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The algorithms given in Karney, J. Geodesy 87, 43-55 (2013), to compute geodesics on terrestrial ellipsoids are extended to apply to ellipsoids of revolution with arbitrary eccentricity. For the direct and inverse geodesic problems, this…
Algorithms for the computation of the forward and inverse geodesic problems for an ellipsoid of revolution are derived. These are accurate to better than 15 nm when applied to the terrestrial ellipsoids. The solutions of other problems…
We investigate the curves in the complex plane which are generated by sequences of real numbers being the lifts of the points on the orbit of an orientation preserving circle homeomorphism. Geometrical properties of these curves such as…
An algorithm and a program for detecting the boundaries of water bodies for the autopilot module of asurface robot are proposed. A method for detecting water objects on satellite maps by the method of finding a color in the HSV color space,…
In this paper, we use permutation elements to record cylinder decompositions of a square-tiled surface $X$. Collecting all such possible permutation elements that record cylinder decompositions, we can enumerate the $SL_2(\mathbb{Z})$ orbit…
We develop and test high-order methods for integration on surface point clouds. The task of integrating a function on a surface arises in a range of applications in engineering and the sciences, particularly those involving various integral…
Generating realistic clothing for virtual applications like online retail and digital avatars is crucial but requires expert knowledge of 3D tools to generating believable simulations. Recently, a number of works proposed to estimate cloth…
Exploiting elastic instability in thin films has proven a robust method for creating complex patterns and structures across a wide range of lengthscales. Even the simplest of systems, an elastic membrane with a lattice of pores, under…
Self-occlusion is challenging for cloth manipulation, as it makes it difficult to estimate the full state of the cloth. Ideally, a robot trying to unfold a crumpled or folded cloth should be able to reason about the cloth's occluded…
In a previous paper, we examined a class of possible conformations for helically patterned filaments in contact with a bonding surface. In particular, we investigated geometries where contact between the pattern and the surface was improved…
We characterise when a set of simple closed curves in an orientable surface forms a bouquet, in terms of relations between the corresponding Dehn twists.
A simple, discrete, parametric model is proposed to describe conditional (correlated) deposition of particles on a surface and formation of a connecting (percolating) cluster. The surface changes spontaneously its properties (phase…
This paper presents a new method to model X-ray scattering on random rough surfaces. It combines the approaches we presented in two previous papers -- \zs\cite{zhao03} \& \pz\cite{zhao15}. An actual rough surface is (incompletely) described…
In the process of projecting the surface of a three-dimensional object onto a two-dimensional surface, due to the perspective distortion, the image on the surface of the object will have different degrees of distortion according to the…
Understanding the stroke-based evolution of visual artworks is useful for advancing artwork learning, appreciation, and interactive display. While the stroke sequence of renowned artworks remains largely unknown, formulating this sequence…
We present a new robotic drawing system based on stroke-based rendering (SBR). Our motivation is the artistic quality of the whole performance. Not only should the generated strokes in the final drawing resemble the input image, but the…
Non-relativistic particles that are effectively confined to two dimensions can in general move on curved surfaces, allowing dynamical phenomena beyond what can be described with scalar potentials or even vector gauge fields. Here we…
Visualization of implicit surfaces is an actively researched topic. While raytracing can produce high quality images, it is not well suited for creating a quick preview of the surface. Indirect algorithms (e.g. Marching Cubes) create an…
We introduce a numerical method for reconstructing a multidimensional surface using the gradient of the surface measured at some values of the coordinates. The method consists of defining a multidimensional spline function and minimizing…
This paper explores the challenge of teaching a machine how to reverse-engineer the grid-marked surfaces used to represent data in 3D surface plots of two-variable functions. These are common in scientific and economic publications; and…