A survey of curve and surface methods in CAGD
Computer Aided Geometric Design
Curves and surfaces for computer aided geometric design
Curves and surfaces for computer aided geometric design
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Curvature approximation for triangulated surfaces
Geometric modelling
Fundamentals of computer aided geometric design
Fundamentals of computer aided geometric design
A data reduction scheme for triangulated surfaces
Computer Aided Geometric Design
Piecewise smooth surface reconstruction
SIGGRAPH '94 Proceedings of the 21st annual conference on Computer graphics and interactive techniques
The NURBS book
MAPS: multiresolution adaptive parameterization of surfaces
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
On levels of detail in terrains
Graphical Models and Image Processing
Multiresolution signal processing for meshes
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
Constructing Hierarchies for Triangle Meshes
IEEE Transactions on Visualization and Computer Graphics
Data Structures for Simplicial Multi-complexes
SSD '99 Proceedings of the 6th International Symposium on Advances in Spatial Databases
Polygonal Simplification: An Overview
Polygonal Simplification: An Overview
An algebraic spline model of molecular surfaces
Proceedings of the 2007 ACM symposium on Solid and physical modeling
Topologically correct reconstruction of tortuous contour forests
Proceedings of the 14th ACM Symposium on Solid and Physical Modeling
An Algebraic Spline Model of Molecular Surfaces for Energetic Computations
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Topologically correct reconstruction of tortuous contour forests
Computer-Aided Design
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We present an adaptive, hierarchical Hh-multiresolution reconstruction algorithm to model shell surface objects from a matched pair of triangulated surfaces. Shell surfaces are an interval of contours of trivariate functions with prismatic support. In the H-direction, a hierarchical representation of the scaffold is constructed. For any adaptively extracted scaffold from the hierarchy, a sequence of functions in the h-direction (regularly subdivided mesh) is constructed so that their contours approximate the input shell to within a given error ε. The shell surfaces can be made to capture sharp curve creases on the shell while being C1 smooth everywhere else. Using an interval of iso-contours of smooth trivariate spline functions, rather than a pair of inner and outer surface splines, one avoids the need for interference checks between the inner and outer surface boundaries.