sdf

Generate 3D meshes based on SDFs (signed distance functions) with a dirt simple Python API.

Special thanks to Inigo Quilez for his excellent documentation on signed distance functions:

Example

Here is a complete example that generates the model shown. This is the canonical Constructive Solid Geometry example. Note the use of operators for union, intersection, and difference.

from sdf import *

f = sphere(1) & box(1.5)

c = cylinder(0.5)
f -= c.orient(X) | c.orient(Y) | c.orient(Z)

f.save('out.stl')

Yes, that's really the entire code! You can 3D print that model or use it in a 3D application.

More Examples

Have a cool example? Submit a PR!

gearlike.py	knurling.py	blobby.py	weave.py

More examples!

pawn.py	steering_wheel.py	spinning_top.py

Requirements

Note that the dependencies will be automatically installed by setup.py when following the directions below.

Python 3
matplotlib
meshio
numpy
Pillow
scikit-image
scipy

Installation

Use the commands below to clone the repository and install the sdf library in a Python virtualenv.

git clone https://github.com/fogleman/sdf.git
cd sdf
virtualenv env
. env/bin/activate
pip install -e .

Confirm that it works:

python examples/example.py # should generate a file named out.stl

You can skip the installation if you always run scripts that import sdf from the root folder.

File Formats

sdf natively writes binary STL files. For other formats, meshio is used (based on your output file extension). This adds support for over 20 different 3D file formats, including OBJ, PLY, VTK, and many more.

Viewing the Mesh

Find and install a 3D mesh viewer for your platform, such as MeshLab.

I have developed and use my own cross-platform mesh viewer called meshview (see screenshot). Installation is easy if you have Go and glfw installed:

$ brew install go glfw # on macOS with homebrew
$ go get -u github.com/fogleman/meshview/cmd/meshview

Then you can view any mesh from the command line with:

$ meshview your-mesh.stl

See the meshview README for more complete installation instructions.

On macOS you can just use the built-in Quick Look (press spacebar after selecting the STL file in Finder) in a pinch.

API

In all of the below examples, f is any 3D SDF, such as:

f = sphere()

Bounds

The bounding box of the SDF is automatically estimated. Inexact SDFs such as non-uniform scaling may cause issues with this process. In that case you can specify the bounds to sample manually:

f.save('out.stl', bounds=((-1, -1, -1), (1, 1, 1)))

Resolution

The resolution of the mesh is also computed automatically. There are two ways to specify the resolution. You can set the resolution directly with step:

f.save('out.stl', step=0.01)
f.save('out.stl', step=(0.01, 0.02, 0.03)) # non-uniform resolution

Or you can specify approximately how many points to sample:

f.save('out.stl', samples=2**24) # sample about 16M points

By default, samples=2**22 is used.

Tip: Use the default resolution while developing your SDF. Then when you're done, crank up the resolution for your final output.

Fast Quadric Mesh Simplification

Simplification of the mesh can be accomplished at the same time by using:

f.save('out.stl', samples=2**24, simplify=True)
# to simplify (remove 80%) of the mesh after rendering, use:
f.save('out.stl', samples=2**24, simplify=True, simp_ratio=0.2)
# to change the simplification agressive value use
f.save('out.stl', samples=2**24, simplify=True, simp_agressive=5)

or generate once and then simplify afterwards:

points = f.generate()
points = simplify(points)
save_mesh("test_output.stl",points)  # save as STL file
#save_mesh("test_output.stp",points)  # save as STEP file

By default, simp_ratio=0.5, simp_agressive=7 is used.

