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docs/lib2-bspline_curve.md

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+# bspline_curve
+
+[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.
+
+## Parameters
+
+- `t_step` : The increment amount along the curve in the [0, 1] range.
+- `degree` : The degree of B-spline. Must be less than or equal to `len(points) - 1`.
+- `points` : A list of `[x, y]` or `[x, y, z]` control points. 
+- `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.
+- `weights` : The weights of control points. If not provided, the weight of each point is 1.
+
+## Examples
+
+    include <bspline_curve.scad>;
+    
+	points = [
+		[-10, 0],
+		[-5,  5],
+		[ 5, -5],
+		[ 10, 0]
+	];
+
+	color("red") for(p = points) {
+		translate(p) 
+			sphere(0.5);
+	}
+
+    // knots: [0, 1, 2, 3, 4, 5, 6]
+	// weights: [1, 1, 1, 1]
+	for(p = bspline_curve(0.01, 2, points)) {
+		translate(p) 
+			sphere(0.1);
+	}
+
+![bspline_curve](images/lib2-bspline_curve-1.JPG)
+
+    include <bspline_curve.scad>;
+    
+	points = [
+		[-10, 0],
+		[-5,  5],
+		[ 5, -5],
+		[ 10, 0]
+	];
+
+    // a non-uniform B-spline curve
+    knots = [0, 1/8, 1/4, 1/2, 3/4, 4/5, 1];
+    
+	color("red") for(p = points) {
+		translate(p) 
+			sphere(0.5);
+	}
+
+	for(p = bspline_curve(0.01, 2, points, knots)) {
+		translate(p) 
+			sphere(0.1);
+	}
+
+![bspline_curve](images/lib2-bspline_curve-2.JPG)
+
+	include <bspline_curve.scad>;
+		
+	points = [
+		[-10, 0],
+		[-5,  5],
+		[ 5, -5],
+		[ 10, 0]
+	];
+
+	// For a clamped B-spline curve, the first knot and the last knot must be of multiplicity degree + 1. 
+	knots = [0, 0, 0, 1, 2, 2, 2];
+
+	color("red") for(p = points) {
+		translate(p) 
+			sphere(0.5);
+	}
+
+	for(p = bspline_curve(0.01, 2, points, knots)) {
+		translate(p) 
+			sphere(0.1);
+	}
+
+![bspline_curve](images/lib2-bspline_curve-3.JPG)