Trip-lets: Constructability of trip-lets in theory and in practice

Abstract

A trip-let is an object defined by Walderveen et al. as: a solid, three-dimensional object that, when viewed from three orthogonal directions, shows three different shapes. In this thesis we consider problems related to constructing such objects for a given set of polygonal shapes. First, we want to know whether the silhouettes of the object correspond to the shapes we used to make the object. Second, we are interested in the connectedness of the final object: is it one solid object? We present proof on the combinatorial complexity of objects and silhouettes for shapes given as general or rectilinear polygons with holes. We present algorithms to solve the problems efficiently for validity in the rectilinear case and connectedness in the simple rectilinear case, and prove their time complexity.

The goal of the second part of the thesis is twofold. The first goal is to develop software to design trip-lets using a simple system of triangular and square base shapes. The second goal is to extract data on how many combinations of letters designed using the above software give valid and connected trip-lets. We will present the software that has been developed, including its features and development process as well as the design decisions. We will also present the experiment setup and its results.