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spline representation of a spiral

asked 2012-09-26 05:45:58 -0500

Maxx gravatar image

Hello all, I'm new to this forum. :)

I'm trying to represent a spiral as a spline and was wondering how I could do it. My spiral has very specific properties which may make the representation easier (or not?)

At the bottom of this post is a representation of Euclidean 2D space with numbers ranging from 1 to C (hex numbers). These are the points, numbered in order, that the spiral must go through. Each + is separated by 4 (i.e. these are 1/4th divisions) for convenience and is to scale.

Does anyone have any idea how I would represent this using a spline? Your help is much appreciated.

Maxx

+   +   +   +   +   +   +   +   +
                |                
                |                
                A                
+   +   +   +   +   +   +   +   +
                |                
                |                
                6                
+   +   +   +   +   +   +   +   +
                |                
                |                
                2                
+   +   +   +   +   +   +   +   +
                |                
                |                
                |                
+-B-+-7-+-3-+---|---1---5---9---+
                |                
                |                
                |                
+   +   +   +   +   +   +   +   +
                |                
                |                
                4                
+   +   +   +   +   +   +   +   +
                |                
                |                
                8                
+   +   +   +   +   +   +   +   +
                |                
                |                
                C                
+   +   +   +   +   +   +   +   +
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answered 2012-09-28 19:34:48 -0500

benjaminfjones gravatar image

Why do you want a spline? Why not a parametric curve? You could cook up a simple parametric curve that passed through those points by modifying a well-known curve like $x(t) = tcos(t), y(t) = tsin(t)$.

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Asked: 2012-09-26 05:45:58 -0500

Seen: 157 times

Last updated: Sep 28 '12