Iterative solution of nonlinear equations in several variables
Iterative solution of nonlinear equations in several variables
A Generalization of Algebraic Surface Drawing
ACM Transactions on Graphics (TOG)
An improved illumination model for shaded display
Communications of the ACM
Computational Geometry for Design and Manufacture
Computational Geometry for Design and Manufacture
Ray tracing algebraic surfaces
SIGGRAPH '83 Proceedings of the 10th annual conference on Computer graphics and interactive techniques
Ray tracing parametric patches
SIGGRAPH '82 Proceedings of the 9th annual conference on Computer graphics and interactive techniques
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 '86 Proceedings of the 13th annual conference on Computer graphics and interactive techniques
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
Ray tracing complex models containing surface tessellations
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Discrete simulation of NC machining
SCG '87 Proceedings of the third annual symposium on Computational geometry
Accurate color reproduction for computer graphics applications
SIGGRAPH '89 Proceedings of the 16th annual conference on Computer graphics and interactive techniques
SIGGRAPH '89 Proceedings of the 16th annual conference on Computer graphics and interactive techniques
Ray tracing trimmed rational surface patches
SIGGRAPH '90 Proceedings of the 17th annual conference on Computer graphics and interactive techniques
Rendering curves and surfaces with hybrid subdivision and forward differencing
ACM Transactions on Graphics (TOG)
Interval analysis for computer graphics
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Illumination from curved reflectors
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
An updated cross-indexed guide to the ray-tracing literature
ACM SIGGRAPH Computer Graphics
Interval methods for multi-point collisions between time-dependent curved surfaces
SIGGRAPH '93 Proceedings of the 20th annual conference on Computer graphics and interactive techniques
Ray-Tracing Triangular Trimmed Free-Form Surfaces
IEEE Transactions on Visualization and Computer Graphics
IEEE Computer Graphics and Applications
Computer graphics for water modeling and rendering: a survey
Future Generation Computer Systems - Special issue: Computer graphics and geometric modeling
Robust and numerically stable Bézier clipping method for ray tracing NURBS surfaces
Proceedings of the 21st spring conference on Computer graphics
Direct evaluation of NURBS curves and surfaces on the GPU
Proceedings of the 2007 ACM symposium on Solid and physical modeling
Performing efficient NURBS modeling operations on the GPU
Proceedings of the 2008 ACM symposium on Solid and physical modeling
Direct trimming of NURBS surfaces on the GPU
ACM SIGGRAPH 2009 papers
Computation of singularities and intersections of offsets of planar curves
Computer Aided Geometric Design
A new method for speeding up ray tracing NURBS surfaces
Computers and Graphics
Optimized GPU evaluation of arbitrary degree NURBS curves and surfaces
Computer-Aided Design
Computer graphics for water modeling and rendering: a survey
Future Generation Computer Systems
SIAM Journal on Scientific Computing
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
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 second order geometric method for ray/parametric surface intersection
Computer Aided Geometric Design
| Hi-index | 0.01 |
A new method for ray tracing parametric surfaces is presented. The new algorithm solves the ray surface intersection directly using multivariate Newton iteration. This provides enough generality to render surfaces which could not be ray traced using existing methods. To overcome the problem of finding a starting point for the Newton algorithm, techniques from Interval Analysis are employed. The results are presented in terms of solving a general nonlinear system of equations f(x)= 0, and thus can be extended to a large class of problems which arise in computer graphics.