For more information see https://github.com/sp4cerat/Fast-Quadric-Mesh-Simplification

Batches

The SDF is sampled in batches. By default the batches have 32**3 = 32768 points each. This batch size can be overridden:

f.save('out.stl', batch_size=64) # instead of 32

The code attempts to skip any batches that are far away from the surface of the mesh. Inexact SDFs such as non-uniform scaling may cause issues with this process, resulting in holes in the output mesh (where batches were skipped when they shouldn't have been). To avoid this, you can disable sparse sampling:

f.save('out.stl', sparse=False) # force all batches to be completely sampled

Worker Threads

The SDF is sampled in batches using worker threads. By default, multiprocessing.cpu_count() worker threads are used. This can be overridden:

f.save('out.stl', workers=1) # only use one worker thread

Without Saving

You can of course generate a mesh without writing it to an STL file:

points = f.generate() # takes the same optional arguments as `save`
print(len(points)) # print number of points (3x the number of triangles)
print(points[:3]) # print the vertices of the first triangle

If you want to save an STL after generate, just use:

write_binary_stl(path, points)

Reading and Saving Mesh Files

To read the points from a mesh file use read_mesh(file) and to save use save_mesh(file, points). The format of the file is determined by the suffix. For a full list of supported formats, refer to meshio. The additonal STEP file format is only available for saving.

An example of reading a STL file, simplifying it, and then writing it out as a STEP file:

points = read_mesh("my_mesh.stl")  # This reads a STL file
points = simplify(points)          # Reduce the mesh to about half
save_mesh("my_mesh.stp",points)    # Write the mesh out to a STEP file

Visualizing the SDF

You can plot a visualization of a 2D slice of the SDF using matplotlib. This can be useful for debugging purposes.

f.show_slice(z=0)
f.show_slice(z=0, abs=True) # show abs(f)

You can specify a slice plane at any X, Y, or Z coordinate. You can also specify the bounds to plot.

Note that matplotlib is only imported if this function is called, so it isn't strictly required as a dependency.

How it Works

The code simply uses the Marching Cubes algorithm to generate a mesh from the Signed Distance Function.

This would normally be abysmally slow in Python. However, numpy is used to evaluate the SDF on entire batches of points simultaneously. Furthermore, multiple threads are used to process batches in parallel. The result is surprisingly fast (for marching cubes). Meshes of adequate detail can still be quite large in terms of number of triangles.

The core "engine" of the sdf library is very small and can be found in mesh.py.

In short, there is nothing algorithmically revolutionary here. The goal is to provide a simple, fun, and easy-to-use API for generating 3D models in our favorite language Python.

Files

sdf/d2.py: 2D signed distance functions
sdf/d3.py: 3D signed distance functions
sdf/dn.py: Dimension-agnostic signed distance functions
sdf/ease.py: Easing functions that operate on numpy arrays. Some SDFs take an easing function as a parameter.
sdf/mesh.py: The core mesh-generation engine. Also includes code for estimating the bounding box of an SDF and for plotting a 2D slice of an SDF with matplotlib.
sdf/progress.py: A console progress bar.
sdf/stl.py: Code for writing a binary STL file.
sdf/text.py: Generate 2D SDFs for text (which can then be extruded)
sdf/util.py: Utility constants and functions.

SDF Implementation

It is reasonable to write your own SDFs beyond those provided by the built-in library. Browse the SDF implementations to understand how they are implemented. Here are some simple examples:

@sdf3
def sphere(radius=1, center=ORIGIN):
    def f(p):
        return np.linalg.norm(p - center, axis=1) - radius
    return f

An SDF is simply a function that takes a numpy array of points with shape (N, 3) for 3D SDFs or shape (N, 2) for 2D SDFs and returns the signed distance for each of those points as an array of shape (N, 1). They are wrapped with the @sdf3 decorator (or @sdf2 for 2D SDFs) which make boolean operators work, add the save method, add the operators like translate, etc.

@op3
def translate(other, offset):
    def f(p):
        return other(p - offset)
    return f

An SDF that operates on another SDF (like the above translate) should use the @op3 decorator instead. This will register the function such that SDFs can be chained together like:

f = sphere(1).translate((1, 2, 3))

Instead of what would otherwise be required:

f = translate(sphere(1), (1, 2, 3))

Remember, it's Python!

Remember, this is Python, so it's fully programmable. You can and should split up your model into parameterized sub-components, for example. You can use for loops and conditionals wherever applicable. The sky is the limit!

See the customizable box example for some starting ideas.

