One of my favorite representations of geometry is the combination of explicit and implicit encodings used in computer-aided design (CAD). CAD programs allow you to specify explicit constraints on objects (for example, the center of this circle is at the center of the canvas), but also allow you to specify more abstract constraints, like "this line is tangent to the first circle". This combination of explicit and implicit constraints can make it very easy to construct geometrically complex objects which can be easily modified through parameter modification.
NURBS: Non-uniform rational basis spline
One of my favorite representations of geometry is the combination of explicit and implicit encodings used in computer-aided design (CAD). CAD programs allow you to specify explicit constraints on objects (for example, the center of this circle is at the center of the canvas), but also allow you to specify more abstract constraints, like "this line is tangent to the first circle". This combination of explicit and implicit constraints can make it very easy to construct geometrically complex objects which can be easily modified through parameter modification.