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, N)

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

Arg	What it is
bezier	The array of bezier points.
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.

Arg	What it is
p0	The first point.
p1	The second point.
p2	The third point.
r	The radius of the fillet.

fillet_path(pts, fillet)

Takes a 3D polyline path and fillets the corners, returning a 3d cubic (N=3) bezier path.

Arg	What it is
pts	The array of path points.
fillet	Radius of fillets to make.

bezier_close_to_axis(bezier, N)

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

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

bezier_offset(inset, bezier, N)

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
inset	Amount to inset return path towards the X axis.
bezier	The array of bezier points.
N	The number of points in each bezier segment. Default=3 (cubic bezier)

Modules

bezier_polygon(bezier, splinesteps, N)

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

Arg	What it is
bezier	The closed array of 2D bezier points.
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)

linear_extrude_bezier(bezier, splinesteps, N, center, convexity, twist, scale, slices)

Takes a closed 2D bezier path, centered on the XY plane, and extrudes it linearly upwards, forming a solid.

Arg	What it is
bezier	Array of 2D points of a bezier path, to be extruded.
splinesteps	Number of steps to divide each bezier segment into. Default: 16
N	Number of points in each extruded bezier segment. Default: 3 (cubic)
center	If true, the extruded solid is centered vertically at z=0.
convexity	Max number of walls a line could pass through, for preview. Default: 10
twist	Degrees to twist over length of extrusion. Default: 0
scale	Relative size of top of extrusion to the bottom. Default: 1.0
slices	Number of vertical slices to use for twisted extrusion. Default: 20

Example:

bez = [
    [-10,   0],  [-15,  -5],
    [ -5, -10],  [  0, -10],  [ 5, -10],
    [ 10,  -5],  [ 15,   0],  [10,   5],
    [  5,  10],  [  0,  10],  [-5,  10],
    [ 25, -15],  [-10,   0]
];
linear_extrude_bezier(bez, height=20, splinesteps=32);

rotate_extrude_bezier(bezier, slinesteps, N, convexity, angle)

Takes a closed 2D bezier and rotates it around the Z axis, forming a solid. Behaves like rotate_extrude(), except for beziers instead of shapes.

Arg	What it is
bezier	Array of 2D points for the bezier path to rotate.
splinesteps	Number of line segments to divide each bezier segment into.
N	The number of points in each bezier segment. Default=3 (cubic bezier)
convexity	Max number of walls a line could pass through, for preview. Default: 10
angle	Degrees of sweep to make. (Requires OpenSCAD 2016.XX or higher) Default: 360

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]
];
rotate_extrude_bezier(path, splinesteps=32, $fn=180);

revolve_bezier(bezier, splinesteps, N)

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(bezier, splinesteps, N)

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(bezier, offset, splinesteps, N)

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(bezier, splinesteps, N)

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) {
	circle(r=10, center=true);
}

extrude_bezier_along_bezier(bezier, path, pathsteps, bezsteps, bezN, pathN)

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 = [
    [-10,   0],  [-15,  -5],
    [ -5, -10],  [  0, -10],  [ 5, -10],
    [ 10,  -5],  [ 15,   0],  [10,   5],
    [  5,  10],  [  0,  10],  [-5,  10],
    [ 25, -15],  [-10,   0]
];
path = [ [0, 0, 0], [33, 33, 33], [66, -33, -33], [100, 0, 0] ];
extrude_bezier_along_bezier(bez, path, pathsteps=32, bezsteps=16);