Function Reference

3D Primitives

sphere

Draw a sphere with the radius centered around center, by default this is the origin (0,0,0).

sphere(radius=1, center=ORIGIN)

f = sphere() # unit sphere
f = sphere(2) # specify radius
f = sphere(1, (1, 2, 3)) # translated sphere

box

Draw a 3D box with sides specified centered around center, by default this is the origin (0,0,0).

box(size=1, center=ORIGIN, a=None, b=None)

f = box(1) # all side lengths = 1, like a cube
f = box((1, 2, 3)) # different side lengths
f = box(a=(-1, -1, -1), b=(3, 4, 5)) # specified by bounds

rounded_box

Draw a 3D rounded box with sides specified centered around center, by default this is the origin (0,0,0). The radius of curvature is specified by radius.

rounded_box(size, radius, center=ORIGIN)

f = rounded_box((1, 2, 3), 0.25)

wireframe_box

Draw a 3D box with round wires (diameter is specified by thickness) and centered around center, by default this is the origin (0,0,0). The radius of curvature is specified by radius.

wireframe_box(size, thickness)

f = wireframe_box((1, 2, 3), 0.05)

torus

torus is like a doughnut shape, like a circle with radius, r2, rotated around the Z axis at a radius, r1, from the center.

torus(r1, r2)

f = torus(1, 0.25)

capsule

capsule is a cylinder with rounded ends extending from -Z to Z and having the radius, radius.

capsule(a, b, radius)

f = capsule(-Z, Z, 0.5)

capped_cylinder

capped_cylinder is a flat ended cylinder extending from a to b, both 3D vectors, and having the radius, radius.

capped_cylinder(a, b, radius)

# note: Z = np.array((0, 0, 1))
f = capped_cylinder(-Z, Z, 0.5)

rounded_cylinder

rounded_cylinder is a flat ended cylinder with curved edges extending from a to b, scalers along the Z axis, and having the radius, ra, and the edges having a radius of rb.

rounded_cylinder(ra, rb, h)

f = rounded_cylinder(0.5, 0.1, 2)

capped_cone

capped_cone is a flat ended cone extending from a to b, both 3D vectors, and having the radii, ra and rb.

capped_cone(a, b, ra, rb)

# note: Z = np.array((0, 0, 1))
f = capped_cone(-Z, Z, 1, 0.5)

rounded_cone

rounded_cone is a hemisphere ended cone extending along the Z axis from 0 to h, and having the radii, r1 and r2.

rounded_cone(r1, r2, h)

f = rounded_cone(0.75, 0.25, 2)

ellipsoid

ellipsoid is like a distored sphere centered at the origin, size is specified by a 3D array of scalars.

ellipsoid(size)

f = ellipsoid((1, 2, 3))

pyramid

pyramid is the simplest 3D flat sided object, consisting of one side being a triangle at the base and 3 more equal sized triangles matching those edges and meeting at the point h along the Z axis.

pyramid(h)

f = pyramid(1)

Platonic Solids

tetrahedron

tetrahedron(r)

f = tetrahedron(1)

octahedron

octahedron(r)

f = octahedron(1)

dodecahedron

dodecahedron(r)

f = dodecahedron(1)

icosahedron

icosahedron(r)

f = icosahedron(1)

Infinite 2D Primitives

The following SDFs extend to infinity in some or all axes. They can only effectively be used in combination with other shapes, as shown in the examples below.

line

line(normal=UP, point=ORIGIN)

line is an infinite cut line, with the positive side being inside and the negative side being outside.

f = (circle() & line()).extrude(0.1)

crop

crop(x0=None, y0=None, x1=None, y1=None, k=None)

crop is useful for cutting a shape on one or more axis-aligned planes. Note that one can accomplish the same affect by four line cuts with axis normals and points defined on the edges.

f = (circle() & crop(y0=-0.5, y1=0.5, x0=0)).extrude(0.1)

Infinite 3D Primitives

The following SDFs extend to infinity in some or all axes. They can only effectively be used in combination with other shapes, as shown in the examples below.

plane

plane(normal=UP, point=ORIGIN)

plane is an infinite plane, with the positive side being inside and the negative side being outside.

