The curved surfaces in SketchUp are not mathematically accurate, so volumetric calculations on curved surfaces aren’t exact.

I’d like to propose a curved surface toolset that makes mathematical curves and surfaces to increase the accuracy of SketchUp. I’m not sure what types of tools would be in the toolset or how SketchUp could make accurate non-polygonal spheres, but I’d like a minimal amount of tools (for ease of use) that can make almost any type of curved surface. A sphere only has one measurement, the radius, so SketchUp shouldn’t need to store the coordinates of all the vertices in a sphere if it only need a radius to define the sphere. The new SketchUp sphere could be a single two-sided surface instead of being made of many faces. I’m not sure if this would be possible, but for more complex geometry, maybe SketchUp could store mathematical equations to define the curved surfaces. To clarify, the user wouldn’t have to input mathematical equations, but SketchUp would store curved geometry with mathematical equations in it’s memory. Equations are usually shorter than a list of coordinates for thousands of points.