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Curv: a language for making art using mathematics

By Doug Moen <>

twistor shreks_donut

Curv is a programming language for creating art using mathematics. It's a 2D and 3D geometric modelling tool that supports full colour, animation and 3D printing.


  • Curv is a simple, powerful, dynamically typed, pure functional programming language.
  • Curv is easy to use for beginners. It has a standard library of predefined geometric shapes, plus operators for transforming and combining shapes. These can be plugged together like Lego to make 2D and 3D models.
  • Coloured shapes are represented using Function Representation (F-Rep). They can be infinitely detailed, infinitely large, and any shape or colour pattern that can be described using mathematics can be represented exactly.
  • Curv exposes the full power of F-Rep programming to experts. The standard geometry library is written entirely in Curv. Many of the demos seen on can be reproduced in Curv, using shorter, simpler programs. Experts can package techniques used on shadertoy as high level operations for use by beginners.
  • Rendering is GPU accelerated. Curv programs are compiled into fragment shaders which are executed on the GPU.
  • Curv can export meshes to STL, OBJ and X3D files for 3D printing. The X3D format supports full colour 3D printing (on, at least). These meshes are defect free: watertight, manifold, with no self intersections, degenerate triangles, or flipped triangles.

Getting Started

  • To install the software, see
  • The documentation is here: docs/README.rst.
  • Mailing list: You can join the mailing list using your Google account (or you'll be prompted to create an account). If you don't want to have a Google account, then send email to and I will send you an invitation to join the list.
  • To contribute, see

Hardware Requirements

Linux, MacOS and Windows are supported.

Precisely, Ubuntu LTS and MacOS are currently tested by me, @doug-moen. The Windows port is tested by @ComFreek.

Curv uses OpenGL 3.3. The recommended configuration is a GPU made by Intel, AMD or Nvidia, using a known working GPU driver (see below).

  • On Linux, the GPU needs to be modern enough to be supported by the latest driver version from the GPU vendor. Any GPU from 2012 or later will work. Some older GPUs may work: check the list of supported hardware for the driver.

  • On Macintosh, I recommend the current release of MacOS, or 1 or 2 releases earlier. More precisely, Curv works on any version of MacOS supported by Homebrew. (For older systems, you would need to resurrect an older version of Homebrew. Also, on a pre-Metal system (hardware from 2011 or earlier), some Curv programs may not work correctly due to the GPU.)

  • On Windows, you can use MSYS to build and run a native executable. Alternatively, you can use Windows Subystem for Linux (WSL) for building and running non-natively. However, this alternative is much slower than MSYS since WSL has no GPU rendering support so far, which forces us to fall back to software rendering. See issue #88 for details.

  • Raspberry Pi isn't supported yet.

    • Raspberry Pi 4 support is planned. I believe that Curv could be ported without a great effort. Curv uses X11 and GLX to create an OpenGL context. Curv requests an OpenGL 3.3 context, which isn't supported, but OpenGL ES 3.1 is supported. It might just be a matter of changing the context type, and possibly other small changes. The Raspberry Pi 4 hardware supports all of the features that I plan to use in future releases of Curv.
    • Raspberry Pi 3 won't be supported. At best, it supports OpenGL ES 2.0, which is not good enough: APIs currently used by Curv are missing.
  • On Linux, you have 3 choices:

    • An Nvidia GPU, with the Nvidia closed source driver. Any GPU supported by the latest Nvidia driver will work with Curv.

      The open source Nouveau driver is slow and buggy. Curv runs too slow, with visual glitches. If you don't mind driver hacking, there are some mitigations you can try. See issue #78.

    • An Intel GPU, using the Intel supplied open source driver (based on Mesa). Any GPU supported by the latest Intel driver will work with Curv (this means: Intel HD Graphics or later).

    • An AMD GPU with the open source Mesa driver, version 19.x or later. The AMDGPU-PRO (closed source) driver should work, but I have no testing reports for it.

      Mesa version 18.x or earlier has a bug on AMD (issue #30) which prevents some Curv programs from running.

  • If Curv is invoked within a VNC session, then it might not have direct access to GPU hardware (a slow software renderer is used instead of the GPU). Curv requires a GPU accelerated VNC server. Try TurboVNC combined with VirtualGL.

  • If Curv is run inside a VM, then it might not have direct access to the GPU. You need to ensure that the VM is GPU accelerated.

Why is Curv so picky about GPU drivers and hardware, when [some old 3D software] runs just fine? The answer is that old 3D software relies primarily on triangle meshes for representing and rendering 3D shapes, whereas Curv uses signed distance fields to represent shapes. Signed distance fields are a powerful, hot new technology that is only made practical by modern GPUs. Curv uses shader programs to render shapes, and uses larger and more complex shader programs than [some old 3D software]. This places a heavy and atypical load on the GPU driver and hardware, which old hardware and old, outdated driver software may not be prepared to deal with.

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