Scan line methods for displaying parametrically defined surfaces
Communications of the ACM
An improved illumination model for shaded display
Communications of the ACM
Simulation of wrinkled surfaces
SIGGRAPH '78 Proceedings of the 5th annual conference on Computer graphics and interactive techniques
A 3-dimensional representation for fast rendering of complex scenes
SIGGRAPH '80 Proceedings of the 7th 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.
Ray tracing objects defined by sweeping planar cubic splines
ACM Transactions on Graphics (TOG)
Ray tracing generalized cylinders
ACM Transactions on Graphics (TOG)
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
Trimmed-surface algorithms for the evaluation and interrogation of solid boundary representations
IBM Journal of Research and Development
Ray tracing complex models containing surface tessellations
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
Accurate color reproduction for computer graphics applications
SIGGRAPH '89 Proceedings of the 16th annual conference on Computer graphics and interactive techniques
On Recognizing and Positioning Curved 3-D Objects from Image Contours
IEEE Transactions on Pattern Analysis and Machine Intelligence
Ray tracing trimmed rational surface patches
SIGGRAPH '90 Proceedings of the 17th annual conference on Computer graphics and interactive techniques
An updated cross-indexed guide to the ray-tracing literature
ACM SIGGRAPH Computer Graphics
Solving polynomial systems for curve, surface and solid modeling
SMA '93 Proceedings on the second ACM symposium on Solid modeling and applications
Interactive display of large-scale NURBS models
I3D '95 Proceedings of the 1995 symposium on Interactive 3D graphics
Implicitization using moving curves and surfaces
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
The power of coherence: fast tessellation of surfaces
Proceedings of the twelfth annual symposium on Computational geometry
Accelerated walkthrough of large spline models
Proceedings of the 1997 symposium on Interactive 3D graphics
I3D '99 Proceedings of the 1999 symposium on Interactive 3D graphics
On ray tracing parametric surfaces
SIGGRAPH '85 Proceedings of the 12th annual conference on Computer graphics and interactive techniques
Watertight tessellation using forward differencing
Proceedings of the ACM SIGGRAPH/EUROGRAPHICS workshop on Graphics hardware
Fast computation of the Bezout and Dixon resultant matrices
Journal of Symbolic Computation
Multiresolution rendering by sewing trimmed NURBS surfaces
Proceedings of the seventh ACM symposium on Solid modeling and applications
Computational experiments with resultants for scaled Bernstein polynomials
Mathematical Methods for Curves and Surfaces
Interactive Display of Large NURBS Models
IEEE Transactions on Visualization and Computer Graphics
IEEE Computer Graphics and Applications
Solving Systems of Polynomial Equations
IEEE Computer Graphics and Applications
Elimination and Resultants - Part 1: Elimination and Bivariate Resultants
IEEE Computer Graphics and Applications
Polynomial Discriminants-Part 1: Matrix Magic
IEEE Computer Graphics and Applications
Budget sampling of parametric surface patches
I3D '03 Proceedings of the 2003 symposium on Interactive 3D graphics
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
Global and local deformations of solid primitives
SIGGRAPH '84 Proceedings of the 11th annual conference on Computer graphics and interactive techniques
Ray tracing of Steiner patches
SIGGRAPH '84 Proceedings of the 11th annual conference on Computer graphics and interactive techniques
SIGGRAPH '84 Proceedings of the 11th annual conference on Computer graphics and interactive techniques
A mapping-independent primitive for the triangulation of parametric surfaces
Graphical Models - Special issue on SMI 2002
Applied Numerical Mathematics
SIGGRAPH '05 ACM SIGGRAPH 2005 Courses
High quality rendering using ray tracing and photon mapping
ACM SIGGRAPH 2007 courses
Advanced global illumination using photon mapping
ACM SIGGRAPH 2008 classes
Direct trimming of NURBS surfaces on the GPU
ACM SIGGRAPH 2009 papers
Fast visualization of complex 3D models using displacement mapping
Proceedings of Graphics Interface 2009
A new method for speeding up ray tracing NURBS surfaces
Computers and Graphics
Journal of Computational and Applied Mathematics
Computing exact aspect graphs of curved objects: parametric surfaces
AAAI'90 Proceedings of the eighth National conference on Artificial intelligence - Volume 2
Direct ray tracing of Phong Tessellation
ACM SIGGRAPH ASIA 2010 Sketches
Technical Section: Real-time ray casting of algebraic B-spline surfaces
Computers and Graphics
Planar piecewise algebraic curves
Computer Aided Geometric Design
The Cayley method in computer aided geometric design
Computer Aided Geometric Design
Journal of Computational and Applied Mathematics
Direct ray tracing of phong tessellation
EGSR'11 Proceedings of the Twenty-second Eurographics conference on Rendering
A VLSI chip for ray tracing bicubic patches
EGGH'86 Proceedings of the First Eurographics conference on Advances in Computer Graphics Hardware
Ray tracing rational B-spline patches in VLSI
EGGH'87 Proceedings of the Second Eurographics conference on Advances in Computer Graphics Hardware
An architecture for ray - bezier patch intersection
EGGH'93 Proceedings of the Eighth Eurographics conference on Graphics Hardware
Hybrid ray tracing and path tracing of Bezier surfaces using a mixed hierarchy
Proceedings of the Eighth Indian Conference on Computer Vision, Graphics and Image Processing
A geometric strategy for computing intersections of two spatial parametric curves
The Visual Computer: International Journal of Computer Graphics
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This paper describes an algorithm that uses ray tracing techniques to display bivariate polynomial surface patches. A new intersection algorithm is developed which uses ideas from algebraic geometry to obtain a numerical procedure for finding the intersection of a ray and a patch without subdivision. The algorithm may use complex coordinates for the (u, v)-parameters of the patches. The choice of these coordinates makes the computations more uniform, so that there are fewer special cases to be considered. In particular, the appearance and disappearance of silhouette edges can be handled quite naturally. The uniformity of these techniques may be suitable for implementation on either a general purpose pipelined machine, or on special purpose hardware.