Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
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
Interval analysis for computer graphics
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Introduction to Implicit Surfaces
Introduction to Implicit Surfaces
Implicit linear interval estimations
SCCG '02 Proceedings of the 18th spring conference on Computer graphics
Interval Methods for Ray Casting Implicit Surfaces with Affine Arithmetic
SIBGRAPI '99 Proceedings of the XII Brazilian Symposium on Computer Graphics and Image Processing
Simulation of natural scenes using textured quadric surfaces
SIGGRAPH '84 Proceedings of the 11th annual conference on Computer graphics and interactive techniques
Combining Multiple Inclusion Representations in Numerical Constraint Propagation
ICTAI '04 Proceedings of the 16th IEEE International Conference on Tools with Artificial Intelligence
Isotopic approximation of implicit curves and surfaces
Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Towards more efficient interval analysis: corner forms and a remainder interval newton method
Towards more efficient interval analysis: corner forms and a remainder interval newton method
Ray casting implicit fractal surfaces with reduced affine arithmetic
The Visual Computer: International Journal of Computer Graphics
Implicit Curves and Surfaces: Mathematics, Data Structures and Algorithms
Implicit Curves and Surfaces: Mathematics, Data Structures and Algorithms
Real-Time Ray Tracing of Implicit Surfaces on the GPU
IEEE Transactions on Visualization and Computer Graphics
Verified spatial subdivision of implicit objects using implicit linear interval estimations
Proceedings of the 7th international conference on Curves and Surfaces
Multi-scale space-variant FRep cellular structures
Computer-Aided Design
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Techniques based on interval and affine arithmetic and their modifications are shown to provide reliable function range evaluation for the purposes of surface interrogation. In this paper we present a technique for the reliable interrogation of implicit surfaces using a modification of affine arithmetic called revised affine arithmetic. We extend the range of functions presented in revised affine arithmetic by introducing affine operations for arbitrary functions such as set-theoretic operations with R-functions, blending and conditional operators. The obtained affine forms of arbitrary functions provide faster and tighter function range evaluation. Several case studies for operations using affine forms are presented. The proposed techniques for surface interrogation are tested using ray-surface intersection for ray-tracing and spatial cell enumeration for polygonisation. These applications with our extensions provide fast and reliable rendering of a wide range of arbitrary procedurally defined implicit surfaces (including polynomial surfaces, constructive solids, pseudo-random objects, procedurally defined microstructures, and others). We compare the function range evaluation technique based on extended revised affine arithmetic with other reliable techniques based on interval and affine arithmetic to show that our technique provides the fastest and tightest function range evaluation for fast and reliable interrogation of procedurally defined implicit surfaces.