Determining Bezier-spline next to other spline
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Posted 19 November 2007 - 01:21 AM
I'm looking for a method to calculate the control points of a Bezier-spline at a distance d from a Bezier-spline I have. So, say spline B describes the middle of a road, I want to determine the spline C that is the middle of one lane. This is in 2D, so I can calculate every point of C by determining the derivative of B at a certain t, finding the perpendicular (y, -x) and offsetting by my distance d. However, what I want is the control points. I thought I could do this by choosing to points on B (e.g. t=1/3, t=2/3), calculating the points on C with the method above, and then solving the Bezier-spline-equation with these points. However, it seems I cannot assume that the t of these points on C are 1/3 and 2/3 as well. Could somebody please point me in the right direction?