SIAM Journal on Computing
Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Shortest paths on a polyhedron
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
Umbilics and lines of curvature for shape interrogation
Computer Aided Geometric Design
Computing vertex normals from polygonal facets
Journal of Graphics Tools
I3D '01 Proceedings of the 2001 symposium on Interactive 3D graphics
Curves and surfaces for CAGD: a practical guide
Curves and surfaces for CAGD: a practical guide
Shape Interrogation for Computer Aided Design and Manufacturing
Shape Interrogation for Computer Aided Design and Manufacturing
Anisotropic polygonal remeshing
ACM SIGGRAPH 2003 Papers
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
ReMESH: An Interactive Environment to Edit and Repair Triangle Meshes
SMI '06 Proceedings of the IEEE International Conference on Shape Modeling and Applications 2006
IEEE Computer Graphics and Applications
Extracting lines of curvature from noisy point clouds
Computer-Aided Design
Improving Chen and Han's algorithm on the discrete geodesic problem
ACM Transactions on Graphics (TOG)
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In many engineering applications, a smooth surface is often approximated by a mesh of polygons. In a number of downstream applications, it is frequently necessary to estimate the differential invariant properties of the underlying smooth surfaces of the mesh. Such applications include first-order surface interrogation methods that entail the use of isophotes, reflection lines, and highlight lines, and second-order surface interrogation methods such as the computation of geodesics, geodesic offsets, lines of curvature, and detection of umbilics. However, we are not able to directly apply these tools that were developed for B-spline surfaces to tessellated surfaces. This article describes a unifying technique that enables us to use the shape interrogation tools developed for B-spline surface on objects represented by triangular meshes. First, the region of interest of a given triangular mesh is transformed into a graph function (z=h(x,y)) so that we can treat the triangular domain within the rectangular domain. Each triangular mesh is then converted into a cubic graph triangular Bézier patch so that the positions as well as the derivatives of the surface can be evaluated for any given point (x,y) in the domain. A number of illustrative examples are given that show the effectiveness of our algorithm.