f = sphere() & plane()

slab

slab(x0=None, y0=None, z0=None, x1=None, y1=None, z1=None, k=None)

slab is useful for cutting a shape on one or more axis-aligned planes. Note that the same effect can be accomplished by using multiple planes cutting with a normal starting at points on the cut plane.

f = sphere() & slab(z0=-0.5, z1=0.5, x0=0)

cylinder

cylinder(radius)

cylinder is an infinite cylinder along the Z axis. This is useful for cutting a hole in an object (- operation) or widdling down an object so it fits within a cylinder (& operation).

f = sphere() - cylinder(0.5)

Text

Yes, even text is supported!

text(font_name, text, width=None, height=None, pixels=PIXELS, points=512)

FONT = 'Arial'
TEXT = 'Hello, world!'

w, h = measure_text(FONT, TEXT)

f = rounded_box((w + 1, h + 1, 0.2), 0.1)
f -= text(FONT, TEXT).extrude(0.2).k(0.05)

Note: PIL.ImageFont, which is used to load fonts, does not search for the font by name on all operating systems. For example, on Ubuntu the full path to the font has to be provided. (e.g. /usr/share/fonts/truetype/freefont/FreeMono.ttf)

Images

Image masks can be extruded and incorporated into your 3D model.

image(path_or_array, width=None, height=None, pixels=PIXELS)

IMAGE = 'examples/butterfly.png'

w, h = measure_image(IMAGE)

f = rounded_box((w * 1.1, h * 1.1, 0.1), 0.05)
f |= image(IMAGE).extrude(1) & slab(z0=0, z1=0.075)

Positioning

translate

translate(other, offset)

f = sphere().translate((0, 0, 2))

scale

Scale and figure larger or smaller with factor. Unity, 1.0, will leave the object the same and smaller numbers will shrink, such as 0.5 which scales to half the size, and 2.0 which scales to double the size.

scale(other, factor)

Note that non-uniform scaling is an inexact SDF.

f = sphere().scale(2)
f = sphere().scale((1, 2, 3)) # non-uniform scaling

rotate and rotateD

Given an angle and rotation vector, rotate the figure by angle in radians (for rotate) or degrees (for rotateD), around the vector axis. So a rotation around Z will translate points around the X-Y plane and leave the Z values the same.

rotate(other, angle, vector=Z) rotateD(other, angle_in_degrees, vector=Z)

f = capped_cylinder(-Z, Z, 0.5).rotate(pi / 4, X)
f = capped_cylinder(-Z, Z, 0.5).rotateD(45, X)

mirror

This function reflects the 3d image over the plane specified by the vector. For example, using Z will reflect across the Z plane mapping every positive Z point to it's negative counterpart and vice versa.

mirror(other, vector, center=ORIGIN)

f = circle(3).taper_extrude(3,1).translate((0,0,-3))
# draw it again upside down
f |= circle(3).taper_extrude(3,1).translate((0,0,-3)).mirror([0,0,1])

mirror_copy

mirror_copy(other, vector, center=ORIGIN)

f = circle(3).taper_extrude(3,1).translate((0,0,-3)).mirror_copy([0,0,1])

orient

orient(other, axis)

orient rotates the shape such that whatever was pointing in the +Z direction is now pointing in the specified direction.

c = capped_cylinder(-Z, Z, 0.25)
f = c.orient(X) | c.orient(Y) | c.orient(Z)

Boolean Operations

The following primitives a and b are used in all of the following boolean operations.

a = box((3, 3, 0.5))
b = sphere()

The named versions (union, difference, intersection) can all take one or more SDFs as input. They all take an optional k parameter to define the amount of smoothing to apply. When using operators (|, -, &) the smoothing can still be applied via the .k(...) function.

