Bezier曲线上的等距点 [英] Equidistant points across Bezier curves
问题描述
P_0和P_3之间的距离形式),是的,但我认为你知道这一点,直截了当。
曲线上的距离只是弧长:
fig 1 http://www.codecogs.com/eq.latex?%5Cint_%7Bt_0%7D%5E%7Bt_1%7D%20%7B%20|P'(t)| %20dt
其中:
可能你会有t_0 = 0,t_1 = 1.0,dz(t)= 0(二维平面)。
Currently, I'm attempting to make multiple beziers have equidistant points. I'm currently using cubic interpolation to find the points, but because the way beziers work some areas are more dense than others and proving gross for texture mapping because of the variable distance. Is there a way to find points on a bezier by distance rather than by percentage? Furthermore, is it possible to extend this to multiple connected curves?
distance between P_0 and P_3 (in cubic form), yes, but I think you knew that, is straight forward.
Distance on a curve is just arc length:
fig 1 http://www.codecogs.com/eq.latex?%5Cint_%7Bt_0%7D%5E%7Bt_1%7D%20%7B%20|P'(t)|%20dt
where:
Probably, you'd have t_0 = 0, t_1 = 1.0, and dz(t) = 0 (2d plane).
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