Talk by Arvin Rasoulzadeh and Kiumars Sharifmoghaddam on
Class-preserving Isometric Deformations of T-surfaces with Applications in Transformable Designs
Wednesday 12 May 2021, 11:00 am, online.
Abstract: A Smooth T-surface can be thought of as a generalization of a surface of revolution in such a way that the axis of rotation is not fixed at one point but rather traces a smooth path on the base plane. Furthermore, the action, by which the aforementioned surface is obtained does not need to be merely rotation but any “suitable” planar affine transformation applied to the points of a certain smooth profile curve.
In analogy to the smooth setting, if the axis foot points sweep a polyline on the base plane and if the profile curve is discretely chosen then a T-hedra (discrete T-surface) with planar trapezoidal faces is obtained.
From an applied point of view, the straightforwardness of the generation of these surfaces predestines them for building and design processes. In fact, one can find many built objects belonging to the sub-classes of T-surfaces such as Surfaces of Revolution and Translational Surfaces. Furthermore, in the discrete version, possessing the flat trapezoidal faces, paves the way for steel/glass construction in industry.
The goal of the first part of the talk is to give a rigorous definition of the T-surfaces/T-hedra by introducing suitable parametrizations. In doing so a kinematic approach is taken into account, where the aforementioned parametrizations are obtained based on the action of elements of some certain motion paths in the group of planar equiform motions on a planar (profile) curve in three dimensional real space. Furthermore, the class-preserving isometric deformations (i.e. the isometries that preserve the surface of revolution) of these surfaces are computed based on the changes of the motion paths and the profile curve.
In the second part of the talk, we present a Rhino/Grasshopper plugin developed with C#, which makes the design space of T-hedra accessible for designers and engineers. Our components enable a user to design a T-hedron interactively and visualize its deformation in real-time based on a recursive parametrization of the quad-mesh vertices under the associated isometric deformation. Finally, there is an interesting option to evaluate the force transmission characteristic within the surface by considering each four planes with a common node as a spherical 4-bar linkage.
Arvin Rasoulzadeh: defended his PhD on Geometrical Kinematics in 2020, and is currently working as a PostDoc at TU Wien, Austria in the SP7 subproject of the SFB-acd under the supervision of Ivan Izmestiev and Georg Nawratil. Currently his area of research is related to the isometric deformation of smooth and discrete surfaces.
Kiumars Sharifmoghaddam: accomplished his Masters on computational geometry in 2019 at SBU Tehran, Iran. He is working as a project assistant in the SP7 subproject of the SFB-acd under the supervision of Ivan Izmestiev and Georg Nawratil, mainly on plug-in development for Rhino/Grasshopper.