RoboFont › Forums › Help / General › Scripting: nearest oncurve point for a given coordinate
Tagged: Scripting
This topic contains 2 replies, has 2 voices, and was last updated by Jens K. 2 months, 1 week ago.

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June 24, 2017 at 16:32 #6320
AnonymousDear Robofonters,
I’ve just started testing this wonderful app for the first time in my life and I’m planning to rewrite my (at least for me) very useful plugin from the GlyphsApp: StemThickness (https://github.com/RafalBuchner/StemThickness).
For this purpose I need to find the nearest oncurve point for the coordinate of the cursor point. And I’ve found it:
(here: https://groups.google.com/forum/#!topic/robofab/YAG1RQO_mcc )Right now I’m looking for something I would call “time of the oncurve point”. This is the ratio needed for further calculation for my extension.
Following equation is the standard equation for the bezier curve.
I have given B (coordinates of the nearest oncurve point), A, B, C, D (curve’s control points). I’m looking for “t” value:B = (1 – t)^3*A + 3*(1 – t)^2 *t*B + 3*(1 – t) *t^2 *C + t^3 * D
, 0 <= t <= 1, t=?Do you guys know any fast method for finding “t” value of given oncurve point and bezeir curve’s control points?
I hope that this message is quite clear :) I’m not the best at explaining math stuff at forums.Cheers
RafałJuly 14, 2017 at 08:17 #6322I 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 :)
July 14, 2017 at 08:25 #6323I 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 precalculated 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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