Concepts

Computational Geometry

That is, computational geometry without regard to rendering. Tons of stuff on Wikipedia about all this stuff.

General (Topology?)

• Sets (open and closed, real and integer, etc.)
• glb, lub, limits
• Distance
• Curvature
• Polytope
• Vertex
• Edge
• Face
• Angle
• etc.

Coordinate Spaces

The set of real pairs, plus axes, plus orientation, plus designated origin, etc.

Geometries

Zero-Dimensional Geometry

Points

Ops

Distance; nearest neighbor; etc.

1-Dimensional

Lines and curves. Curves can be thought of as 1-dimensional objects embedded in 2-dimensional space. After all, curved and straight lines alike have no "height". One way to conceptualize this is the think of each point on a line in terms of distance from the beginning and curvature.

Ops

tangent to a point on a line; perpendicular to a line (general; through a specific point); pct-of-the-way; etc.

2-Dimensional

Surfaces: polygons, parallelograms, convex and concave, etc. Tessellation.

Operations

union, intersection, etc. Smallest containing circle, incircle, centroid, etc.

min/max on each axis;

3-Dimensional

Solids: polyhedra

Transformations

Rendering

Color, line width, etc.