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Unformatted text preview: initial object and by verifying the specifications using the "best" solution. The anticipated benefit of this methodology is to always give a solution to the problem posed, either an accurate solution or the "nearest" solution for the initial object when there is no solution that accurately verifies the constraints. 3.7. Algebraic expression of constraints Specification of the metric tensor ( G final ) = SPECi , j i, j
Given the list of angle specifications SPECi , j = (( I n + Ω ) ⋅ Ginit ⋅ t ( I n + Ω ) )i , j Eq3 where Ginit is known and Ω undetermined. Specification of the possible closure constraint, where ∆L represents the perturbation of the lengths of vectors of the loop under consideration: ∆L ⋅ ( I n + Ω ) ⋅ Ginit ⋅ t ( I n + Ω ) ⋅ t ∆L = 0 Eq4 Since the problem is still underconstrained, we will seek the Ω matrix that verifies all the Eq3 and Eq4 type specifications, at the same time minimising the function ( Ω2 + ∆L2 ) . The problem is properly posed: search for the minimum of a convex function subjected to convex constraints. Any off-the-shelf software such as Matlab, automatically...
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This note was uploaded on 08/03/2010 for the course DD 1234 taught by Professor Zczxc during the Spring '10 term at Magnolia Bible.
- Spring '10
- The Land