Surface simplification using quadric error metrics
Proceedings of the 24th annual conference on Computer graphics and interactive techniques
Computing vertex normals from polygonal facets
Journal of Graphics Tools
Weights for computing vertex normals from facet normals
Journal of Graphics Tools
A survey of methods for recovering quadrics in triangle meshes
ACM Computing Surveys (CSUR)
Computer Aided Geometric Design
Restricted delaunay triangulations and normal cycle
Proceedings of the nineteenth annual symposium on Computational geometry
Estimating the tensor of curvature of a surface from a polyhedral approximation
ICCV '95 Proceedings of the Fifth International Conference on Computer Vision
A novel cubic-order algorithm for approximating principal direction vectors
ACM Transactions on Graphics (TOG)
Estimating normal vectors and curvatures by centroid weights
Computer Aided Geometric Design
Normal Based Estimation of the Curvature Tensor for Triangular Meshes
PG '04 Proceedings of the Computer Graphics and Applications, 12th Pacific Conference
Continuous Shading of Curved Surfaces
IEEE Transactions on Computers
Robust denoising of point-sampled surfaces
WSEAS Transactions on Computers
Computing vertex normals from arbitrary meshes
ISCGAV'09 Proceedings of the 9th WSEAS international conference on Signal processing, computational geometry and artificial vision
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The local geometric properties such as curvatures and normal vectors play important roles in analyzing the local shape of objects. The result of the geometric operations such as mesh simplification and mesh smoothing is dependent on how to compute the normal vectors and the curvatures of vertices, because there are no exact definitions of the normal vector and the discrete curvature in meshes. Therefore, the discrete curvature and normal vector estimation play the fundamental roles in the fields of computer graphics and computer vision. In this paper, we propose new methods for computing normal vector and curvature well, which are more intuitive than the previous methods. Our normal vector computation algorithm is able to compute the normal vectors more accurately and is available to meshes of arbitrary topology. It is due to the properties of local conformal mapping and the mean value coordinates. Secondly, we point out the fatal error of the previous discrete curvature estimations, and then propose a new discrete sectional-curvature estimation to be able to overcome the error. The method is based on the parabola interpolation and the geometric properties of Bezier curve. It is confirmed by experiment that the normal vector and the curvature generated by our algorithm are more accurate than that of the previous methods.