Paraboloid of Scad Cylinders

thingiverse

I discovered a collection of paraboloids on Thingiverse, but none were presented concisely. This 26-line Scad script may be brief, yet it generates a smooth paraboloid, albeit with an extended rendering time - a limitation inherent to OpenScad. It essentially boils down to a loop of Scad cylinders, which can be dissected into cones, the fundamental element employed here. The radius is directly proportional to the square root of the height, a concept that should be mastered by students in calculus 2. However, there's a primary drawback to this approach: OpenScad generates end faces on the chopped cones (the primitive cylinder element), whereas we only require visible surfaces. This necessitates the computer to process numerous invisible surfaces, leading to slow rendering times.