Types of 3D modeling

what type of modeling software is Sketchup? is there a way to show/see the mathematics of how sketchup displays and represents figures and solids? I am comparing the ways Solidworks and Sketchup construct and represent figures constructed in the software platform. If anyone can point me in the direction of somewhere where I can find more information, that would be best. thanks!

How about Wikipedia?

A Polygon Modeler, where surfaces consist of a finite number of planar polygons (facets). SketchUp supports facets with more than 3 sides (which can be represented as triangles where needed without the user noticing anything).

Alternatives would be Surface Modelers with NURBS or subdivision surfaces, or Procedural Modelers with a sequence of parametrized operations that modify object primitives (CSG).

That is intellectual property of Trimble and unknown. The binary in-memory representation (at runtime) as well as .skp files are not publicly documented.
However, the Ruby API gives a very good idea of how SketchUp’s scene graph is organized. For an efficient representation of faces, see the winged edge datastructure.

Rasterization where each facet is projected into the image plane and filled with color. This is done by passing model data (coordinates) to OpenGL APIs and then receiving pixel data.

An alternative would be raytracing where for each individual pixel the color is determined by sending a ray to the scene (which can be of whatever representation, not necessarily facets).

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Besides … https://en.wikipedia.org/wiki/OpenGL

… also see: https://www.opengl.org/