This topic contains 2 replies, has 2 voices, and was last updated by Jens K. 3 years, 3 months ago.
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I have looked for a solution to this myself, and actually ended up taking your numerical approach from the Glyphs plugin ;)
As I understand it, there may not be a solution to the equation if the given point is not exactly on the curve, which may already happen because floating point numbers are not exact. So you need to find t so that the distance of P(t) to the given point is minimized.
This stackexchange answer may be something, but I didn’t understand the stuff about inversions: https://math.stackexchange.com/a/535785
If you can make any sense of it, I am very interested :)
I found a way to speed up the brute force approach though. If you can use external Python modules:
from scipy import spatial tree = spatial.KDTree(t_list) # t_list is a list of pre-calculated point coordinate tuples on the cubic curve distance, index = tree.query(pt) # pt is the given point coordinate tuple t_for_pt = float(index) / (len(tree.data) - 1)
t_list must be constructed in a way that the first entry is for t = 0 and the last entry for t = 1. It doesn’t matter how many points for increments of t you calculate, as long as the index in t_list is proportional to t. Smaller increments of t increase the precision of the result, but the list takes longer to build.
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