Logarithmic Spiral - Is Point on Spiral (cartesian coordinates
<p>Lets Say I have a 3d Cartesian grid. Lets also assume that there are one or more log spirals emanating from the origin on the horizontal plane.</p>

<p>If I then have a point in the grid I want to test if that point is in one of the spirals. I acutally want to test if it within a certain range of the spirals but determining if it is on the point is a good start.</p>

<p>So I guess the question has a couple parts.</p>

<p>1) How to generate the arms from parameters (direction, tightness)</p>

<p>2) How to tell if a point in the grid is in one of the spiral arms</p>

<p>Any ideas? I have been googling all day and don't feel I am any closer to a solution than when I started.</p>

<p>Here is a bit more information that might help:</p>

<p>I don't actually need to render the spirals. I want to set the pitch and rotation and then pass a point to a method that can tell me if the point I passed is within the spiral (within a given range of any point on the spiral). Based on the value returned (true or false) my program will make a decision on whether or not something exists at the point in space. </p>

<p>1) How to parametrically define the log spirals (pitch and rotation and ??)</p>

<p>2) Test if a point (x, y, z) is withing a given range of any point on the spiral.</p>

<p>Note: Both of the above would be just on the horizontal plane</p>
