Topology

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

Resources

• GeoJSON
• JTS Topology Suite
• OpenGIS Simple Feature Access
• Cargograms

Mike Bostock (creator of D3, TopoJSON, etc):

• D3
• TopoJSON (Wiki; Gallery)
• How to Infer Topology.
• Line Simplification

Color

Computational Geometry

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

Euclidean space: abstract model of our experience of space.

Cartesian space: algebraic model of Euclidean space.

Euclidean and cartesian geometries are abstract, colorless; to get visuals we have to add color.

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:

Circles

Ellipse as distorted circle; Arbelos; Pappus Chain; Steiner Chain

Polygons

Parallelograms, rhomboids and rhombi, convex and concave, etc. Regular and irregular polygons. Tessellation.

Mixed

Closed figures with straight and curved sides

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.