I am looking for a software able to ray-trace implicit surfaces (defined by f(x,y,z)=0 for a smooth enough function f) with simulation of diffuse light. Speed is not important (I'm doing high quality renders for short clips, not real time rendering).

  • Surfer can do this but does not have diffuse light.
  • POV-Ray can do this but it is not maintained anymore and diffuse light is complicated to set up (they call this radiosity), very slow, and I do not like the result.
  • Blender can only render a small set of implicit surface, that they call metaballs (they get converted to meshes just before getting rendered), but metaballs are not good enough for what I want to render (think of a perfectly round torus that start getting deformed asymmetrically); its render engine Cycles has the right quality for me.
  • I am currently working with CGAL to create a mesh sequence and Blender to render them with the plug in Stop Motion OBJ to load mesh sequence, but the workflow is cumbersome and takes time, CGAL is very complicated to use, the meshes are not very good, I failed to fix them with CGAL so I fix them through Blender but some of the fixes cannot be applied in batches (through what they call modifiers), and the resulting objects wobble and the normals need to be fixed but I do not know how.

2 Answers 2


Blender can generate meshes from any math function you can define in Python.

The builting addon Add Mesh: Extra Objects as XYZ math functions, Z math functions, and an assortment of regular solids.

Rendering and raytracing can be done with Cycles like you already found out.

  • Thank you. These kind of surfaces are called sometimes called "parametrically" defined as opposed to "implicitly". A parametric equation for a circle is t -> (cos(t), sin(t)) whereas an implicit equation for a circle is x^2 + y^2 = 1. The surfaces I want to draw are implicitly defined ans I am not able to parametrize them.
    – Arnaud
    Apr 8, 2022 at 7:08
  • Ah I see. Blender may still be part of the workflow for rendering part, if you can get the meshes from elsewhere. There is also a Animation Nodes addon which might be able to define implicit functions, but that is above my head. Apr 8, 2022 at 10:52
  • Thanks for this link with a very detailed and beautiful technique. I tried to look at the Animation Nodes addon but did not find there what I look for.
    – Arnaud
    Apr 9, 2022 at 19:03

graphing calculator(graphing calculator) by pacific software does the job i guess

  • Thanks. They do not simulate diffuse light. The web site looks like it is 20 years old.
    – Arnaud
    Jan 16 at 20:29
  • @ARnaud, yes, but the end result is quite robust! Jan 22 at 1:24
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