Abstract:
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We present a method to construct a patch of parametric surface of
degree k+1 that fills a n-sided hole, with bigger than 2, and whose
boundary coincides with a B-Spline, thus, the resulting patch can be
easily connected with given B-Spline surfaces with fixed continuity
conditions. The method is based on the generic approach by the same
authors to con-struct free form surfaces, which gives a family of
practical schemes to design surfaces from an arbitrary given mesh,
using the differentiable manifold the-ory. The proposal uses a star
shaped mesh which describes a generic n-hole and a surface in a
neighborhood of the hole. From this mesh, a set of charts is defined,
one associated to each vertex or face of the mesh, depending on the
parity of the input parameter k. A basis function and a control point
is defined from each chart, and the surface is obtained as a
baricentric combination of the control points using the defined basis
functions. The main advantages of the method are the following:
arbitrary order k continuity conditions can be imposed; the involved
hole can have an arbitrary number of sides and arbitrary shape (convex
or not) the simplicity of the construction process gives an easy and
flexible method; and finally, the surface near the boundary is a
B-Spline with piecewise uniform knot sequences and whose control
points are vertices of the given mesh. Implementation details to
evaluate a surface point are given, showing that the de Boor algorithm
can be exploited for efficiency. |