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 Pr October 3, 2003 03:40

Normal to a curve

Is there any mathematical formula available for getting a normal or perpendicular to a curve from some arbitrary points. Thanks for any help Pr

 xueying October 3, 2003 11:53

Re: Normal to a curve

Map the curve to an easy shape, and the mapping if matrix F.

! ==> Normal

! recall: n = cofF . N / mu in rheology class note

! Fij = dx_i/dxi_j = XY_XIETA

!

! -T

! F . N

! n = ------------

! -T

! | F . N |

!

n is the unit normal vector that you want, N is the unit normal vector in reference domain.

 TPallidum October 4, 2003 13:01

Re: Normal to a curve

Given some points on a curve, use your favorite method to numerically evaluate the gradient.

 Ag Gaire. October 6, 2003 05:52

Re: Normal to a curve

n = -(GRAD Phi)/|GRAD Phi|). See Anton, "Calculus" for an excellent explaination of all sorts of this type of idea.

 Pr October 6, 2003 06:08

Re: Normal to a curve

Hey thanks for the solution. But actually I want to argue with your answer. You had written for gradients.I can calculate gradient of curve at certain discrete points at which function or curve is defined.let us say I have 50 points I can get 50 values. But from arbitrary point(A) which does not lie on the curve I want to find the normal.so one or more lines from point A to the 50 points on the curve will be normal. This procedure becomes time consuming when curve ponts increases. So I want to ask here is there any other method to do this. Pr

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