This thesis focuses on generating and exploring design variations for architectural and urban layouts. I propose to study this general problem in three selected contexts.

First, I introduce a framework to generate many variations of a facade design that look similar to a given facade layout. Starting from an input image, the facade is hierarchically segmented and labeled with a collection of manual and automatic tools. The user can then model constraints that should be maintained in any variation of the input facade design. Subsequently, facade variations are generated for different facade sizes, where multiple variations can be produced for a certain size.

Second, I propose a method for a user to understand and systematically explore good building layouts. Starting from a discrete set of good layouts, I analytically characterize the local shape space of good layouts around each initial layout, compactly encode these spaces, and link them to support transitions across the different local spaces. I represent such transitions in the form of a portal graph. The user can then use the portal graph, along with the family of local shape spaces, to globally and locally explore the space of good building layouts.

Finally, I propose an algorithm to computationally design street networks that balance competing requirements such as quick travel time and reduced through traffic in residential neighborhoods. The user simply provides high-level functional specifications for a target neighborhood, while my algorithm best satisfies the specification by solving for both connectivity and geometric layout of the network.