Surface construction by fitting unorganized curves

Authors:
T. Maekawa;K. H. Ko
Affiliations:
Design Laboratory, Department of Ocean Engineering, Massachusetts Institute of Technology, Cambridge, MA;Design Laboratory, Department of Ocean Engineering, Massachusetts Institute of Technology, Cambridge, MA
Venue:
Graphical Models
Year:
2002

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Abstract

We present a novel technique to construct a B-spline surface from unorganized curves in 3D space. Unlike the lofting or skinning methods, where the family of curves to be lofted form isoparametric lines of the resulting surface, our method relaxes this restriction and allows a set of curves to take arbitrary orientation and possibly intersect each other. We employ the concept of a curve on a surface which is used in obtaining the arc element of a curve on the surface in differential geometry. This novel technique is useful in surface construction or creation where surfaces are created based on sketches. The surface creation has applications in aesthetic shape design, reverse engineering, computer graphics, and computer animation. This technique is also useful in surface reconstruction where surfaces are constructed from stripes which are made of a series of points lined up in a sequential manner.