Drawing antialiased cubic spline curves
ACM Transactions on Graphics (TOG)
Integer forward differencing of cubic polynomials: analysis and algorithms
ACM Transactions on Graphics (TOG)
Accelerated walkthrough of large spline models
Proceedings of the 1997 symposium on Interactive 3D graphics
Quadratic Bezier triangles as drawing primitives
HWWS '98 Proceedings of the ACM SIGGRAPH/EUROGRAPHICS workshop on Graphics hardware
Scan line methods for displaying parametrically defined surfaces
Communications of the ACM
Simulation of wrinkled surfaces
SIGGRAPH '78 Proceedings of the 5th annual conference on Computer graphics and interactive techniques
Multiresolution rendering by sewing trimmed NURBS surfaces
Proceedings of the seventh ACM symposium on Solid modeling and applications
Budget sampling of parametric surface patches
I3D '03 Proceedings of the 2003 symposium on Interactive 3D graphics
An algorithm and data structure for 3D object synthesis using surface patch intersections
SIGGRAPH '82 Proceedings of the 9th annual conference on Computer graphics and interactive techniques
On display of space filling atomic models in real-time
SIGGRAPH '78 Proceedings of the 5th annual conference on Computer graphics and interactive techniques
Transparency for computer synthesized images
SIGGRAPH '79 Proceedings of the 6th annual conference on Computer graphics and interactive techniques
SIGGRAPH '79 Proceedings of the 6th annual conference on Computer graphics and interactive techniques
A scan line algorithm for displaying parametrically defined surfaces
ACM SIGGRAPH Computer Graphics
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The conventional procedure for generating shaded images of curved surfaces is to approximate each surface element by a mosaic of polygons and to then apply one of several established polygon display algorithms. The method described here extends these polygon based techniques to produce an excellent approximation of bi-cubic parametric surfaces in scan line order. Each surface patch is described in terms of cubic edge curves, including parametric curves on the interior of the patch as well as the patch boundaries. Specifying interior edges has the effect of subdividing the patch and generally results in a more accurate image. The silhouette, approximated by a piecewise cubic interpolant, further divides the patch into front facing and rear facing portions. The edge curves are intersected by successive scanning planes to form the endpoints of scan line segments. Depth and surface normal are linearly interpolated between the endpoint values. Visibility is calculated for each segment by a hybrid priority/z-buffer scheme. Shading is computed using Phong's illumination model with the interpolated surface normal. The algorithm is currently used for display of B-spline surfaces as part of an experimental display processor.