The three-body problem defines dynamics on the space of triangles in the plane. The shape sphere is the moduli space of oriented similarity classes of planar triangles and lies inside shape space, a Euclidean three-space parameterizing oriented congruence classes of triangles. We derive and investigate the geometry and dynamics induced on these spaces by the three-body problem. We present two t...

Out-of-plane tissue deformations are key morphogenetic events during plant and animal development that generate 3D shapes, such as flowers or limbs. However, the mechanisms by which spatiotemporal patterns of gene expression modify cellular behaviours to generate such deformations remain to be established. We use the Snapdragon flower as a model system to address this problem. Combining cellula...

A self calibration algorithm for direction finding in the presence of arbitrary shape 3D scatterers of resonating size is presented. This algorithm removes the effects of mutual coupling and 3D scatterers on direction of arrival estimation. The scatterers and wire type antenna array are excited by incident plane waves of arbitrary direction. The 3D scatterers shape is approximated as a sphere, ...

1. Abstract We model an electrified droplet spreading a solid surface. The model consists to seek a drop shape minimizing its total energy (capillary, electrostatic and gravitational). We derive the equations and the shape gradient; we detail the shape optimization algorithm and present some numerical results. Our numerical results fit the predictions of Lippman’s equation (plane capacitor appr...

Any subset of the plane can be approximated by a set of square pixels. This transition from a shape to its pixelation is rather brutal since it destroys geometric and topological information about the shape. Using a technique inspired by Morse Theory, we algorithmically produce a PL approximation of the original shape using only information from its pixelation. This approximation converges to t...

Let shape P be any simply-connected set in the plane, bounded by a Jordan curve, that is not a circular disk. We say that a set of points I on the boundary of P immobilize the shape if any rigid motion of P in the plane causes at least one point of I to penetrate the interior of P. We prove that four points always suffice to immobilize any shape. For a large class of shapes, which includes poly...

The spatial organization of cells depends on their ability to sense their own shape and size. Here, we investigate how cell shape affects the positioning of the nucleus, spindle and subsequent cell division plane. To manipulate geometrical parameters in a systematic manner, we place individual sea urchin eggs into microfabricated chambers of defined geometry (e.g., triangles, rectangles, and el...

An optimization protocol for a high authority shape morphing plate is described. The shape morphing design incorporates an active back-plane comprising a Kagome truss, capable of changing the shape of a solid face, connected to the back-plane by means of a tetrahedral truss core. Several members of the Kagome truss are replaced by actuators, enabling the structure to deform. The trusses to be r...

Let 〈Gr, Gb〉 be a pair of plane st-graphs with the same vertex set V . A simultaneous visibility representation with L-shapes of 〈Gr, Gb〉 is a pair of bar visibility representations 〈Γr, Γb〉 such that, for every vertex v ∈ V , Γr(v) and Γb(v) are a horizontal and a vertical segment, which share an end-point. In other words, every vertex is drawn as an L-shape, every edge of Gr is a vertical vis...

We evaluated some arbitrary-shape ROI (Region of Interest) coding techniques for three-dimensional volumetric images, and through the observation we propose a flexible ROI coding with efficient compression performance. In arbitrary-shape ROI coding, the object in an image is coded with higher fidelity than the rest of the image, together with the shape information, which indicates the region of...