union

f = a | b
f = union(a, b) # equivalent

difference

f = a - b
f = difference(a, b) # equivalent

intersection

f = a & b
f = intersection(a, b) # equivalent

smooth_union

f = a | b.k(0.25)
f = union(a, b, k=0.25) # equivalent

smooth_difference

f = a - b.k(0.25)
f = difference(a, b, k=0.25) # equivalent

smooth_intersection

f = a & b.k(0.25)
f = intersection(a, b, k=0.25) # equivalent

Repetition

repeat

repeat(other, spacing, count=None, padding=0)

repeat can repeat the underlying SDF infinitely or a finite number of times. If finite, the number of repetitions must be odd, because the count specifies the number of copies to make on each side of the origin. If the repeated elements overlap or come close together, you may need to specify a padding greater than zero to compute a correct SDF.

f = sphere().repeat(3, (1, 1, 0))

circular_array

circular_array(other, count, offset)

circular_array makes count copies of the underlying SDF, arranged in a circle around the Z axis. offset specifies how far to translate the shape in X before arraying it. The underlying SDF is only evaluated twice (instead of count times), so this is more performant than instantiating count copies of a shape.

f = capped_cylinder(-Z, Z, 0.5).circular_array(8, 4)

Miscellaneous

Some of the functions demonstrated below use an example as a starting point:

f = sphere(1) & box(1.5)
c = cylinder(0.5)
f -= c.orient(X) | c.orient(Y) | c.orient(Z)
example = f

blend

Blending of two objects using the scalar distance function between values of two objects with scalar k.

blend(a, *bs, k=0.5)

f = sphere().blend(box())

dilate

Decrease the scalar distance value by radius, r, making the object edges dilate, or appear to inflate.

dilate(other, r)

f = example.dilate(0.1)

erode

Increase the scalar distance value by radius, r, making the object edges erode, or appear to deflate.

erode(other, r)

f = example.erode(0.1)

shell

Create a shell at every boundary, where the scalar distance value crosses positive and negative values. The thickness of the shell created on the edge is defined by thickness.

shell(other, thickness)

f = sphere().shell(0.05) & plane(-Z)

elongate

elongate(other, size)

f = example.elongate((0.25, 0.5, 0.75))

twist

twist(other, k)

f = box().twist(pi / 2)

bend

bend(other, k)

f = box().bend(1)

bend_linear

bend_linear(other, p0, p1, v, e=ease.linear)

f = capsule(-Z * 2, Z * 2, 0.25).bend_linear(-Z, Z, X, ease.in_out_quad)

bend_radial

bend_radial(other, r0, r1, dz, e=ease.linear)

f = box((5, 5, 0.25)).bend_radial(1, 2, -1, ease.in_out_quad)

transition_linear

transition_linear(f0, f1, p0=-Z, p1=Z, e=ease.linear)

f = box().transition_linear(sphere(), e=ease.in_out_quad)

transition_radial

transition_radial(f0, f1, r0=0, r1=1, e=ease.linear)

f = box().transition_radial(sphere(), e=ease.in_out_quad)

wrap_around

This function will take an XYZ cartesian coordinate space and convert into polar coordinates where the X axis is mapped into the radial axis, Y axis into the angular, and Z is left alone.

wrap_around(other, x0, x1, r=None, e=ease.linear)

FONT = 'Arial'
TEXT = ' wrap_around ' * 3
w, h = measure_text(FONT, TEXT)
f = text(FONT, TEXT).extrude(0.1).orient(Y).wrap_around(-w / 2, w / 2)

2D to 3D Operations

extrude

extrude(other, h)

f = hexagon(1).extrude(1)

rounded_extrude

Extrude a 2D and add round edges on border.

rounded_extrude(other, h, radius=0)

f = hexagon(10).rounded_extrude(5, radius=2)

Note: when using a negative value, the rounding will go in the opposite direction.

f = hexagon(10).rounded_extrude(5, radius=-2)

rounded_extrude_stack

Extrude two 2D images and add round edges on border and at the intersection weld the joints.

rounded_extrude_stack(other_bottom, other_top, height_bottom, height_top, radius)

To increase tensile strength, sometimes it is useful to add more material at joints, so increasing the weld_radius will add more fill.

