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add bspline_curve

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Justin Lin 2019-07-28 17:22:34 +08:00
parent 749a9a95ae
commit f400281c15
1 changed files with 68 additions and 0 deletions
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src/bspline_curve.scad Normal file
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function _bspline_curve_knots(n, degree) =
let(end = n + degree + 1)
[for(i = 0; i < end; i = i + 1) i];
function _bspline_curve_weights(n) = [for(i = 0; i < n; i = i + 1) 1];
function _bspline_curve_ts(ot, degree, knots) =
let(
domain = [degree, len(knots) - 1 - degree],
low = knots[domain[0]],
high = knots[domain[1]],
t = ot * (high - low) + low,
s = _bspline_curve_s(domain[0], domain[1], t, knots)
)
[t, s];
function _bspline_curve_s(s, end, t, knots) =
t >= knots[s] && t <= knots[s+1] ?
s : _bspline_curve_s(s + 1, end, t, knots);
function _bspline_curve_alpha(i, l, t, degree, knots) =
(t - knots[i]) / (knots[i + degree + 1 - l] - knots[i]);
function _bspline_curve_nvi(v, i, l, t, degree, knots) =
let(
alpha = _bspline_curve_alpha(i, l, t, degree, knots)
)
[[for(j = 0; j< 4; j = j + 1) ((1 - alpha) * v[i - 1][j] + alpha * v[i][j])]];
function _bspline_curve_nvl(v, l, s, t, degree, knots, i) =
i == (s - degree - 1 + l) ? v :
let(
nvi = _bspline_curve_nvi(v, i, l, t, degree, knots),
nv = concat(
[for(j = 0; j < i; j = j + 1) v[j]],
nvi,
[for(j = i + 1; j < len(v); j = j + 1) v[j]]
)
)
_bspline_curve_nvl(nv, l, s, t, degree, knots, i - 1);
function _bspline_curve_v(v, s, t, degree, knots, l = 1) =
l > degree + 1 ? v :
let(nv = _bspline_curve_nvl(v, l, s, t, degree, knots, s))
_bspline_curve_v(nv, s, t, degree, knots, l + 1);
function _bspline_curve_interpolate(t, degree, points, knots, weights) =
let(
n = len(points),
kts = is_undef(knots) ? _bspline_curve_knots(n, degree) : knots,
wts = is_undef(weights) ? _bspline_curve_weights(n) : weights,
v = [
for(i = 0; i < n; i = i + 1)
let(p = points[i] * wts[i])
[p[0], p[1], p[2], wts[i]]
],
ts = _bspline_curve_ts(t, degree, kts),
nt = ts[0],
s = ts[1],
nv = _bspline_curve_v(v, s, nt, degree, kts)
)
[for(i = 0; i < 3; i = i + 1) nv[s][i] / nv[s][3]];
function bspline_curve(t_step, degree, points, knots, weights) =
[
for(t = 0; t < 1; t = t + t_step)
_bspline_curve_interpolate(t, degree, points, knots, weights)
];