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:
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.
Have a cool example? Submit a PR!
Note that the dependencies will be automatically installed by setup.py when following the directions below.
- Python 3
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.
Viewing the Mesh
Find and install a 3D mesh viewer for your platform, such as MeshLab.
$ 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.
In all of the below examples,
f is any 3D SDF, such as:
f = sphere()
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)))
The resolution of the mesh is also computed automatically. There are two ways to specify the resolution. You can set the resolution directly with
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
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.
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
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
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:
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.
matplotlib is only imported if this function is called, so it isn’t strictly required as a dependency.
How it Works
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.
- 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.
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
@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.
f = sphere() # unit sphere f = sphere(2) # specify radius f = sphere(1, (1, 2, 3)) # translated sphere
box(size=1, center=ORIGIN, a=None, b=None)
f = box(1) # all side lengths = 1 f = box((1, 2, 3)) # different side lengths f = box(a=(-1, -1, -1), b=(3, 4, 5)) # specified by bounds
f = rounded_box((1, 2, 3), 0.25)
f = wireframe_box((1, 2, 3), 0.05)
f = torus(1, 0.25)
capsule(a, b, radius)
f = capsule(-Z, Z, 0.5)
capped_cylinder(a, b, radius)
f = capped_cylinder(-Z, Z, 0.5)
rounded_cylinder(ra, rb, h)
f = rounded_cylinder(0.5, 0.1, 2)
capped_cone(a, b, ra, rb)
f = capped_cone(-Z, Z, 1, 0.5)
rounded_cone(r1, r2, h)
f = rounded_cone(0.75, 0.25, 2)
f = ellipsoid((1, 2, 3))
f = pyramid(1)
f = tetrahedron(1)
f = octahedron(1)
f = dodecahedron(1)
f = icosahedron(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 is an infinite plane, with one side being positive (outside) and one side being negative (inside).
f = sphere() & plane()
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.
f = sphere() & slab(z0=-0.5, z1=0.5, x0=0)
cylinder is an infinite cylinder along the Z axis.
f = sphere() - cylinder(0.5)
Yes, even text is supported!
text(name, text, width=None, height=None, texture_point_size=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(1)
f = sphere().translate((0, 0, 2))
Note that non-uniform scaling is an inexact SDF.
f = sphere().scale(2) f = sphere().scale((1, 2, 3)) # non-uniform scaling
rotate(other, angle, vector=Z)
f = capped_cylinder(-Z, Z, 0.5).rotate(pi / 4, X)
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)
The following primitives
b are used in all of the following boolean operations.
a = box((3, 3, 0.5)) b = sphere()
The named versions (
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
f = a | b f = union(a, b) # equivalent
f = a - b f = difference(a, b) # equivalent
f = a & b f = intersection(a, b) # equivalent
f = a | b.k(0.25) f = union(a, b, k=0.25) # equivalent
f = a - b.k(0.25) f = difference(a, b, k=0.25) # equivalent
f = a & b.k(0.25) f = intersection(a, b, k=0.25) # equivalent
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 made need to specify a
padding greater than zero to compute a correct SDF.
f = sphere().repeat(3, (1, 1, 0))
circular_array(other, count, offset)
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)
blend(a, *bs, k=0.5)
f = sphere().blend(box())
f = example.dilate(0.1)
f = example.erode(0.1)
f = sphere().shell(0.05) & plane(-Z)
f = example.elongate((0.25, 0.5, 0.75))
f = box().twist(pi / 2)
f = box().bend(1)
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(other, r0, r1, dz, e=ease.linear)
f = box((5, 5, 0.25)).bend_radial(1, 2, -1, ease.in_out_quad)
transition_linear(f0, f1, p0=-Z, p1=Z, e=ease.linear)
f = box().transition_linear(sphere(), e=ease.in_out_quad)
transition_radial(f0, f1, r0=0, r1=1, e=ease.linear)
f = box().transition_radial(sphere(), e=ease.in_out_quad)
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
f = hexagon(1).extrude(1)
extrude_to(a, b, h, e=ease.linear)
f = rectangle(2).extrude_to(circle(1), 2, ease.in_out_quad)
f = hexagon(1).revolve(3)
3D to 2D Operations
f = example.translate((0, 0, 0.55)).slice().extrude(0.1)