Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Nonobtuse triangulation of polygons
Discrete & Computational Geometry
Guaranteed-quality mesh generation for curved surfaces
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
Linear-size nonobtuse triangulation of polygons
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
Multiresolution analysis of arbitrary meshes
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Surface simplification using quadric error metrics
Proceedings of the 24th annual conference on Computer graphics and interactive techniques
Object-oriented software for quadratic programming
ACM Transactions on Mathematical Software (TOMS)
Global conformal surface parameterization
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
ACM SIGGRAPH 2010 Courses
Obtuse triangle suppression in anisotropic meshes
Computer Aided Geometric Design
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Quality meshing in 2D and 3D domains is an important problem in geometric modeling and scientific computing. We are concerned with triangle meshes having only nonobtuse angles. Specifically, we propose a solution for guaranteed nonobtuse remeshing and nonobtuse mesh decimation. Our strategy for the remeshing problem is to first convert an input mesh, using a modified Marching Cubes algorithm, into a rough approximate mesh that is guaranteed to be nonobtuse. We then apply iterative "deform-to-fit" via constrained optimization to obtain a high-quality approximation, where the search space is restricted to be the set of nonobtuse meshes having a fixed connectivity. With a detailed nonobtuse mesh in hand, we apply constrained optimization again, driven by a quadric-based error, to obtain a hierarchy of nonobtuse meshes via mesh decimation.