Solid shape
Curvature approximation for triangulated surfaces
Geometric modelling
Weights for computing vertex normals from facet normals
Journal of Graphics Tools
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
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
Estimating differential quantities using polynomial fitting of osculating jets
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
A novel cubic-order algorithm for approximating principal direction vectors
ACM Transactions on Graphics (TOG)
Normal Based Estimation of the Curvature Tensor for Triangular Meshes
PG '04 Proceedings of the Computer Graphics and Applications, 12th Pacific Conference
Modelling Reflections via Multiperspective Imaging
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 1 - Volume 01
Introduction to discrete differential geometry: the geometry of plane curves
SIGGRAPH '05 ACM SIGGRAPH 2005 Courses
Robust principal curvatures on multiple scales
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
Freeform surfaces from single curved panels
ACM SIGGRAPH 2008 papers
Line-art illustration of dynamic and specular surfaces
ACM SIGGRAPH Asia 2008 papers
Fast, robust, and faithful methods for detecting crest lines on meshes
Computer Aided Geometric Design
Data-driven curvature for real-time line drawing of dynamic scenes
ACM Transactions on Graphics (TOG)
Ray geometry in non-pinhole cameras: a survey
The Visual Computer: International Journal of Computer Graphics
Discrete line congruences for shading and lighting
SGP '13 Proceedings of the Eleventh Eurographics/ACMSIGGRAPH Symposium on Geometry Processing
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The differential geometry of smooth three-dimensional surfaces can be interpreted from one of two perspectives: in terms of oriented frames located on the surface, or in terms of a pair of associated focal surfaces. These focal surfaces are swept by the loci of the principal curvatures' radii. In this article, we develop a focal-surfacebased differential geometry interpretation for discrete mesh surfaces. Focal surfaces have many useful properties. For instance, the normal of each focal surface indicates a principal direction of the corresponding point on the original surface. We provide algorithms to robustly approximate the focal surfaces of a triangle mesh with known or estimated normals. Our approach locally parameterizes the surface normals about a point by their intersections with a pair of parallel planes. We show neighboring normal triplets are constrained to pass simultaneously through two slits, which are parallel to the specified parametrization planes and rule the focal surfaces. We develop both CPU and GPU-based algorithms to efficiently approximate these two slits and, hence, the focal meshes. Our focal mesh estimation also provides a novel discrete shape operator that simultaneously estimates the principal curvatures and principal directions.