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87 lines
2.0 KiB
Markdown
87 lines
2.0 KiB
Markdown
# bspline_curve
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[B-spline](https://en.wikipedia.org/wiki/B-spline) interpolation using [de Boor's algorithm](https://en.wikipedia.org/wiki/De_Boor%27s_algorithm). This function returns points of the B-spline path. Combined with the `polyline`, `polyline3d` or `hull_polyline3d` module, you can create a B-spline curve.
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**Since:** 2.1
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## Parameters
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- `t_step` : The increment amount along the curve in the [0, 1] range.
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- `degree` : The degree of B-spline. Must be less than or equal to `len(points) - 1`.
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- `points` : A list of `[x, y]` or `[x, y, z]` control points.
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- `knots` : The knot vector. It's a non-decreasing sequence with length `len(points) + degree + 1`. If not provided, a uniform knot vector is generated automatically.
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- `weights` : The weights of control points. If not provided, the weight of each point is 1.
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## Examples
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include <bspline_curve.scad>;
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points = [
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[-10, 0],
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[-5, 5],
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[ 5, -5],
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[ 10, 0]
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];
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color("red") for(p = points) {
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translate(p)
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sphere(0.5);
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}
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// knots: [0, 1, 2, 3, 4, 5, 6]
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// weights: [1, 1, 1, 1]
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for(p = bspline_curve(0.01, 2, points)) {
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translate(p)
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sphere(0.1);
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}
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include <bspline_curve.scad>;
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points = [
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[-10, 0],
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[-5, 5],
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[ 5, -5],
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[ 10, 0]
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];
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// a non-uniform B-spline curve
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knots = [0, 1/8, 1/4, 1/2, 3/4, 4/5, 1];
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color("red") for(p = points) {
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translate(p)
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sphere(0.5);
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}
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for(p = bspline_curve(0.01, 2, points, knots)) {
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translate(p)
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sphere(0.1);
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}
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include <bspline_curve.scad>;
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points = [
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[-10, 0],
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[-5, 5],
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[ 5, -5],
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[ 10, 0]
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];
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// For a clamped B-spline curve, the first knot and the last knot must be of multiplicity degree + 1.
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knots = [0, 0, 0, 1, 2, 2, 2];
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color("red") for(p = points) {
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translate(p)
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sphere(0.5);
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}
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for(p = bspline_curve(0.01, 2, points, knots)) {
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translate(p)
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sphere(0.1);
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}
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