configurational studies

configurational studies

1975-present

I have long been interested in characterizing spatial designs with distinctive properties. My doctoral dissertation was on such spatial problems—in fact, on finding computational solutions to a number of otherwise hard to count generative problems, for example, finding connected arrangements of non-overlapping regions into a region with or without certain symmetry properties. Spatially, such configurations resemble layouts. The approach is to specify a provably correct algorithm to generate all possible designs that satisfy the constraints or requirements.

The picture below shows the possible interior joints formed when boxes pack into boxes without overlap.

Joints of the kind numbered 1,2 and 3 produce boxes in which each cross-section yields an arrangement of overlapping rectangles within a rectangle in which lines do not cross to form a ‘+’ shape and only meet at ‘T’s. With appropriate perturbations all other kinds of interior joints can be made into one of these three.

If a configuration has a type 3 joint (called a lock), then it contains interlocking volumes. The smallest example is shown on the right.

publications

R Krishnamurti. On a method of Flemming: Wall representation and orthogonal structures. Generative CAD Systems (eds. Ö Akin, R Krishnamurti and K-P Lam), pp 31-60, School of Architecture, Carnegie Mellon University, Pittsburgh, July 2004

R Krishnamurti and CF Earl. Densely packed rectangulations. Environment & Planning B: Planning and Design, 25, 773-787, 1998

R Krishnamurti. 3-rectangulations: an algorithm to generate box packings. Environment & Planning B: Planning and Design, 6, 331–352, 1979

R Krishnamurti and PH O'N Roe. On the generation and enumeration of tessellation designs. Environment & Planning B: Planning and Design, 6, 191–260, 1979

R Krishnamurti and CJ Bloch. The counting of rectangular dissections. Environment & Planning B: Planning and Design, 5, 207–214, 1978

R Krishnamurti and PH O'N Roe. Algorithmic aspects of plan generation and enumeration. Environment & Planning B: Planning and Design, 5, 157–177, 1978

Rules to generate all possible arrangements of nonoverlapping boxes within a box without locks