# spline representation of a spiral

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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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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