I was wondering whether anyone could help me understand how I can convert the resolved force to the distance a point should move.
Theoretically Hook's Law applies only to the change in length, but in computing the natural length can be 0 and we can alter the k-value of a spring once it's in existence as well.
Below is a simple grid of springs. The springs connecting vertices 3,4,6 & 7 have had their k-values altered from 1.0 to 0.5. consequently their lengths should change. I've done part of the workings under the line sketch - but not sure where to go from there
256—— 6-----<0.5>-----7-----<1.0>-----8
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<0.5> <0.5> <1.0>
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0 —— 3-----<0.5>-----4-----<1.0>-----5
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<1.0> <1.0> <1.0>
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-256—— 0-----<1.0>-----1-----(1.0)-----2
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-256 0 +256
The vertices on the edges need to stay on the edges,it is the central vertices that alter their positions - in this case there is only one though! This is just an example but the non-corner vertices would slide along their respective edges too.
Using Hooks law - resolve for Vertex 4:
LeftSpring = 0.5 * (-256, 0, 0) = (-128, 0, 0)
RightSpring = 1.0 * (+256, 0, 0) = (+256, 0, 0)
UpSpring = 0.5 * (0, +256, 0) = (0, +128, 0)
DownSpring = 1.0 * (0, -256, 0) = (0, -256, 0)
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SumForce = (-128, 128, 0)
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... So how do I get the distance Vertex 4 should move?
I am fairly certain it's resting place is not (192, -128, 0).
Many Thanks in advance
[Edited by - Will-O on February 17, 2008 9:57:00 PM]