Curvature approximation of 3D manifolds in 4D space
Computer Aided Geometric Design
Umbilics and lines of curvature for shape interrogation
Computer Aided Geometric Design
Proceedings of the 24th 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
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Anisotropic Diffusion in Vector Field Visualization on Euclidean Domains and Surfaces
IEEE Transactions on Visualization and Computer Graphics
Intrinsic Surface Properties from Surface Triangulation
ECCV '92 Proceedings of the Second European Conference on Computer Vision
Estimating the tensor of curvature of a surface from a polyhedral approximation
ICCV '95 Proceedings of the Fifth International Conference on Computer Vision
Texture Synthesis for 3D Shape Representation
IEEE Transactions on Visualization and Computer Graphics
Ridge-valley lines on meshes via implicit surface fitting
ACM SIGGRAPH 2004 Papers
Estimating differential quantities using polynomial fitting of osculating jets
Computer Aided Geometric Design
Fast and robust detection of crest lines on meshes
Proceedings of the 2005 ACM symposium on Solid and physical modeling
A Sampling Framework for Accurate Curvature Estimation in Discrete Surfaces
IEEE Transactions on Visualization and Computer Graphics
Cycle shading for the assessment and visualization of shape in one and two codimensions
GI '06 Proceedings of Graphics Interface 2006
Geometric modeling based on triangle meshes
ACM SIGGRAPH 2006 Courses
A 3D object classifier for discriminating manufacturing processes
Computers and Graphics
Fast and accurate estimation of principal curvatures and directions for morphable models
ACM SIGGRAPH 2007 posters
Smooth feature lines on surface meshes
SGP '05 Proceedings of the third Eurographics symposium on Geometry processing
SGP '05 Proceedings of the third Eurographics symposium on Geometry processing
Robust principal curvatures on multiple scales
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
Robust statistical estimation of curvature on discretized surfaces
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
Focal surfaces of discrete geometry
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
Principal curvatures from the integral invariant viewpoint
Computer Aided Geometric Design
Exact and interpolatory quadratures for curvature tensor estimation
Computer Aided Geometric Design
Moving parabolic approximation of point clouds
Computer-Aided Design
Technical Section: A direction-oriented sharpness dependent filter for 3D polygon meshes
Computers and Graphics
Consistent computation of first- and second-order differential quantities for surface meshes
Proceedings of the 2008 ACM symposium on Solid and physical modeling
Line-art illustration of dynamic and specular surfaces
ACM SIGGRAPH Asia 2008 papers
Feature Extraction from the Mesh Model with Some Noise
SG '07 Proceedings of the 8th international symposium on Smart Graphics
Automatic Detection of the Back Valley on Scoliotic Trunk Using Polygonal Surface Curvature
ICIAR '08 Proceedings of the 5th international conference on Image Analysis and Recognition
Fast, robust, and faithful methods for detecting crest lines on meshes
Computer Aided Geometric Design
Integral invariants for robust geometry processing
Computer Aided Geometric Design
Extracting lines of curvature from noisy point clouds
Computer-Aided Design
Computer Aided Geometric Design
Curvature-aware adaptive re-sampling for point-sampled geometry
Computer-Aided Design
Robust principal curvatures using feature adapted integral invariants
2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling
Estimating differential quantities using polynomial fitting of osculating jets
Computer Aided Geometric Design
Finding ridges and valleys in a discrete surface using a modified MLS approximation
Computer-Aided Design
Curvature estimation scheme for triangle meshes using biquadratic Bézier patches
Computer-Aided Design
Finding ridges and valleys in a discrete surface using a modified MLS approximation
Computer-Aided Design
Mesh saliency and human eye fixations
ACM Transactions on Applied Perception (TAP)
New computation of normal vector and curvature
WSEAS Transactions on Computers
Separatrix persistence: extraction of salient edges on surfaces using topological methods
SGP '09 Proceedings of the Symposium on Geometry Processing
Distance-aware smoothing of surface meshes for surgical planning
Proceedings of the First International Workshop on Digital Engineering
A local tangential lifting differential method for triangular meshes
Mathematics and Computers in Simulation
Regional registration for expression resistant 3-D face recognition
IEEE Transactions on Information Forensics and Security
A training-free nose tip detection method from face range images
Pattern Recognition
GPU curvature estimation on deformable meshes
I3D '11 Symposium on Interactive 3D Graphics and Games
Single-tooth modeling for 3D dental model
Journal of Biomedical Imaging
Generalized shape operators on polyhedral surfaces
Computer Aided Geometric Design
Real-time and interactive rendering for translucent materials such as human skin
HCII'11 Proceedings of the 1st international conference on Human interface and the management of information: interacting with information - Volume Part II
3D Facial expression recognition based on histograms of surface differential quantities
ACIVS'11 Proceedings of the 13th international conference on Advanced concepts for intelligent vision systems
Estimating principal properties on triangular meshes
ICHIT'11 Proceedings of the 5th international conference on Convergence and hybrid information technology
Curvature estimation for meshes based on vertex normal triangles
Computer-Aided Design
3D shape from unorganized 3d point clouds
ISVC'05 Proceedings of the First international conference on Advances in Visual Computing
Brain image analysis using spherical splines
EMMCVPR'05 Proceedings of the 5th international conference on Energy Minimization Methods in Computer Vision and Pattern Recognition
Couple points --- a local approach to global surface analysis
Proceedings of the 7th international conference on Curves and Surfaces
Fast Grasp Synthesis for Various Shaped Objects
Computer Graphics Forum
Tensor scale: An analytic approach with efficient computation and applications
Computer Vision and Image Understanding
Graphical Models
3D/4D facial expression analysis: An advanced annotated face model approach
Image and Vision Computing
Local shape descriptors, a survey and evaluation
EG 3DOR'11 Proceedings of the 4th Eurographics conference on 3D Object Retrieval
SHREC'11 track: 3D face models retrieval
EG 3DOR'11 Proceedings of the 4th Eurographics conference on 3D Object Retrieval
Staircase-aware smoothing of medical surface meshes
EG VCBM'10 Proceedings of the 2nd Eurographics conference on Visual Computing for Biology and Medicine
3D orientation of archaeological fragments coming from a Gothic spire
VAST'04 Proceedings of the 5th International conference on Virtual Reality, Archaeology and Intelligent Cultural Heritage
Generating time lines with virtual words for time-varying data visualization
Proceedings of the 5th International Symposium on Visual Information Communication and Interaction
Technical Section: Pencil rendering on 3D meshes using convolution
Computers and Graphics
A Machine-Learning Approach to Keypoint Detection and Landmarking on 3D Meshes
International Journal of Computer Vision
Skeleton extraction of vertex sets lying on arbitrary triangulated 3d meshes
DGCI'13 Proceedings of the 17th IAPR international conference on Discrete Geometry for Computer Imagery
Curvature tensor computation by piecewise surface interpolation
Computer-Aided Design
Visualization and analysis of 3D time-varying simulations with time lines
Journal of Visual Languages and Computing
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There are a number of applications in computer graphics that require as a first step the accurate estimation of principal direction vectors at arbitrary vertices on a triangulated surface. Although several methods for calculating principal directions over such models have been previously proposed, we have found in practice that all exhibit unexplained large errors in some cases. In this article, we describe our theoretical and experimental investigations into possible sources of errors in the approximation of principal direction vectors from triangular meshes, and suggest a new method for estimating principal directions that can yield better results under some circumstances.