Architecture builds on geometry by a cartesian (a) colocation and (b) disposition of its parts. For architecture as composition its parts are defined as designed objects. Withdrawn, the designed object becomes congruent to the geometrical term of a point. The term of a point must than be congruent to the architectural view of a designed object. The term point has to be extended by (a) thickness as containment of that which is in. Additionally axioms have to describe (b) directionality as that in which it is. Then architecture as composition is nothing more than the difference between (a) being-inside and (b) being-outside.
For architecture (a) a term is the colocation of that which is in. (b) A axiom is that in which it is: the premise how to dispose.
Made in Processing and punktiert library with an upcoming OpenCL support.