Computer Graphics is about digital models for threedimensional geometric objects as well as images. These shapes and images may represent approximations of the real world or could be synthetic, i.e., exist only in the computer. Goals of computer graphics research are the generation of plausible and informative images, and computation with reasonable resources, i.e. in a short amount of time with little storage requirements. The models and algorithms for this task combine knowledge from different areas of mathematics and computer science.
We introduce an algorithm and representation for fabricating 3D shape abstractions using mutually intersecting planar cut-outs. The planes have prefabricated slits at their intersections and are assembled by sliding them together. Based on an analysis of construction rules, we propose an extended binary space partitioning tree as an efficient representation of such cardboard models which allows us to quickly evaluate the feasibility of newly added planar elements. The complexity of insertion order quickly increases with the number of planar elements and manual analysis becomes intractable. We provide tools for generating cardboard sculptures with guaranteed constructibility.