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Normalized Parallel Curves
In the curvature section, we introduced the concept of parallel curves
at a given distance
d. At each stage we may scale the image so that it fits
on the screen by multiplying the parallel curve
Xd(t)
=X(t)
+dU(t) by v = The Parallel at Distance v/(1-v) window shows the curve along with the parallel at its actual distance. When the distance gets large, you will have to rescale the display (by pressing the "s" key with the mouse cursor in the window) in order to see the parallel curve; as you do this, you can see that the original curve diminishes to a point in relative size. The Normalized Parallel Curve window shows the curve, along with the parallel curve scaled according to the function Xv(t) . The size of the original curve is not being changed in any way. You can set v between 0 and 1 using the slider in the Parallels window. The purpose of this demo is to help visualize the interpolation between the parallel curves and the normal image of a curve. |