@rich o brien said:
Blender can do this with the Poke tool.
Also displacement modifiers can help.
Thanks for these tips! The poke tool short screen capture tutorial was perfect. My Blender skills are really rusty because I have not used Blender for years. With the Poke functionality and Loop Cuts I can already create really nice parametric surfaces.
The displace modifier could be a really powerful way to create these kind of parametric surfaces. I will need to examine it more. Is it so that I should be able modify the surface geometry to match the displacement texture with the help of this modifier?
So far I have not been able to get it done but I assume that I will need to have the UV mapping and subdivisions correct to get it working.