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IEEE Computer Graphics and Applications
Marching cubes: A high resolution 3D surface construction algorithm
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Applications of surface networks to sampling problems in computer graphics
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A Generalization of Algebraic Surface Drawing
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VVS '90 Proceedings of the 1990 workshop on Volume visualization
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ACM Transactions on Graphics (TOG)
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VVS '94 Proceedings of the 1994 symposium on Volume visualization
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ACM Transactions on Graphics (TOG)
IEEE Computer Graphics and Applications
Adaptive Polygonalization of Implicitly Defined Surfaces
IEEE Computer Graphics and Applications
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IEEE Computer Graphics and Applications
Interval arithmetic and interval analysis: an introduction
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VIS '92 Proceedings of the 3rd conference on Visualization '92
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GRAPHITE '05 Proceedings of the 3rd international conference on Computer graphics and interactive techniques in Australasia and South East Asia
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SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
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ICCS '07 Proceedings of the 7th international conference on Computational Science, Part II
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ACM SIGGRAPH ASIA 2008 courses
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PPAM'07 Proceedings of the 7th international conference on Parallel processing and applied mathematics
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CGI'06 Proceedings of the 24th international conference on Advances in Computer Graphics
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VG'05 Proceedings of the Fourth Eurographics / IEEE VGTC conference on Volume Graphics
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In this paper, we present a robust and mathematically sound ray-intersection algorithm for implicit surfaces. The algorithm is guaranteed to numerically find the nearest intersection of the surface with a ray, and is guaranteed not to miss fine features of the surface. It does not require fine tuning or human choice of interactive parameters. Instead, it requires two upper bounds: "L" that limits the net rate of change of the implicit surface function f(x,y,z) and "G" that limits the rate of change of the gradient. We refer to an implicit surface with these rate limits as an "LG-implicit surface."Existing schemes to intersect a ray with an implicit surface have typically been guaranteed to work only for a limited set of implicit functions, such as quadric surfaces or polynomials, or else have been ad-hoc and have not been guaranteed to work. Our technique significantly extends the ability to intersect rays with implicit surfaces in a guaranteed fashion.