3D Modeling

There are many ways to create a 3D form, I feature on a few basic ones:

  • constructive solid geometry (CSG): union, intersection, difference, exclusive
  • extruding linear and rotational
  • hulling

Constructive Solid Geometry (CSG)

One of the easiest approaches to 3D modeling comes with CSG which provides 3 main operations:

  • union
  • intersection
  • difference

Union, Intersection, Difference

Given a sphere and a cube to illustrate the 3 main CSG operations:

The results are a single solid or mesh, possibly discontinuous.


As part of a discussion with Brian Spilsbury, who conceived this operation as ‘assembly’, I see it as part of the CSG fundamentals as exclusive as chained operation of difference of multiple parts, for example a sphere and two cubes:

As in material or physical reality no part can occupy the same space at the same time, the parts give way or yield to each other:

The result of exclusive operation are multiple solids or meshs.


The main idea is using a 2D shape to create a 3D shape or form:

Linear Extruding

A 2D shape or form in X, Y space is extruded into the 3rd dimension Z, even with a slight twist as well:


Linear extruding allows to create:

  • cube, cylinder, prism and
  • twisted variants of such

Rotate Extruding

Another intuitive approach is to use a 2D shape or form and rotate or sweep it around an axis, and describe a 3D form as such, for example by using a circle or square as 2D form, and rotate or sweep it in different ways:

Rotate extruding allows to create:

  • cube, sphere, cone, torus and
  • many special cases of such


A more advanced operation is hulling points or other forms:

Other Operations

  • point cloud: scanning an object or environment
  • sculpting like Blender or ZBrush: natural forms

Continue to explore 3D Modeling Software, where some of those described operations are implemented.