On k-hulls and related problems
SIAM Journal on Computing
Hierarchical Z-buffer visibility
SIGGRAPH '93 Proceedings of the 20th annual conference on Computer graphics and interactive techniques
Computing depth contours of bivariate point clouds
Computational Statistics & Data Analysis - Special issue on classification
Snap rounding line segments efficiently in two and three dimensions
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Fast computation of generalized Voronoi diagrams using graphics hardware
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
Data structures for mobile data
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Interactive multi-pass programmable shading
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Fast implementation of depth contours using topological sweep
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Hardware-assisted view-dependent map simplification
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
A user-programmable vertex engine
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Near Real-Time CSG Rendering Using Tree Normalization and Geometric Pruning
IEEE Computer Graphics and Applications
A hardware-assisted visibility-ordering algorithm with applications to volume rendering
EGVISSYM'01 Proceedings of the 3rd Joint Eurographics - IEEE TCVG conference on Visualization
Application of the two-sided depth test to CSG rendering
I3D '03 Proceedings of the 2003 symposium on Interactive 3D graphics
Fast computation of database operations using graphics processors
SIGMOD '04 Proceedings of the 2004 ACM SIGMOD international conference on Management of data
Performance evaluation of programmable graphics hardware for image filtering and stereo matching
Proceedings of the ACM symposium on Virtual reality software and technology
Fast computation of database operations using graphics processors
SIGGRAPH '05 ACM SIGGRAPH 2005 Courses
Multi-visibility maps of triangulated terrains
International Journal of Geographical Information Science
Computing terrain multi-visibility maps for a set of view segments using graphics hardware
ICCSA'06 Proceedings of the 6th international conference on Computational Science and Its Applications - Volume Part I
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Given a set of points P in the plane, the location depth of a point u is the minimum number of points of P lying in a closed halfplane defined by a line through u. The set of all points in the plane having location depth at least k is called the depth contour of depth k. In this paper, we present an algorithm that makes extensive use of modern graphics architectures to compute the approximate depth contours of a set of points. The output of our algorithm presents the contours as a coloring of each point with its depth value, as opposed to computing the geometric description of the contour boundary. Our algorithm performs significantly better than currently known implementations, outperforming them by at least one order of magnitude and having a strictly better asymptotic growth rate.