A review of recent developments in solving ODEs
ACM Computing Surveys (CSUR) - Annals of discrete mathematics, 24
SIGGRAPH '86 Proceedings of the 13th annual conference on Computer graphics and interactive techniques
SIGGRAPH '85 Proceedings of the 12th annual conference on Computer graphics and interactive techniques
Bounding ellipsoids for ray-fractal intersection
SIGGRAPH '85 Proceedings of the 12th annual conference on Computer graphics and interactive techniques
On ray tracing parametric surfaces
SIGGRAPH '85 Proceedings of the 12th annual conference on Computer graphics and interactive techniques
Numerical Initial Value Problems in Ordinary Differential Equations
Numerical Initial Value Problems in Ordinary Differential Equations
New techniques for ray tracing procedurally defined objects
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
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
Principles and applications of pencil tracing
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Ray tracing JELL-OTM Brand Gelatin
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Accurate triangulations of deformed, intersecting surfaces
SIGGRAPH '87 Proceedings of the 14th 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
Ray tracing Jell-O brand gelatin
Communications of the ACM
Ray tracing deterministic 3-D fractals
SIGGRAPH '89 Proceedings of the 16th annual conference on Computer graphics and interactive techniques
Efficient antialiased rendering of 3-D linear fractals
Proceedings of the 18th annual conference on Computer graphics and interactive techniques
Generative modeling: a symbolic system for geometric modeling
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
Interactive Space Deformation with Hardware-Assisted Rendering
IEEE Computer Graphics and Applications
Nonlinear Projection: Using Deformations in 3D Viewing
Computing in Science and Engineering
VG '03 Proceedings of the 2003 Eurographics/IEEE TVCG Workshop on Volume graphics
Displaying voxel-based objects according to their qualitative shape synthesis
VIS '90 Proceedings of the 1st conference on Visualization '90
Ryan: rendering your animation nonlinearly projected
Proceedings of the 3rd international symposium on Non-photorealistic animation and rendering
Nonlinear Perspective Projections and Magic Lenses: 3D View Deformation
IEEE Computer Graphics and Applications
Feature Aligned Volume Manipulation for Illustration and Visualization
IEEE Transactions on Visualization and Computer Graphics
Programmable shaders for deformation rendering
Proceedings of the 22nd ACM SIGGRAPH/EUROGRAPHICS symposium on Graphics hardware
Efficient displacement mapping by image warping
EGWR'99 Proceedings of the 10th Eurographics conference on Rendering
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A collection of new methods for ray tracing differentiable surfaces is developed. The methods are general, and extend the set of "ray-traceable" surfaces suitable for use in geometric modeling. We intersect a ray l = at + b, t > 0 with a parametric surface x = f(u, v), and with implicit surfaces f(x,y,z) = 0. A smooth surface is treated as a deformation of a flat sheet; the intersection problem is converted to a new coordinate system in which the surfaces are flat, and the rays are bent. We develop methods for providing good initial estimates of the parametric intersection values, and a "closeness criterion," to reduce computation. These same criteria help us substitute a set of simpler surfaces for the more complex surface. The parametric method produces the intersection values of u, v, and t. These are suitable for shading calculations and for mapping textures onto the surface; they can also produce the local coordinate frame values, suitable for anisotropic lighting models.