Curves and surfaces for computer aided geometric design
Curves and surfaces for computer aided geometric design
Weights for computing vertex normals from facet normals
Journal of Graphics Tools
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
Computing vertex normals from arbitrary meshes
ISCGAV'09 Proceedings of the 9th WSEAS international conference on Signal processing, computational geometry and artificial vision
New computation of normal vector and curvature
WSEAS Transactions on Computers
A local tangential lifting differential method for triangular meshes
Mathematics and Computers in Simulation
A simple differential theory for digital curves
ACOS'06 Proceedings of the 5th WSEAS international conference on Applied computer science
Derivatives estimation for 2D digital data points
ACOS'06 Proceedings of the 5th WSEAS international conference on Applied computer science
An accurate vertex normal computation scheme
CGI'06 Proceedings of the 24th international conference on Advances in Computer Graphics
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The tensors of curvature play an important role in differential geometry. In surface theory (1990), it is determined by the derivative of unit normal vectors of tangent spaces of the underlying surface. However every geometric object in computation is a discrete model. We can only approximate them. In estimating the curvature on polyhedral surfaces, how to approximate normal vectors is a crucial step. Chen and Schmitt (1992) and Taubin (1995) described two simple methods to estimate the principal curvatures. The weights they choose is related to the triangle areas. But this choice not the best. Max (1999) presented a new kind of weight to estimate the normal vector.In this paper, we will present a new set of weights from duality and gravity. We choose the centroid weights to approximate normal vectors and estimate the principle curvatures. This will lead to a better estimation than the area-weights. Our results are also comparable with Max's weights.