beziers.scad

Bezier functions and modules.

Functions

bez_point(curve, u)

Formula to calculate points on an N-point bezier curve. N=len(curve)-1

Arg	What it is
curve	An array of control point vectors.
u	Part of curve to get point of. 0 <= u <= 1

bezier_polyline(bezier, splinesteps=16, N=3)

Takes an array of bezier points and converts it into a 3D polyline.

Arg	What it is
splinesteps	The number of line segments to divide each bezier segment into.
N	The number of points in each bezier segment. Default=3 (cubic bezier)

bezier_polygon(bezier, splinesteps=16)

Takes a closed 2D bezier path, and creates a 2D polygon from it.

Arg	What it is
splinesteps	The number of line segments to divide each bezier segment into.
N	The number of points in each bezier segment. Default=3 (cubic bezier)

fillet3pts(p0, p1, p2, r)

Generate a cubic (N=3) bezier curve to fillet 2 line segments between 3 points. Returns two path points with surrounding cubic (N=3) bezier control points.

fillet_path(pts, fillet)

Takes a 3D polyline path and fillets it into a 3d cubic (N=3) bezier path.

bezier_close_to_axis(bezier, N=3)

Takes a 2D bezier path and closes it to the X axis.

Arg	What it is
N	The number of points in each bezier segment. Default=3 (cubic bezier)

bezier_offset(inset, bezier, N=3)

Takes a bezier curve and closes it with a matching path that is lowered by a given amount towards the X axis.

Arg	What it is
N	The number of points in each bezier segment. Default=3 (cubic bezier)

Modules

revolve_bezier()

Takes a closed 2D bezier and rotates it around the X axis, forming a solid.

Arg	What it is
bezier	Array of points for the bezier path to rotate.
splinesteps	Number of segments to divide each bezier segment into.
N	The number of points in each bezier segment. Default=3 (cubic bezier)

Example:

path = [
    [  0, 10], [ 50,  0], [ 50, 40],
    [ 95, 40], [100, 40], [100, 45],
    [ 95, 45], [ 66, 45], [  0, 20],
    [  0, 12], [  0, 12], [  0, 10],
    [  0, 10]
];
revolve_bezier(path, splinesteps=32, $fn=180);

revolve_bezier_solid_to_axis()

Takes a 2D bezier and rotates it around the X axis, forming a solid.

Arg	What it is
bezier	array of points for the bezier path to rotate.
splinesteps	number of segments to divide each bezier segment into.
N	The number of points in each bezier segment. Default=3 (cubic bezier)

Example:

path = [ [0, 10], [33, 10], [66, 40], [100, 40] ];
revolve_bezier_solid_to_axis(path, splinesteps=32, $fn=72);

revolve_bezier_offset_shell()

Takes a 2D bezier and rotates it around the X axis, into a hollow shell.

Arg	What it is
bezier	array of points for the bezier path to rotate.
offset	the thickness of the created shell.
splinesteps	number of segments to divide each bezier segment into.
N	The number of points in each bezier segment. Default=3 (cubic bezier)

Example:

path = [ [0, 10], [33, 10], [66, 40], [100, 40] ];
revolve_bezier_offset_shell(path, offset=1, splinesteps=32, $fn=72);

extrude_2d_shapes_along_bezier()

Extrudes 2D children along a bezier path.

Arg	What it is
bezier	array of points for the bezier path to extrude along.
splinesteps	number of segments to divide each bezier segment into.
N	The number of points in each bezier segment. Default=3 (cubic bezier)

Example:

path = [ [0, 0, 0], [33, 33, 33], [66, -33, -33], [100, 0, 0] ];
extrude_2d_shapes_along_bezier(path, splinesteps=32) {
    circle(r=10, center=true);
}

extrude_bezier_along_bezier()

Takes a closed 2D bezier path, centered on the XY plane, and extrudes it perpendicularly along a 3D bezier path, forming a solid.

Arg	What it is
bezier	Array of points of a bezier path, to be extruded.
path	Array of points of a bezier path, to extrude along.
pathsteps	number of steps to divide each path segment into.
bezsteps	number of steps to divide each bezier segment into.
bezN	The number of points in each extruded bezier segment. Default=3 (cubic bezier)
pathN	The number of points in each path bezier segment. Default=3 (cubic bezier)

Example:

bez = [
    [-15,   0],  [ 25, -15],
    [ -5,  10],  [  0,  10],  [ 5,  10],
    [ 10,   5],  [ 15,   0],  [10,  -5],
    [  5, -10],  [  0, -10],  [-5, -10],
    [-10,  -5],  [-15,   0]
];
path = [ [0, 0, 0], [33, 33, 33], [66, -33, -33], [100, 0, 0] ];
extrude_bezier_along_bezier(bez, path, pathsteps=64, bezsteps=32);