On algebraic surfaces meeting with geometric continuity
On algebraic surfaces meeting with geometric continuity
Comparison of three curve intersection algorithms
Computer-Aided Design
The characterization of parametric surface sections
Computer Vision, Graphics, and Image Processing
On the numerical condition of polynomials in Berstein form
Computer Aided Geometric Design
Algorithms for polynomials in Bernstein form
Computer Aided Geometric Design
Polygonization of implicit surfaces
Computer Aided Geometric Design
Curves and surfaces for computer aided geometric design: a practical guide
Curves and surfaces for computer aided geometric design: a practical guide
Proceedings on Mathematics of surfaces II
Algorithm for algebraic curve intersection
Computer-Aided Design
Blend surfaces for set theoretic volume modelling systems
SIGGRAPH '85 Proceedings of the 12th annual conference on Computer graphics and interactive techniques
Ray tracing algebraic surfaces
SIGGRAPH '83 Proceedings of the 10th annual conference on Computer graphics and interactive techniques
Topologically reliable display of algebraic curves
SIGGRAPH '83 Proceedings of the 10th annual conference on Computer graphics and interactive techniques
Interactive techniques for implicit modeling
I3D '90 Proceedings of the 1990 symposium on Interactive 3D graphics
Integer forward differencing of cubic polynomials: analysis and algorithms
ACM Transactions on Graphics (TOG)
Interval arithmetic recursive subdivision for implicit functions and constructive solid geometry
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Second-order surface analysis using hybrid symbolic and numeric operators
ACM Transactions on Graphics (TOG)
Surfaces: Techniques for Cubic Algebraic Surfaces
IEEE Computer Graphics and Applications
Accurate display of tensor product isosurfaces
VIS '90 Proceedings of the 1st conference on Visualization '90
Visualization of equations in an interactive environment
VIS '91 Proceedings of the 2nd conference on Visualization '91
Point based rendering of non-manifold surfaces with contours
Proceedings of the 2nd international conference on Computer graphics and interactive techniques in Australasia and South East Asia
Real-time GPU rendering of piecewise algebraic surfaces
ACM SIGGRAPH 2006 Papers
Point rendering of non-manifold surfaces with features
Proceedings of the 5th international conference on Computer graphics and interactive techniques in Australia and Southeast Asia
Technical Section: Real-time ray casting of algebraic B-spline surfaces
Computers and Graphics
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A robust algorithm is presented for scan line display of algebraic surfaces of arbitrary degree and topology. The algorithm correctly displays singularities of any complexity, even those missed by ray tracing or polygonization, and (for surfaces of degree less than eight) offers a significant speed improvement over ray tracing. Antialiasing can generally be accomplished very quickly. In addition to its typical function of shaded raster display, the algorithm is particularly adept at quickly plotting silhouette and intersection curves. A practical use for the algorithm is to display boolean combinations of algebraic half spaces, including blend surfaces.A new polynomial basis is introduced, referred to as the Bernstein pyramid polynomial basis, which enhances numerical stability and which simplifies several computations such as scan planesurface intersection and silhouette detection.