This research paints a comprehensive picture of the current state of the conception and engineering of non-orthogonal architectural surfaces. The present paradigm in the design and engineering of these elaborate building structures is such that the overall form is decided first and it is then broken down into building components (façade cladding, or structural or shell elements) retrospectively. Subsequently, there is a division between the creation of the design and then the reverse engineering of it. In most of these projects, the discretisation of elaborate architectural surfaces into building components has little to do with how the form has been created, and the logic of the global form and its local subdivision are not of the same order. Experience gained through project work in the sponsoring company Buro Happold has been harnessed to inform the implementation of a design tool prototype. It is an open, extendable system. The development of the tool aims at stepping outside the current paradigm in practice; provides an integrated process of bottom-up generation of form and top-down search and optimisation, using an evolutionary method. The assertion of this thesis is that non-orthogonal design, which mimics a natural form in appearance, can be derived using mechanisms found in nature. These mechanisms, e.g. growth and evolution, can be transferred in such a way that they integrate aspects of the aesthetic, manufacturing, construction or performance. Designs are then created with an inherent logic. Growing form by adding discrete local geometries to produce larger componential surfaces ensures that the local parts and the global geometry are coherent and of the same kind. The aspiration is to make use of computational methods to contribute to the design and buildability of non-orthogonal architectural surfaces, and to further the discussion, development and application of digital design tools in practice.