The approximation power of moving least-squares
Mathematics of Computation
Smooth surface reconstruction via natural neighbour interpolation of distance functions
Proceedings of the sixteenth annual symposium on Computational geometry
Pointshop 3D: an interactive system for point-based surface editing
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
Computing and Rendering Point Set Surfaces
IEEE Transactions on Visualization and Computer Graphics
Shape modeling with point-sampled geometry
ACM SIGGRAPH 2003 Papers
Approximating Bounded, Non-Orientable Surfaces from Points
SMI '04 Proceedings of the Shape Modeling International 2004
ACM SIGGRAPH 2004 Papers
Interpolating and approximating implicit surfaces from polygon soup
ACM SIGGRAPH 2004 Papers
Provably good moving least squares
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
ACM SIGGRAPH 2006 Papers
An adaptive MLS surface for reconstruction with guarantees
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
On normals and projection operators for surfaces defined by point sets
SPBG'04 Proceedings of the First Eurographics conference on Point-Based Graphics
Interactive ray tracing of point-based models
SPBG'05 Proceedings of the Second Eurographics / IEEE VGTC conference on Point-Based Graphics
A sampling theorem for MLS surfaces
SPBG'05 Proceedings of the Second Eurographics / IEEE VGTC conference on Point-Based Graphics
Multiresolution point-set surfaces
GI '08 Proceedings of graphics interface 2008
Multi-level partition of unity algebraic point set surfaces
Journal of Computer Science and Technology
A height-difference-based ray tracing of point models
Proceedings of the 10th International Conference on Virtual Reality Continuum and Its Applications in Industry
A survey of methods for moving least squares surfaces
SPBG'08 Proceedings of the Fifth Eurographics / IEEE VGTC conference on Point-Based Graphics
Journal of Scientific Computing
Generalized Hermitian Radial Basis Functions Implicits from polygonal mesh constraints
The Visual Computer: International Journal of Computer Graphics
Hi-index | 0.01 |
Point set surfaces define a (typically) manifold surface from a set of scattered points. The definition involves weighted centroids and a gradient field. The data points are interpolated if singular weight functions are used to define the centroids. While this way of deriving an interpolatory scheme appears natural, we show that it has two deficiencies: Convexity of the input is not preserved and the extension to Hermite data is numerically unstable. We present a generalization of the standard scheme that we call Hermite point set surface. It allows interpolating, given normal constraints in a stable way. It also yields an intuitive parameter for shape control and preserves convexity in most situations. The analysis of derivatives also leads to a more natural way to define normals, in case they are not supplied with the point data. We conclude by comparing to similar surface definitions.