rounded_extrude_stack(other_bottom, other_top, height_bottom, height_top, radius, weld_radius)

f = rounded_extrude_stack(rectangle([16,6]),rectangle([6,16]), 5, 7, radius=1)
# to alter the weld radius between the two objects:
f = rounded_extrude_stack(rectangle([16,6]),rectangle([6,16]), 5, 7, radius=1, weld_radius=2):

extrude_to

extrude_to takes two different 2D objects and blends them together by an ease operator, by default it is linear, so as to make a smooth transition between the two objects.

extrude_to(a, b, h, e=ease.linear)

f = rectangle(2).extrude_to(circle(1), 2, ease.in_out_quad)

taper_extrude

In taper_extrude, slope is the amount of contracting per unit Z over the height of the extrude. A negative value will cause the image to expand and corners will become a larger rounded edge.

taper_extrude(other, height, slope=0, e=ease.linear)

f = rectangle(10).taper_extrude(6, slope=0.1)

revolve

revolve takes a 2D object and rotates it around the Z axis. Offset is how far the center point is moved away from the origin on the XY plane.

revolve(other, offset=0)

f = hexagon(1).revolve(3)

helix_revolve

helix_revolve will take a 2D object and rotate it around the Z axis while linearly moving in a helix toward positive Z. A practical use for this is to create threads. By negating pitch, one can reverse the thread, changing the rotation from right-handed to left-handed.

helix_revolve(other, offset=0, pitch=1, rotations=1)

f = polygon([[3,0],[4,.5],[4,1],[3,1.5]]).helix_revolve(pitch=2, rotations=4.3)

3D to 2D Operations

slice

slice(other)

f = example.translate((0, 0, 0.55)).slice().extrude(0.1)

2D Primitives

Note: The examples 2D functions below are called and then extruded to show how to convert a 2D to a 3D.

circle

circle(radius=1, center=ORIGIN)

f = circle(2).extrude(0.1)

rectangle

rectangle(size=1, center=ORIGIN, a=None, b=None)

f = rectangle([2,1]).extrude(0.1)
# or you can specify the corners:
f = rectangle(a=[-2,-1],b=[2,1]).extrude(0.1)

rounded_rectangle

rounded_rectangle(size=1, radius=0.1, center=ORIGIN, a=None, b=None)

f = rounded_rectangle([2,1],0.2).extrude(0.1)
# or you can specify the corners:
f = rectangle(a=[-2,-1],b=[2,1],radius=0.2).extrude(0.1)

equilateral_triangle

equilateral_triangle(r, center=ORIGIN)

f = equilateral_triangle(3).extrude(0.1)

hexagon

hexagon(r)

f = hexagon(2).extrude(0.1)

equilateral_polygon

equilateral_polygon(n, r)

equilateral_polygon makes a shape with equal sides, for example n=3 is a triangle, n=4 is square, n=5 is a pentagon, and so forth. Note: The right edge will always be vertical and the radius is the distance to the center of a flat face.

f = equilateral_polygon(5,10).extrude(0.1)

rounded_x

rounded_x(w, r)

f = rounded_x(10,2).extrude(0.1)

rounded_cog

rounded_cog(outer_r, cog_r, num)

f = rounded_cog(38, 6, 14).extrude(0.1)

polygon

polygon(points)

f = polygon([[-16,-16],[14,-8],[3,4],[0,12]]).extrude(0.1)

rounded_polygon

The points provided to the curve polygon are in the form of [x,y,curve_radius] where a curve_radius value of negative will create an arc in the left hand rotation and positive in the right hand rotation. A curve_radius of 0 implies a straight line.

rounded_polygon(points_with_curve)

f = rounded_polygon([[-2,0,0],[0,2,-2**0.5],[2,0,-2**0.5],[0,-2,0]]).extrude(0.1)

Rounded Polygon Operations

round_polygon_corners

This function will change When matching three curves, concave-convex-concave or convex-concave-convex, this function will move the points along the outer curves in order to match the center curve exactly.

round_polygon_corners(points_with_curve, radius) round_polygon_corners(points_with_curve, [radii...], [index_of_vertex...])

