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 |
---|---|---|---|
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.
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)
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
sphere(radius=1, center=ORIGIN)
f = sphere() # unit sphere
f = sphere(2) # specify radius
f = sphere(1, (1, 2, 3)) # translated sphere
box
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
rounded_box
rounded_box(size, radius)
f = rounded_box((1, 2, 3), 0.25)
wireframe_box
wireframe_box(size, thickness)
f = wireframe_box((1, 2, 3), 0.05)
torus
torus(r1, r2)
f = torus(1, 0.25)
capsule
capsule(a, b, radius)
f = capsule(-Z, Z, 0.5)
capped_cylinder
capped_cylinder(a, b, radius)
f = capped_cylinder(-Z, Z, 0.5)
rounded_cylinder
rounded_cylinder(ra, rb, h)
f = rounded_cylinder(0.5, 0.1, 2)
capped_cone
capped_cone(a, b, ra, rb)
f = capped_cone(-Z, Z, 1, 0.5)
rounded_cone
rounded_cone(r1, r2, h)
f = rounded_cone(0.75, 0.25, 2)
ellipsoid
ellipsoid(size)
f = ellipsoid((1, 2, 3))
pyramid
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 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 one side being positive (outside) and one side being negative (inside).
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.
f = sphere() & slab(z0=-0.5, z1=0.5, x0=0)
cylinder
cylinder(radius)
cylinder
is an infinite cylinder along the Z axis.
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(1)
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(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
rotate(other, angle, vector=Z)
f = capped_cylinder(-Z, Z, 0.5).rotate(pi / 4, X)
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
blend
blend(a, *bs, k=0.5)
f = sphere().blend(box())
dilate
dilate(other, r)
f = example.dilate(0.1)
erode
erode(other, r)
f = example.erode(0.1)
shell
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
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)
extrude_to
extrude_to(a, b, h, e=ease.linear)
f = rectangle(2).extrude_to(circle(1), 2, ease.in_out_quad)
revolve
revolve(other, offset=0)
f = hexagon(1).revolve(3)
3D to 2D Operations
slice
slice(other)
f = example.translate((0, 0, 0.55)).slice().extrude(0.1)