add bspline_curve

src/bspline_curve.scad

@@ -0,0 +1,68 @@
+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)
+    ];