Computational geometry: an introduction
Computational geometry: an introduction
Voronoi diagrams and arrangements
Discrete & Computational Geometry
Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
Randomized incremental construction of Delaunay and Voronoi diagrams
Proceedings of the seventeenth international colloquium on Automata, languages and programming
IEEE Computer Graphics and Applications - Special issue on computer-aided geometric design
Computing optimal triangulations using simulated annealing
Selected papers of the international symposium on Free-form curves and free-form surfaces
A data reduction scheme for triangulated surfaces
Computer Aided Geometric Design
Multiresolution analysis of arbitrary meshes
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
BLaC-Wavelets: a multiresolution analysis with non-nested spaces
Proceedings of the 7th conference on Visualization '96
Simplification of tetrahedral meshes
Proceedings of the conference on Visualization '98
Numerical Recipes in C: The Art of Scientific Computing
Numerical Recipes in C: The Art of Scientific Computing
Constructing Hierarchies for Triangle Meshes
IEEE Transactions on Visualization and Computer Graphics
On a Construction of a Hierarchy of Best Linear Spline Approximations Using Repeated Bisection
IEEE Transactions on Visualization and Computer Graphics
Optimal Linear Spline Approximation of Digitized Models
IV '99 Proceedings of the 1999 International Conference on Information Visualisation
Automated meshing of sparse 3D point clouds
ACM SIGGRAPH 2003 Sketches & Applications
Scattered data selection for dense sensor networks
Proceedings of the 3rd international symposium on Information processing in sensor networks
SVG rendering of real images using data dependent triangulation
Proceedings of the 20th spring conference on Computer graphics
A Frequency-Sensitive Point Hierarchy for Images and Volumes
Proceedings of the 14th IEEE Visualization 2003 (VIS'03)
Technical Section: Parallel GPU-based data-dependent triangulations
Computers and Graphics
Image compression using data-dependent triangulations
ISVC'07 Proceedings of the 3rd international conference on Advances in visual computing - Volume Part I
On digital image representation by the delaunay triangulation
PSIVT'07 Proceedings of the 2nd Pacific Rim conference on Advances in image and video technology
A proper choice of vertices for triangulation representation of digital images
ICCVG'10 Proceedings of the 2010 international conference on Computer vision and graphics: Part II
Adaptive mesh generation of MRI images for 3D reconstruction of human trunk
ICIAR'07 Proceedings of the 4th international conference on Image Analysis and Recognition
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We describe a method to create optimal linear spline approximations to arbitrary functions of one or two variables, given as scattered data without known connectivity. We start with an initial approximation consisting of a fixed number of vertices and improve this approximation by choosing different vertices, governed by a simulated annealing algorithm. In the case of one variable, the approximation is defined by line segments; in the case of two variables, the vertices are connected to define a Delaunay triangulation of the selected subset of sites in the plane. In a second version of this algorithm, specifically designed for the bivariate case, we choose vertex sets and also change the triangulation to achieve both optimal vertex placement and optimal triangulation. We then create a hierarchy of linear spline approximations, each one being a superset of all lower-resolution ones.