Geometric Classifications of Free-Form Surfaces in the Imaginary Parameter Space of DFT-Based Technique

This paper presents examples of geometric classifications of free-form surfaces in the imaginary parameter space of an initial morphogenesis technique based on Discrete Fourier Transform (DFT), i.e., DFT-based technique. The DFT-based technique can create free-form shells that strictly pass through all the specified control points. Expressive and diverse morphogenesis can be achieved by giving complex values to height coordinates as the control points. It is explained visually and mathematically that the imaginary parts of the complex values play a significant role in determining shape and slope of generated surfaces. It is shown from numerical examples that the geometric shapes of the surfaces are determined by only three parameters of the aforementioned imaginary parts, and geometric classifications of the surfaces are demonstrated as well as mechanical evaluations.