Epsilon geometry: building robust algorithms from imprecise computations
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
Computing the Aspect Graph for Line Drawings of Polyhedral Objects
IEEE Transactions on Pattern Analysis and Machine Intelligence
Adaptive mesh generation for global diffuse illumination
SIGGRAPH '90 Proceedings of the 17th 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
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
Computing the antipenumbra of an area light source
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Discontinuity Meshing for Accurate Radiosity
IEEE Computer Graphics and Applications
Fast object-precision shadow generation for area light sources using BSP trees
I3D '92 Proceedings of the 1992 symposium on Interactive 3D graphics
Visibility computations in densely occluded polyhedral environments
Visibility computations in densely occluded polyhedral environments
A fast shadow algorithm for area light sources using backprojection
SIGGRAPH '94 Proceedings of the 21st annual conference on Computer graphics and interactive techniques
Fast computation of shadow boundaries using spatial coherence and backprojections
SIGGRAPH '94 Proceedings of the 21st annual conference on Computer graphics and interactive techniques
The visibility skeleton: a powerful and efficient multi-purpose global visibility tool
Proceedings of the 24th annual conference on Computer graphics and interactive techniques
Fast calculation of soft shadow textures using convolution
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
Fast and accurate hierarchical radiosity using global visibility
ACM Transactions on Graphics (TOG)
Radiance interpolants for accelerated bounded-error ray tracing
ACM Transactions on Graphics (TOG)
Efficient image-based methods for rendering soft shadows
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Hidden surface removal using polygon area sorting
SIGGRAPH '77 Proceedings of the 4th annual conference on Computer graphics and interactive techniques
Shadow algorithms for computer graphics
SIGGRAPH '77 Proceedings of the 4th annual conference on Computer graphics and interactive techniques
Guaranteed Occlusion and Visibility in Cluster Hierarchical Radiosity
Proceedings of the Eurographics Workshop on Rendering Techniques 2000
Casting curved shadows on curved surfaces
SIGGRAPH '78 Proceedings of the 5th annual conference on Computer graphics and interactive techniques
Combining edges and points for interactive high-quality rendering
ACM SIGGRAPH 2003 Papers
An upper bound on the average size of silhouettes
Proceedings of the twenty-second annual symposium on Computational geometry
ACM SIGGRAPH 2006 Papers
Visibility maps of segments and triangles in 3D
Computational Geometry: Theory and Applications
Technical strategies for massive model visualization
Proceedings of the 2008 ACM symposium on Solid and physical modeling
Massive model visualization techniques: course notes
ACM SIGGRAPH 2008 classes
On the Size of the 3D Visibility Skeleton: Experimental Results
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
On the degree of standard geometric predicates for line transversals in 3D
Computational Geometry: Theory and Applications
Adaptive global visibility sampling
ACM SIGGRAPH 2009 papers
Multirobot rendezvous with visibility sensors in nonconvex environments
IEEE Transactions on Robotics
ACM SIGGRAPH 2009 Courses
Merging and smoothing machining boundaries on cutter location surfaces
Proceedings of the 14th ACM Symposium on Solid and Physical Modeling
Combining higher-order wavelets and discontinuity meshing: a compact representation for radiosity
EGSR'04 Proceedings of the Fifteenth Eurographics conference on Rendering Techniques
FastV: from-point visibility culling on complex models
EGSR'09 Proceedings of the Twentieth Eurographics conference on Rendering
Real-time rendering of massive unstructured raw point clouds using screen-space operators
VAST'11 Proceedings of the 12th International conference on Virtual Reality, Archaeology and Cultural Heritage
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Analytic visibility algorithms, for example methods which compute a subdivided mesh to represent shadows, are notoriously unrobust and hard to use in practice. We present a new method based on a generalized definition of extremal stabbing lines, which are the extremities of shadow boundaries. We treat scenes containing multiple edges or vertices in degenerate configurations, (e.g., collinear or coplanar). We introduce a robust ε method to determine whether each generalized extremal stabbing line is blocked, or is touched by these scene elements, and thus added to the line's generators. We develop robust blocker predicates for polygons which are smaller than ε. For larger ε values, small shadow features merge and eventually disappear. We can thus robustly connect generalized extremal stabbing lines in degenerate scenes to form shadow boundaries. We show that our approach is consistent, and that shadow boundary connectivity is preserved when features merge. We have implemented our algorithm, and show that we can robustly compute analytic shadow boundaries to the precision of our chosen ε threshold for non-trivial models, containing numerous degeneracies.