Binary morphological shape-based interpolation applied to 3-D tooth reconstruction

In this paper we propose an interpolation algorithm using a mathematical morphology morphing approach. The aim of this algorithm is to reconstruct the $n$-dimensional object from a group of (n-1)-dimensional sets representing sections of that object. The morphing transformation modifies pairs of consecutive sets such that they approach in shape and size. The interpolated set is achieved when the two consecutive sets are made idempotent by the morphing transformation. We prove the convergence of the morphological morphing. The entire object is modeled by successively interpolating a certain number of intermediary sets between each two consecutive given sets. We apply the interpolation algorithm for 3-D tooth reconstruction

Assessment criteria for 2D shape transformations in animation

The assessment of 2D shape transformations (or morphing) for animation is a difficult task because it is a multi-dimensional problem. Existing morphing techniques pay most attention to shape information interactive control and mathematical simplicity. This paper shows that it is not enough to use shape information alone, and we should consider other factors such as structure, dynamics, timing, etc. The paper also shows that an overall objective assessment of morphing is impossible because factors such as timing are related to subjective judgement, yet local objective assessment criteria, e.g. based on shape, are available. We propose using “area preservation” as the shape criterion for the 2D case as an acceptable approximation to “volume preservation” in reality, and use it to establish cases in which a number of existing techniques give clearly incorrect results. The possibility of deriving objective assessment criteria for dynamics simulations and timing under certain conditions is discussed

Exploring continuous organisational transformation as a form of network interdependence

In this paper we examine the problematic area of continuous transformation. We conduct our analysis from three theoretical perspectives: the resource based view, social network theory, and stakeholder theory. We found that the continuous transformation can be explained through the concept of Network Interdependence. This paper describes Network Interdependence and develops theoretical propositions from a synthesis of the three theories. Our contribution of Network Interdependence offers fresh insights into managing complex change and offers new ways of looking at organisational transformation

Morphing surfaces for the control of boundary layer transition

A structure configured to modify its surface morphology between a smooth state and a rough state in response to an applied stress. In demonstrated examples, a soft (PDMS) substrate is produced, and is pre-strained. A relatively stiff overlayer of a metal, such as chromium and gold, is applied to the substrate. When the pre-strained substrate is allowed to relax, the free surface of the stiff overlayer is forced to become distorted, yielding a free surface having a roughness of less than 1 millimeter. Repeated application and removal of the applied stress has been shown to yield reproducible changes in the morphology of the free surface. An application of such morphing free surface is to control a boundary layer transition of an aerodynamic fluid flowing over the surface

Morphing of Geometric Composites via Residual Swelling

Understanding and controlling the shape of thin, soft objects has been the focus of significant research efforts among physicists, biologists, and engineers in the last decade. These studies aim to utilize advanced materials in novel, adaptive ways such as fabricating smart actuators or mimicking living tissues. Here, we present the controlled growth--like morphing of 2D sheets into 3D shapes by preparing geometric composite structures that deform by residual swelling. The morphing of these geometric composites is dictated by both swelling and geometry, with diffusion controlling the swelling-induced actuation, and geometric confinement dictating the structure's deformed shape. Building on a simple mechanical analog, we present an analytical model that quantitatively describes how the Gaussian and mean curvatures of a thin disk are affected by the interplay among geometry, mechanics, and swelling. This model is in excellent agreement with our experiments and numerics. We show that the dynamics of residual swelling is dictated by a competition between two characteristic diffusive length scales governed by geometry. Our results provide the first 2D analog of Timoshenko's classical formula for the thermal bending of bimetallic beams - our generalization explains how the Gaussian curvature of a 2D geometric composite is affected by geometry and elasticity. The understanding conferred by these results suggests that the controlled shaping of geometric composites may provide a simple complement to traditional manufacturing techniques