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Rewrote bezier_segment_closest_point() algorithm to search all minima.

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Revar Desmera 2019-06-19 01:35:08 -07:00
parent d069cf39ce
commit 6dbff74f2b
1 changed files with 28 additions and 12 deletions
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40
beziers.scad
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@ -114,19 +114,35 @@ function bezier_curve(curve,n) = [for(i=[0:1:n-1]) bez_point(curve, i/(n-1))];
// trace_bezier(bez, N=len(bez)-1);
// color("red") translate(pt) sphere(r=1);
// color("blue") translate(bez_point(bez,u)) sphere(r=1);
function bezier_segment_closest_point(curve, pt, max_err=0.01, u=0, end_u=1, step_u=undef, min_dist=undef, min_u=undef) =
function bezier_segment_closest_point(curve, pt, max_err=0.01, u=0, end_u=1) =
let(
step = step_u == undef? (end_u-u)/(len(curve)*2) : step_u,
t_u = min(u, end_u),
dist = norm(bez_point(curve, t_u)-pt),
md = (min_dist==undef || dist<min_dist)? dist : min_dist,
mu = (min_dist==undef || dist<min_dist)? t_u : min_u
)
(u>(end_u-step/2))? (
(step<max_err)? mu : bezier_segment_closest_point(curve, pt, max_err, max(0, mu-step/2), min(1, mu+step/2), step/2)
) : (
bezier_segment_closest_point(curve, pt, max_err, u+step, end_u, step, md, mu)
);
steps = len(curve)*3,
path = [for (i=[0:1:steps]) let(v=(end_u-u)*(i/steps)+u) [v, bez_point(curve, v)]],
bracketed = concat([path[0]], path, [path[len(path)-1]]),
minima_ranges = [
for (pts = triplet(bracketed)) let(
d1=norm(pts.x.y-pt),
d2=norm(pts.y.y-pt),
d3=norm(pts.z.y-pt)
) if(d2<=d1 && d2<=d3) [pts.x.x,pts.z.x]
]
) len(minima_ranges)>1? (
let(
min_us = [
for (minima = minima_ranges)
bezier_segment_closest_point(curve, pt, max_err=max_err, u=minima.x, end_u=minima.y)
],
dists = [for (v=min_us) norm(bez_point(curve,v)-pt)],
min_i = min_index(dists)
) min_us[min_i]
) : let(
minima = minima_ranges[0],
p1 = bez_point(curve, minima.x),
p2 = bez_point(curve, minima.y),
err = norm(p2-p1)
) err<max_err? mean(minima) :
bezier_segment_closest_point(curve, pt, max_err=max_err, u=minima.x, end_u=minima.y);