Practical methods of optimization; (2nd ed.)
Practical methods of optimization; (2nd ed.)
Curvature approximation for triangulated surfaces
Geometric modelling
Experiments in Curvature-Based Segmentation of Range Data
IEEE Transactions on Pattern Analysis and Machine Intelligence
Umbilics and lines of curvature for shape interrogation
Computer Aided Geometric Design
New feature points based on geometric invariants for 3D image registration
International Journal of Computer Vision
Proceedings of the 24th annual conference on Computer graphics and interactive techniques
Implicit fairing of irregular meshes using diffusion and curvature flow
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
Line direction matters: an argument for the use of principal directions in 3D line drawings
NPAR '00 Proceedings of the 1st international symposium on Non-photorealistic animation and rendering
Surfels: surface elements as rendering primitives
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
QSplat: a multiresolution point rendering system for large meshes
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
On surface normal and Gaussian curvature approximations given data sampled from a smooth surface
Computer Aided Geometric Design
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Spectral processing of point-sampled geometry
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Pointshop 3D: an interactive system for point-based surface editing
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
Shape Interrogation for Computer Aided Design and Manufacturing
Shape Interrogation for Computer Aided Design and Manufacturing
Proceedings of the conference on Visualization '01
Efficient simplification of point-sampled surfaces
Proceedings of the conference on Visualization '02
Intrinsic Surface Properties from Surface Triangulation
ECCV '92 Proceedings of the Second European Conference on Computer Vision
Restricted delaunay triangulations and normal cycle
Proceedings of the nineteenth annual symposium on Computational geometry
Approximation with Active B-Spline Curves and Surfaces
PG '02 Proceedings of the 10th Pacific Conference on Computer Graphics and Applications
Estimating the tensor of curvature of a surface from a polyhedral approximation
ICCV '95 Proceedings of the Fifth International Conference on Computer Vision
Shape modeling with point-sampled geometry
ACM SIGGRAPH 2003 Papers
Suggestive contours for conveying shape
ACM SIGGRAPH 2003 Papers
Progressive point set surfaces
ACM Transactions on Graphics (TOG)
A novel cubic-order algorithm for approximating principal direction vectors
ACM Transactions on Graphics (TOG)
ACM SIGGRAPH 2004 Papers
Estimating Curvatures and Their Derivatives on Triangle Meshes
3DPVT '04 Proceedings of the 3D Data Processing, Visualization, and Transmission, 2nd International Symposium
Topology and Geometry of Unorganized Point Clouds
3DPVT '04 Proceedings of the 3D Data Processing, Visualization, and Transmission, 2nd International Symposium
Estimating differential quantities using polynomial fitting of osculating jets
Computer Aided Geometric Design
Proceedings of the 14th IEEE Visualization 2003 (VIS'03)
Robust Alignment of Multi-view Range Data to CAD Model
SMI '06 Proceedings of the IEEE International Conference on Shape Modeling and Applications 2006
Fitting B-spline curves to point clouds by curvature-based squared distance minimization
ACM Transactions on Graphics (TOG)
Curvature estimation of point-sampled surfaces and its applications
ICCSA'05 Proceedings of the 2005 international conference on Computational Science and Its Applications - Volume Part III
Estimating the principal curvatures and the Darboux frame from real 3-D range data
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Multiresolution point-set surfaces
GI '08 Proceedings of graphics interface 2008
Simultaneous registration of multiple views with markers
Computer-Aided Design
Reconstructing a mesh from a point cloud by using a moving parabolic approximation
GMP'08 Proceedings of the 5th international conference on Advances in geometric modeling and processing
Adaptive surface reconstruction based on implicit PHT-splines
Proceedings of the 14th ACM Symposium on Solid and Physical Modeling
Parallel and adaptive surface reconstruction based on implicit PHT-splines
Computer Aided Geometric Design
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Using moving parabolic approximations (MPA), we reconstruct an improved point-based model of curve or surface represented as an unorganized point cloud, while also estimating the differential properties of the underlying smooth manifold. We present optimization algorithms to solve these MPA models, and examples which show that our reconstructions of the curve or surface, and estimates of the normals and curvature information, are accurate for precise point clouds and robust in the presence of noise.