First we discuss the construction of the signatures of curves and
surfaces both in smooth and discrete cases. The purpose is to find
appropriate differential and discrete invariants which can be used
as coordinates in the pictures of signature curves and surfaces.
Next we study variational problems for smooth curves and curves
approximated by B-spline curves. Our main application is to the
curve completion problem in 2D and 3D. In the smooth case, the aim
is to find the solution of the smooth Euler-Lagrange equations
which subject to curve completion problems using moving frames and
syzygies. In discrete case, the aim is to find various
aesthetically pleasing solutions as opposed to a solution of a
physical problem. The discrete Lagrangians of interest are
invariant under the special Euclidean group action for which
B-spline approximated curves are well suited. Finally, a brief
discussion of combining moving frames and Conformal Geometric
Algebra is given. Its application in solving curve completion
problems has been discussed in the end.
General
Imprint: |
Lap Lambert Academic Publishing
|
Country of origin: |
Germany |
Release date: |
February 2012 |
First published: |
February 2012 |
Authors: |
Jun Zhao
|
Dimensions: |
229 x 152 x 7mm (L x W x T) |
Format: |
Paperback - Trade
|
Pages: |
120 |
ISBN-13: |
978-3-8484-1365-2 |
Categories: |
Books >
Science & Mathematics >
Mathematics >
General
|
LSN: |
3-8484-1365-5 |
Barcode: |
9783848413652 |
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