Smoothing surfaces using reflection lines for families of splines
Computer-Aided Design - Special issue on the shape of surfaces
Cubic recursive division with bounded curvature
Curves and surfaces
Efficient, fair interpolation using Catmull-Clark surfaces
SIGGRAPH '93 Proceedings of the 20th annual conference on Computer graphics and interactive techniques
The NURBS book
A unified approach to subdivision algorithms near extraordinary vertices
Computer Aided Geometric Design
Non-uniform recursive subdivision surfaces
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
Exact evaluation of Catmull-Clark subdivision surfaces at arbitrary parameter values
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
Piecewise smooth subdivision surfaces with normal control
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Are isophotes and reflection lines the same?
Computer Aided Geometric Design - Pierre Bézier
Geometric Modelling, Dagstuhl, Germany, 1996
Catmull-Clark Surface Fitting for Reverse Engineering Applications
GMP '00 Proceedings of the Geometric Modeling and Processing 2000
ACM SIGGRAPH 2003 Papers
Shape characterization of subdivision surfaces: basic principles
Computer Aided Geometric Design
Shape characterization of subdivision surfaces: case studies
Computer Aided Geometric Design
Lofting curve networks using subdivision surfaces
Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Modified subdivision surfaces with continuous curvature
ACM SIGGRAPH 2006 Papers
Constructing curvature-continuous surfaces by blending
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
Subdivision Surfaces
NURBS with extraordinary points: high-degree, non-uniform, rational subdivision schemes
ACM SIGGRAPH 2009 papers
Subdivision surfaces for CAD-an overview
Computer-Aided Design
G2 tensor product splines over extraordinary vertices
SGP '08 Proceedings of the Symposium on Geometry Processing
Tuning subdivision algorithms using constrained energy optimization
Proceedings of the 12th IMA international conference on Mathematics of surfaces XII
Bounded curvature subdivision without eigenanalysis
Proceedings of the 12th IMA international conference on Mathematics of surfaces XII
A fast interactive reverse-engineering system
Computer-Aided Design
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The main roadblock that has limited the usage of subdivision surfaces in computer-aided design (CAD) systems is the lack of quality and precision that a model must achieve for being suitable in the engineering and manufacturing phases of design. The second roadblock concerns the integration into the modeling workflows, that, for engineering purposes, means providing a precise and controlled way of defining and editing models possibly composed of different geometric representations. This paper documents the experience in the context of a European project whose goal was the integration of subdivision surfaces in a CAD system. To this aim, a new CAD system paradigm with an extensible geometric kernel is introduced, where any new shape description can be integrated through the two successive steps of parameterization and evaluation, and a hybrid boundary representation is used to easily model different kinds of shapes. In this way, the newly introduced geometric description automatically inherits any pre-existing CAD tools, and it can interact in a natural way with the other geometric representations supported by the CAD system. To overcome the irregular behavior of subdivision surfaces in the neighborhood of extraordinary points, we locally modify the limit surface of the subdivision scheme so as to tune the analytic properties without affecting its geometric shape. Such a correction is inspired by the polynomial blending approach in Levin (2006) [1] and Zorin (2006) [2], which we extend in some aspects and generalize to multipatch surfaces evaluable at arbitrary parameter values. Some modeling examples will demonstrate the benefits of the proposed integration, and some tests will confirm the effectiveness of the proposed local correction patching method.