Computational Geometry for Design and Manufacture
Computational Geometry for Design and Manufacture
SURFACES FOR COMPUTER-AIDED DESIGN OF SPACE FORMS
SURFACES FOR COMPUTER-AIDED DESIGN OF SPACE FORMS
Surface construction by fitting unorganized curves
Graphical Models
Constraint-based design of B-spline surfaces from curves
SM '04 Proceedings of the ninth ACM symposium on Solid modeling and applications
Sketching out a freeform surface
International Journal of Computer Applications in Technology
Surface fitting to curves with energy control
ISVC'06 Proceedings of the Second international conference on Advances in Visual Computing - Volume Part I
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In industrial design, the tool of choice for constructing surfaces that interpolate curves is the Boolean sum surface technique. However, if curves do not lie on constant parameter lines, reparametrizations will be needed, and this may introduce derivative discontinuities. A new technique which shows promise in overcoming this problem is described here. The method is based on describing the interpolation problem directly as a system of linear equations rather than as a curve-blending problem. The resulting system of equations is usually underdetermined and can be solved using numerical linear algebra methods without the a priori determination of certain parameters. The “free” parameters can be used to control the shape of the resulting surface. Two examples of the procedure are given.