How to maintain spacing along a new curve?
I'm doing grid deformation and part of the problem requires me to transform one curve (which consists of a no. of grid pts) to another which will give better cell properties in the end.
I know all the pts on the original curve and I know the eqn of the new curve, which is a 3rd polynomial, and also the starting and ending pts of this curve. The starting pt of the 2 curve coincide.
I need to find the pts on the new curve. However, I also want to preserve the original spacing between consecutive pts on the new curve. E.g., from pt1 to pt2, the distance, on the old and new curve must be 0.5. How can I achieve that?
My friend told me to do integration on the new curve to get the arc length etc. but that sounds like a lot of workings. Is there a simplier mtd?
Re: How to maintain spacing along a new curve?
Sounds like your friend has a good suggestion for the problem as you have stated it. Another possibility might be to find points on the curve closest to your data points. If the curve is given parametrically as a function of a variable t, ie x(t)=f(t), y(t)=g(t), find ti such that d^2=(f(ti)-xi)^2+(g(ti)-yi)^2 is a minimum. That is, find ti such that (f(ti)-xi)*f'(ti)+(g(ti)-yi)*g'(ti)=0 for ech node i. Solution is straight-forward, but nonlinear, provided there are no loops in the curve.
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