pts1 = [[10,0,0],[1,1,-20],[3,10,0]]
pts2 = [[-10,0,0],[-1,1,20],[-3,10,0]]
pts3 = [[10,-10,0],[1,-9,-18],[3,0,20]]
pts4 = [[-10,-10,0],[-1,-9,-18],[-3,0,20]]
f = rounded_polygon(pts1).shell(0.1).extrude(0.1)
f |= rounded_polygon(pts2).shell(0.1).extrude(0.1)
f |= rounded_polygon(pts3).shell(0.1).extrude(0.1)
f |= rounded_polygon(pts4).shell(0.1).extrude(0.1)
rpts1 = round_polygon_corners(pts1,1)
rpts2 = round_polygon_corners(pts2,1)
rpts3 = round_polygon_corners(pts3,1)
rpts4 = round_polygon_corners(pts4,1)
f |= rounded_polygon(rpts1).extrude(0.1)
f |= rounded_polygon(rpts2).extrude(0.1)
f |= rounded_polygon(rpts3).extrude(0.1)
f |= rounded_polygon(rpts4).extrude(0.1)

round_polygon_smooth_ends

When matching three curves, concave-convex-concave or convex-concave-convex, this function will move the points along the outer curves in order to match the center curve exactly.

round_polygon_smooth_ends(index_of_side_to_modify)

pts = [[3,0,0],[2,0,-0.75],[1,0,2],[0,0,-0.75],[0,1,0],[3,1,0]]
f = rounded_polygon(pts).translate((0,3)).shell(0.1).extrude(0.1)
rpts = round_polygon_smooth_ends(pts,[1])
f |= rounded_polygon(rpts).shell(0.1).extrude(0.1)

2D Operations

edge

edge(width)

f = rounded_polygon([
   [-4,-1,0],[-6,-1,-1],[-6,1,-1],  [-4,1,-1], [-1,1,0],  # Left
   [-1,4,0], [-1,6,-1], [1,6,-1],   [1,4,-1],  [1,1,0],   # Top
   [4,1,0],  [6,1,-1],  [6,-1,-1],  [4,-1,-1], [1,-1,0],  # Right
   [1,-8,0], [1,-10,-1],[-1,-10,-1],[-1,-8,-1],[-1,-1,0]  # Bottom
   ]).edge(0.1).extrude(0.1)

mirror

mirror(other, axis=Y, center=ORIGIN)

s = circle(2).translate((3,3))
# draw another on the side, mirrored over the negative X
s |= circle(2).translate((3,3)).mirror([1,0])
f = s.extrude(0.1)

mirror_copy

mirror_copy(other, axis=Y, center=ORIGIN)

s = circle(2).translate((3,3)).mirror_copy([1, 0.1])
f = s.extrude(0.1)

Math Functions

Standard math routines provided by Python are available, and additional functions available are:

Trigonometric

arc_sinD(slope) arc_cosD(slope) arc_tanD(slope) arc_tan2D(y,x)

Returns an angle in degrees.

sinD(ang) cosD(ang) tanD(ang)

Takes degrees and returns the trigonometric value.

Building GCODE output

To make GCODE files, one needs to choose between which method to print, either additive method (such as plastic printing) or subtractive (such as CNC milling). These two interfaces rely on external packages, in particular slic3r and pycam. To call them, use the following functions:

f = sphere(1)
points = f.generate(samples=None,step=resolution,batch_size=48, simplify=True, simp_agressive=7,simp_ratio=0.1)

The two methods below use the existing python code for generating a figure.

Slic3r

# Write out gcode for this object for additive manufacturing
# Usage and details can be found https://manual.slic3r.org/
slic3r("steeringwheel.gcode",points,options={'layer-height': 0.2})

#slic3r("steeringwheel.gcode",points,options={
#  'layer-height': 0.2,
#  'nozzle-diameter': 0.35,
#  'filament-diameter': 2.85,
#  'temperature': 185,
#  'first-layer-temperature': 195,
#  'layer-height': 0.2,
#  })

PyCAM

# Write out gcode for this object for cnc manufacturing
pycam("pycnc_steeringwheel_rough.yaml",points)

an example yaml file is provided in the pycam project here:

https://raw.githubusercontent.com/eddeliu/pycam-1/master/yaml_flow_example.yml