Numerical recipes in C (2nd ed.): the art of scientific computing
Numerical recipes in C (2nd ed.): the art of scientific computing
Interactive multi-resolution modeling on arbitrary meshes
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
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
Reconstruction and representation of 3D objects with radial basis functions
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
Point-based modelling and rendering using radial basis functions
Proceedings of the 1st international conference on Computer graphics and interactive techniques in Australasia and South East Asia
Texture Mapping Using Surface Flattening via Multidimensional Scaling
IEEE Transactions on Visualization and Computer Graphics
Computing and Rendering Point Set Surfaces
IEEE Transactions on Visualization and Computer Graphics
Computational Surface Flattening: A Voxel-Based Approach
IEEE Transactions on Pattern Analysis and Machine Intelligence
Hybrid Geodesics as Optimal Solutions to the Collision-Free Motion Planning Problem
HSCC '01 Proceedings of the 4th International Workshop on Hybrid Systems: Computation and Control
Hierarchical mesh decomposition using fuzzy clustering and cuts
ACM SIGGRAPH 2003 Papers
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
3D Scattered Data Approximation with Adaptive Compactly Supported Radial Basis Functions
SMI '04 Proceedings of the Shape Modeling International 2004
ACM SIGGRAPH 2004 Papers
Energy-minimizing splines in manifolds
ACM SIGGRAPH 2004 Papers
Surface Segmentation Using Geodesic Centroidal Tesselation
3DPVT '04 Proceedings of the 3D Data Processing, Visualization, and Transmission, 2nd International Symposium
Similarity-based surface modelling using geodesic fans
Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Fast exact and approximate geodesics on meshes
ACM SIGGRAPH 2005 Papers
Minimal discrete curves and surfaces
Minimal discrete curves and surfaces
Planning Algorithms
An adaptive MLS surface for reconstruction with guarantees
SGP '05 Proceedings of the third Eurographics symposium on Geometry processing
A variational approach to spline curves on surfaces
Computer Aided Geometric Design - Special issue: Geometric modelling and differential geometry
Point cloud surfaces using geometric proximity graphs
Computers and Graphics
A survey of point-based techniques in computer graphics
Computers and Graphics
On normals and projection operators for surfaces defined by point sets
SPBG'04 Proceedings of the First Eurographics 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
Learning a Self-organizing Map Model on a Riemannian Manifold
Proceedings of the 13th IMA International Conference on Mathematics of Surfaces XIII
Spectral-Driven Isometry-Invariant Matching of 3D Shapes
International Journal of Computer Vision
Defining, contouring, and visualizing scalar functions on point-sampled surfaces
Computer-Aided Design
Graph-based representations of point clouds
Graphical Models
Isometry-invariant matching of point set surfaces
EG 3DOR'08 Proceedings of the 1st Eurographics conference on 3D Object Retrieval
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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We present a technique for computing piecewise linear approximations of geodesics on point set surfaces by minimizing an energy function defined for piecewise linear path. The function considers path length, closeness to the surface for the nodes of the piecewise linear path and for the intermediate line segments. Our method is robust with respect to noise and outliers. In order to avoid local minima, a good initial piecewise linear approximation of a geodesic is provided by Dijkstra's algorithm that is applied to a proximity graph constructed over the point set. As the proximity graph we use a sphere-of-influence weighted graph extended for surfel sets. The convergence of our method has been studied and compared to results of other methods by running experiments on surfaces whose geodesics can be computed analytically. Our method is presented and optimized for surfel-based representations but it has been implemented also for MLS surfaces. Moreover, it can also be applied to other surface representations, e.g., triangle meshes, radial-basis functions, etc.