Cubic spline fitting using data dependent triangulations
Computer Aided Geometric Design
Use of simulated annealing to construct triangular facet surfaces
Curves and surfaces
Computing optimal triangulations using simulated annealing
Selected papers of the international symposium on Free-form curves and free-form surfaces
A signal processing approach to fair surface design
SIGGRAPH '95 Proceedings of the 22nd 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
Polyhedral Metrics in Surface Reconstruction
Proceedings of the 6th IMA Conference on the Mathematics of Surfaces
Interactive geometry remeshing
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
On the angular defect of triangulations and the pointwise approximation of curvatures
Computer Aided Geometric Design
A Flexible Similarity Measure for 3D Shapes Recognition
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Sampling Framework for Accurate Curvature Estimation in Discrete Surfaces
IEEE Transactions on Visualization and Computer Graphics
MC*: Star Functions for Marching Cubes
Proceedings of the 14th IEEE Visualization 2003 (VIS'03)
Convergence analysis of a discretization scheme for Gaussian curvature over triangular surfaces
Computer Aided Geometric Design
Extracting feature lines from unstructured meshes using a model feature map
Integrated Computer-Aided Engineering
Computer Vision and Image Understanding
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
Three-Dimensional Surface Mesh Segmentation Using Curvedness-Based Region Growing Approach
IEEE Transactions on Pattern Analysis and Machine Intelligence
Computational Geometry: Theory and Applications
ACIVS '08 Proceedings of the 10th International Conference on Advanced Concepts for Intelligent Vision Systems
Using Non Local Features for 3D Shape Grouping
SSPR & SPR '08 Proceedings of the 2008 Joint IAPR International Workshop on Structural, Syntactic, and Statistical Pattern Recognition
Fairing of Discrete Surfaces with Boundary That Preserves Size and Qualitative Shape
ISVC '08 Proceedings of the 4th International Symposium on Advances in Visual Computing
Dual Marching Tetrahedra: Contouring in the Tetrahedronal Environment
ISVC '08 Proceedings of the 4th International Symposium on Advances in Visual Computing
Discrete Distortion for Surface Meshes
ICIAP '09 Proceedings of the 15th International Conference on Image Analysis and Processing
Convergence analysis of a discretization scheme for Gaussian curvature over triangular surfaces
Computer Aided Geometric Design
Finding ridges and valleys in a discrete surface using a modified MLS approximation
Computer-Aided Design
Finding ridges and valleys in a discrete surface using a modified MLS approximation
Computer-Aided Design
Discrete distortion in triangulated 3-manifolds
SGP '08 Proceedings of the Symposium on Geometry Processing
A feature-preserved simplification for autonomous facial animation from 3D scan data
ICCSA'03 Proceedings of the 2003 international conference on Computational science and its applications: PartIII
Curvature estimation over smooth polygonal meshes using the half tube formula
Proceedings of the 12th IMA international conference on Mathematics of surfaces XII
A multistep approach to restoration of locally undersampled meshes
GMP'08 Proceedings of the 5th international conference on Advances in geometric modeling and processing
Modeling smooth shape using subdivision on differential coordinates
Computer-Aided Design
Obtuse triangle suppression in anisotropic meshes
Computer Aided Geometric Design
3D mesh fairing based on lighting and geometric conditions for interactive smooth rendering
CIS'04 Proceedings of the First international conference on Computational and Information Science
Multiple 3D Medical Data Watermarking for Healthcare Data Management
Journal of Medical Systems
The PR-star octree: a spatio-topological data structure for tetrahedral meshes
Proceedings of the 19th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems
Polyhedral gauss maps and curvature characterisation of triangle meshes
IMA'05 Proceedings of the 11th IMA international conference on Mathematics of Surfaces
Surface simplification with semantic features using texture and curvature maps
ICCSA'05 Proceedings of the 2005 international conference on Computational Science and Its Applications - Volume Part III
Consistent approximations of several geometric differential operators and their convergence
Applied Numerical Mathematics
SMI 2013: Generalized extrinsic distortion and applications
Computers and Graphics
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A tool for constructing a "good" 3D triangulation of a given set of vertices in 3D is developed and studied. The constructed triangulation is "optimal" in the sense that it locally minimizes a cost function which measures a certain discrete curvature over the resulting triangle mesh. Th algorithm for obtaining the optimal trianulation is that of swapping edges sequentially, such that the cost function is reduced maximally by each swap. In this paper three easy-to-compute cost functions are derived using a simple model for defining discrete curvatures of triangle meshes. The results obtained by the different cost functions are compared. Operating on data sampled from simple 3D models, we compare the approximation error of the resulting optimal triangle meshes to the sampled model in various nornms. The conclusion is that all three cost functions lead to similar results, and none of them can be said to be superior to the others. The triangle meshes generated by our algorithm, when serving as initial triangle meshes for the butterfly subdivision scheme, are found to improve significantly the limit butterfly-surfaces compared to arbitrary initial triangulation of the given sets of vertices. Based upon this observation, we believe that any algorithm operating on triangle meshes such as subdivision, finite element solution of PDE, or mesh simplification, can obtain better results if applied to a "good" triangle mesh with small discrete curvatures. Thus our algorithm can serve for modelling surfaces from sampled data as well as for initialization of other triangle mesh based algorithms.