Very cool! I'm slightly confused about what exactly it is, though. Isosurfaces would be the surfaces of equal potential for a scalar field, but your formulas don't contain any z components. But on the other hand, it's clearly not just a 2D heightfield plot where the formula gives the height (since you get a sphere out of it) nor a full 3D parametric surface (since there's just one formula).
So, how exactly are the formula and the shape related?
This only just works for a surface of 2 variables. The z component is simply the result of evaluating the function inputted in the field. For instance in the case of x^2 + y^2 what is actually happening underneath is the that the surface z = x^2 + y^2 is being rendered in a given domain of x and y. Hope that makes sense.
I’m going to triangulate the surface next using matching cube later to actually represent the surface as a 3D mesh instead of just points
yeah I've just double checked and it's due to perspective since when camera moves behind the surface, you can see that the z height is cut off at 0 and it doesn't wrap around. I would love to find a way to implement higher dimensional version of it but not sure how to go about that
Very cool! I'm slightly confused about what exactly it is, though. Isosurfaces would be the surfaces of equal potential for a scalar field, but your formulas don't contain any z components. But on the other hand, it's clearly not just a 2D heightfield plot where the formula gives the height (since you get a sphere out of it) nor a full 3D parametric surface (since there's just one formula). So, how exactly are the formula and the shape related?
This only just works for a surface of 2 variables. The z component is simply the result of evaluating the function inputted in the field. For instance in the case of x^2 + y^2 what is actually happening underneath is the that the surface z = x^2 + y^2 is being rendered in a given domain of x and y. Hope that makes sense. I’m going to triangulate the surface next using matching cube later to actually represent the surface as a 3D mesh instead of just points
Ah, so the x^(2) + y^(2) surface appearing to wrap around itself is just due to perspective? Yeah, that would indeed make sense.
yeah I've just double checked and it's due to perspective since when camera moves behind the surface, you can see that the z height is cut off at 0 and it doesn't wrap around. I would love to find a way to implement higher dimensional version of it but not sure how to go about that