithm is described which renders bicubic patches directly from the parametric description without producing a polygonal approximation. The algorithm is partially based on earlier work by Whitted. A primitive object, called a “curved-edge polygon”, is defined, and an algorithm for breaking down a bicubic patch into the primitive objects is described. A general surface intersection method is employed to provide a robust silhouette edge detector. Shades are computed by calculating a cubic approximation to the normal surface and performing either a cubic or a linear interpolation of the bounding edge normals across the scanline. Subdivision of parametric surfaces is used to reduce the complexity of the surfaces being rendered, providing dramatic improvement in the results of both the silhouette detector and the shading methods.