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Originally Posted by chsahit
What does the spline paramater represent? When discussing 2d hermite cubic spline fits functions are created in terms of "s". Is this time?
Thank you and great presentation!
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Usually 's' is not time; it is just an arbitrary parameter (nominally varying between 0 and 1 for any given segment). You can reparameterize a spline by creating another function that maps 's' to something else, like time or arc length.
In other words, instead of looking up your position by calling a function x(s), you would call x(s(t)), or x(s(arc_length)).
Note that if you are creative, you can formulate the problem in different ways. In 2014, 254 actually created 2D splines by making a single function y(x). In this case, the 's' parameter was actually the x coordinate (shifted and rotated to the origin for each spline segment). There are some pros and cons to doing it this way as opposed to the more common parametric way (where you create two independent splines for x and y).