The NURBS book
Spherical averages and applications to spherical splines and interpolation
ACM Transactions on Graphics (TOG)
The Complex EGI: A New Representation for 3-D Pose Determination
IEEE Transactions on Pattern Analysis and Machine Intelligence
Representation and geometric computation using the extended Gaussian image
Pattern Recognition Letters
A simple algorithm for designing developable Bézier surfaces
Computer Aided Geometric Design
On increasing the developability of a trimmed NURBS surface
Engineering with Computers
The Visual Computer: International Journal of Computer Graphics
Degree elevation and developable Bézier surfaces
Computer Aided Geometric Design
A Constrained Least Squares Approach to Interactive Mesh Deformation
SMI '06 Proceedings of the IEEE International Conference on Shape Modeling and Applications 2006
Geometric modeling with conical meshes and developable surfaces
ACM SIGGRAPH 2006 Papers
B-spline control nets for developable surfaces
Computer Aided Geometric Design
Modeling dynamic developable meshes by the Hamilton principle
Computer-Aided Design
Developable surfaces from arbitrary sketched boundaries
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
Towards flattenable mesh surfaces
Computer-Aided Design
Computer aided geometric design of strip using developable Bézier patches
Computers in Industry
A survey on CAD methods in 3D garment design
Computers in Industry
EasyToy: Plush Toy Design Using Editable Sketching Curves
IEEE Computer Graphics and Applications
Construction of Iso-Contours, Bisectors, and Voronoi Diagrams on Triangulated Surfaces
IEEE Transactions on Pattern Analysis and Machine Intelligence
Industrial design using interpolatory discrete developable surfaces
Computer-Aided Design
Efficient linear system solvers for mesh processing
IMA'05 Proceedings of the 11th IMA international conference on Mathematics of Surfaces
Modeling 3D garments by examples
Computer-Aided Design
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Surface developability is a key feature in many industrial product designs. In this paper, based on a measure defined in an extended Gaussian image, an efficient least squares solution is proposed to achieve an optimal quasi-developable mesh patch. For a free-form mesh model assembled by a set of patches, each patch can be deformed using the least squares solution to obtain the best developability within a user-specified tolerance while the patch boundary remains continuous with neighboring patches. The proposed least squares scheme formulates the quasi-developable mesh approximation problem as a large sparse linear system with its coefficient matrix independent of the mesh vertices@? new positions. We show that this linear system can be efficiently solved by a least squares direct matrix solver. Experimental results and applications are provided to demonstrate the controllability of shape change as well as the effectiveness of mesh developability improvement provided by the proposed solution.