The approximation power of moving least-squares
Mathematics of Computation
Pointshop 3D: an interactive system for point-based surface editing
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
Proceedings of the conference on Visualization '01
Proceedings of the conference on Visualization '01
Computing and Rendering Point Set Surfaces
IEEE Transactions on Visualization and Computer Graphics
Ray Tracing Point Set Surfaces
SMI '03 Proceedings of the Shape Modeling International 2003
Approximating and intersecting surfaces from points
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Iso-Splatting: A Point-Based Alternative to Isosurface Visualization
PG '03 Proceedings of the 11th Pacific Conference on Computer Graphics and Applications
Provable surface reconstruction from noisy samples
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
ACM SIGGRAPH 2004 Papers
Interactive Point-Based Isosurface Extraction
VIS '04 Proceedings of the conference on Visualization '04
Robust moving least-squares fitting with sharp features
ACM SIGGRAPH 2005 Papers
An adaptive MLS surface for reconstruction with guarantees
SGP '05 Proceedings of the third Eurographics symposium on Geometry processing
Surface reconstruction from noisy point clouds
SGP '05 Proceedings of the third Eurographics symposium on Geometry processing
Triangulating point set surfaces with bounded error
SGP '05 Proceedings of the third Eurographics symposium on Geometry processing
A survey of point-based techniques in computer graphics
Computers and Graphics
The domain of a point set surface
SPBG'04 Proceedings of the First Eurographics conference on Point-Based Graphics
Surface reconstruction with enriched reproducing kernel particle approximation
SPBG'05 Proceedings of the Second Eurographics / IEEE VGTC conference on Point-Based Graphics
GPU-based rendering of sparse low-degree implicit surfaces
Proceedings of the 4th international conference on Computer graphics and interactive techniques in Australasia and Southeast Asia
Point-based stream surfaces and path surfaces
GI '07 Proceedings of Graphics Interface 2007
Visual Verification and Analysis of Cluster Detection for Molecular Dynamics
IEEE Transactions on Visualization and Computer Graphics
A survey of methods for moving least squares surfaces
SPBG'08 Proceedings of the Fifth Eurographics / IEEE VGTC conference on Point-Based Graphics
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Point-based models are gaining lately considerable attention as an alternative to traditional surface meshes. In this context, Point Set Surfaces (PSS) were proposed as a modeling and rendering method with important topological and approximation properties. However, ray-tracing PSS is computationally expensive. Therefore, we propose an interactive ray-tracing algorithm for PSS implemented completely on commodity graphics hardware. We also exploit the advantages of PSS to propose a novel technique for extracting surfaces directly from volumetric data. This technique is based on the well known predictor-corrector principle from the numerical methods for solving ordinary differential equations. Our technique provides good approximations to surfaces defined by a certain property in the volume, such as iso-surfaces or surfaces located at regions of high gradient magnitude. Also, local details of the surfaces could be manipulated by changing the local polynomial approximation and the smoothing parameters used. Furthermore, the surfaces generated are smooth and low frequency noise is naturally handled.