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Discrete Invariants of Curves and Surfaces


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  • Product Description

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.

Product Specifications
SKU :COC24488
AuthorJun Zhao
Number of Pages120
Publishing Year2/23/2012
Edition1 st
Book TypeMathematics
Country of ManufactureIndia
Product BrandLAP LAMBERT Academic Publishing
Product Packaging InfoBox
In The Box1 Piece
Product First Available On ClickOnCare.com2015-07-28 00:00:00