ARTSccelerated ray-tracing system
IEEE Computer Graphics and Applications
SIGGRAPH '86 Proceedings of the 13th annual conference on Computer graphics and interactive techniques
Efficient algorithms for 3D scan-conversion of parametric curves, surfaces, and volumes
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Voxel space automata: modeling with stochastic growth processes in voxel space
SIGGRAPH '89 Proceedings of the 16th annual conference on Computer graphics and interactive techniques
Guaranteed ray intersections with implicit surfaces
SIGGRAPH '89 Proceedings of the 16th annual conference on Computer graphics and interactive techniques
What every computer scientist should know about floating-point arithmetic
ACM Computing Surveys (CSUR)
Interval analysis for computer graphics
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
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
Defining and rendering of textured objects through the use of exponential functions
CVGIP: Graphical Models and Image Processing
An improved illumination model for shaded display
Communications of the ACM
IEEE Computer Graphics and Applications
Rasterizing Algebraic Curves and Surfaces
IEEE Computer Graphics and Applications
Interval Methods for Ray Casting Implicit Surfaces with Affine Arithmetic
SIBGRAPI '99 Proceedings of the XII Brazilian Symposium on Computer Graphics and Image Processing
Novel techniques for robust voxelization and visualization of implicit surfaces
Graphical Models - Volume modeling
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Methods and Applications of Interval Analysis (SIAM Studies in Applied and Numerical Mathematics) (Siam Studies in Applied Mathematics, 2.)
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
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A new approach to ray tracing implicit surfaces based on recursive space subdivision is presented in this paper. Interval arithmetic, already used to calculate intersections in ray tracing and ray casting (numerically or subdividing 1D or 2D spaces), is now used here to implement a ray tracing based on reliable rays traversals into a potentially infinite octree-like subdivided space, eliminating explicit intersections. Novel, robust and efficient algorithms for ray voxelization and BSP octant ordering are used to recursively traverse rays through the space. Implicit surfaces are robustly voxelized and hierarchically stored into an octree to a certain given level. During rendering, the subdivision based voxelization of surfaces and rays continues further down until a resolution near the discrete domain of the floating point numbers is acquired. To guarantee robustness of the ray voxelization, interval arithmetic with calculations performed under appropriate rounding modes in Pentium-4 x87 and SSE2 FPUs respectively is applied. The major advantage is that the traversal algorithm is guaranteed to find reliable intersections between the rays and the scene without any explicit intersection calculation, solving a known precision problem of the ray traversal in a previous approach, used here for comparison. The precision of the traversal can be arbitrarily increased within the limitation of the floating point representation.