Membrane packaging has been the main feature of the earliest prototypes of transformablearchitecture. Similar concepts of spatial transformation are encountered in the origami art where aplanar paper surface, after folding, transforms to a 3-dimentional object. The geometric configuration ofcreases on a sheet of paper before folding, as well as the topological properties of 3D origami papermodels, have been recently addressed, and can be used as a guide for the design of new forms.Because membranes in general can be considered surfaces of minimal thickness, principles of theorigami art and math can find applications in the conception and design of transformable membranestructures for architecture. This paper discusses how computer visualization can be used to explorethe potential application of ideas borrowed from the origami art in the conceptual design oftransformable structures. A two-case study that shows how origami math is integrated in the computervisualization of a potential architectural application is included. The same study also shows thatanimated simulations of the transformation process during folding can identify problems in the initialgeometric conception of an origami type structure, and can be used for further morphologicalexplorations.