Ebook: Geometric Modelling: Dagstuhl 1993

Experts from university and industry are presenting new technologies for solving industrial problems and giving many important and practicable impulses for new research. Topics explored include NURBS, product engineering, object oriented modelling, solid modelling, surface interrogation, feature modelling, variational design, scattered data algorithms, geometry processing, blending methods, smoothing and fairing algorithms, spline conversion. This collection of 24 articles gives a state-of-the-art survey of the relevant problems and issues in geometric modelling.

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Experts from university and industry are presenting new technologies for solving industrial problems and giving many important and practicable impulses for new research. Topics explored include NURBS, product engineering, object oriented modelling, solid modelling, surface interrogation, feature modelling, variational design, scattered data algorithms, geometry processing, blending methods, smoothing and fairing algorithms, spline conversion. This collection of 24 articles gives a state-of-the-art survey of the relevant problems and issues in geometric modelling.

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Experts from university and industry are presenting new technologies for solving industrial problems and giving many important and practicable impulses for new research. Topics explored include NURBS, product engineering, object oriented modelling, solid modelling, surface interrogation, feature modelling, variational design, scattered data algorithms, geometry processing, blending methods, smoothing and fairing algorithms, spline conversion. This collection of 24 articles gives a state-of-the-art survey of the relevant problems and issues in geometric modelling.
Content:
Front Matter....Pages i-vii
Parametric Offset Surface Approximation....Pages 1-34
Unimodal Properties of Generalized Ball Bases....Pages 35-41
Nef Polyhedra: A Brief Introduction....Pages 43-60
Complex PDE Surface Generation for Analysis and Manufacture....Pages 61-77
Weight Estimation of Rational B?zier Curves and Surfaces....Pages 79-86
The Use of Multiple Knots for B-spline Finite Element Approximations to PDE Surfaces....Pages 87-99
Geometric Design with Trimmed Surfaces....Pages 101-115
The Shape of the Overhauser Spline....Pages 117-128
Local Energy Fairing of B-spline Curves....Pages 129-147
Integrating Analysis Tools into the Design Process through Constrained Parametric Structures....Pages 149-161
Localized Radial Basis Methods Using Rational Triangle Patches....Pages 163-176
Repeated Knots in Least Squares Multiquadric Functions....Pages 177-187
Stability Concept for Surfaces....Pages 189-198
A Quartic Spline Based on a Variational Approach....Pages 199-210
A Knowledge-Based System for Geometric Design....Pages 211-226
B?zier Representation of Trim Curves....Pages 227-242
Control Point Representations of Trigonometrically Specified Curves and Surfaces....Pages 243-251
Towards Optimality in Automated Feature Recognition....Pages 253-274
Solid Modeling with Constrained Form Features....Pages 275-284
A Hybrid Method for Shape-Preserving Interpolation with Curvature-Continuous Quintic Splines....Pages 285-301
Scale-Invariant Functional for Smooth Curves and Surfaces....Pages 303-321
The C-Tree: A Dynamically Balanced Spatial Index....Pages 323-340
Piecewise Linear Approximation of Trimmed Surfaces....Pages 341-356
An Efficient Algorithm for Evaluating Polynomials in the P?lya Basis....Pages 357-361
Back Matter....Pages 362-364

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Experts from university and industry are presenting new technologies for solving industrial problems and giving many important and practicable impulses for new research. Topics explored include NURBS, product engineering, object oriented modelling, solid modelling, surface interrogation, feature modelling, variational design, scattered data algorithms, geometry processing, blending methods, smoothing and fairing algorithms, spline conversion. This collection of 24 articles gives a state-of-the-art survey of the relevant problems and issues in geometric modelling.
Content:
Front Matter....Pages i-vii
Parametric Offset Surface Approximation....Pages 1-34
Unimodal Properties of Generalized Ball Bases....Pages 35-41
Nef Polyhedra: A Brief Introduction....Pages 43-60
Complex PDE Surface Generation for Analysis and Manufacture....Pages 61-77
Weight Estimation of Rational B?zier Curves and Surfaces....Pages 79-86
The Use of Multiple Knots for B-spline Finite Element Approximations to PDE Surfaces....Pages 87-99
Geometric Design with Trimmed Surfaces....Pages 101-115
The Shape of the Overhauser Spline....Pages 117-128
Local Energy Fairing of B-spline Curves....Pages 129-147
Integrating Analysis Tools into the Design Process through Constrained Parametric Structures....Pages 149-161
Localized Radial Basis Methods Using Rational Triangle Patches....Pages 163-176
Repeated Knots in Least Squares Multiquadric Functions....Pages 177-187
Stability Concept for Surfaces....Pages 189-198
A Quartic Spline Based on a Variational Approach....Pages 199-210
A Knowledge-Based System for Geometric Design....Pages 211-226
B?zier Representation of Trim Curves....Pages 227-242
Control Point Representations of Trigonometrically Specified Curves and Surfaces....Pages 243-251
Towards Optimality in Automated Feature Recognition....Pages 253-274
Solid Modeling with Constrained Form Features....Pages 275-284
A Hybrid Method for Shape-Preserving Interpolation with Curvature-Continuous Quintic Splines....Pages 285-301
Scale-Invariant Functional for Smooth Curves and Surfaces....Pages 303-321
The C-Tree: A Dynamically Balanced Spatial Index....Pages 323-340
Piecewise Linear Approximation of Trimmed Surfaces....Pages 341-356
An Efficient Algorithm for Evaluating Polynomials in the P?lya Basis....Pages 357-361
Back Matter....Pages 362-364
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