ACM Transactions on Graphics (TOG)
Curves and surfaces for computer aided geometric design (3rd ed.): a practical guide
Curves and surfaces for computer aided geometric design (3rd ed.): a practical guide
Optimal surface reconstruction from planar contours
Communications of the ACM
An interactive computer graphics approach to surface representation
Communications of the ACM
A new general triangulation method for planar contours
SIGGRAPH '82 Proceedings of the 9th annual conference on Computer graphics and interactive techniques
Conversion of complex contour line definitions into polygonal element mosaics
SIGGRAPH '78 Proceedings of the 5th annual conference on Computer graphics and interactive techniques
Extracting iso-valued features in 4-dimensional scalar fields
VVS '98 Proceedings of the 1998 IEEE symposium on Volume visualization
Investigations toward Using VRML for Distributed Medical Collaboration
Presence: Teleoperators and Virtual Environments
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We present a method for constructing tensor product Bezier surfaces from contour (cross-section) data. Minimal area triangulations are used to guide the surface construction, and the final surface reflects the optimality of the triangulation. The resulting surface differs from the initial triangulation in two important ways: it is smooth (as opposed to the piecewise planar triangulation), and it is in tensor product form (as opposed to the irregular triangular mesh). The surface reconstruction is efficient because we do not require an exact minimal surface. The triangulations are used as strong hints, but no more than that. The method requires the computation of both open and closed isoparametric curves of the surface, using triangulations as a guide. These isoparametric curves form a tensor product Bezier surface. We show how to control sampling density by filling and pruning isoparametric curves, for accuracy and economy. A rectangular grid of points is produced that is compatible with the expected format for a tensor product surface interpolation, so that a host of well-supported methods are available to generate and manipulate the surface.