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Conformal mapping, a classical topic in complex analysis and differential geometry, has become a subject of great interest in the area of surface parameterization in recent decades with various applications in science and engineering.…
The parameterization of open and closed anatomical surfaces is of fundamental importance in many biomedical applications. Spherical harmonics, a set of basis functions defined on the unit sphere, are widely used for anatomical shape…
Conformal surface parameterization is useful in graphics, imaging and visualization, with applications to texture mapping, atlas construction, registration, remeshing and so on. With the increasing capability in scanning and storing data,…
Surface parameterizations have been widely used in computer graphics and geometry processing. In particular, as simply-connected open surfaces are conformally equivalent to the unit disk, it is desirable to compute the disk conformal…
Surface parameterization plays a fundamental role in many science and engineering problems. In particular, as genus-0 closed surfaces are topologically equivalent to a sphere, many spherical parameterization methods have been developed over…
With the advancement in 3D scanning technology, there has been a surge of interest in the use of point clouds in science and engineering. To facilitate the computations and analyses of point clouds, prior works have considered…
Surface parameterization is widely used in computer graphics and geometry processing. It simplifies challenging tasks such as surface registrations, morphing, remeshing and texture mapping. In this paper, we present an efficient algorithm…
Seamless global parametrization of surfaces is a key operation in geometry processing, e.g. for high-quality quad mesh generation. A common approach is to prescribe the parametric domain structure, in particular the locations of…
Volumetric parameterization problem refers to parameterization of both the interior and boundary of a 3D model. It is a much harder problem compared to surface parameterization where a parametric representation is worked out only for the…
Density-equalizing map is a shape deformation technique originally developed for cartogram creation and sociological data visualization on planar geographical maps. In recent years, there has been an increasing interest in developing…
Boundary conforming coordinates are commonly used in plasma physics to describe the geometry of toroidal domains, for example, in three-dimensional magnetohydrodynamic equilibrium solvers. The magnetohydrodynamic equilibrium configuration…
Surface parameterization is a fundamental concept in fields such as differential geometry and computer graphics. It involves mapping a surface in three-dimensional space onto a two-dimensional parameter space. This process allows for the…
We develop a new optimisation technique that combines multiresolution subdivision surfaces for boundary description with immersed finite elements for the discretisation of the primal and adjoint problems of optimisation. Similar to wavelets…
The aim of this study is to analyze the properties of harmonic fields in the vicinity of rough boundaries where either a constant potential or a zero flux is imposed, while a constant field is prescribed at an infinite distance from this…
Conformal and quasi-conformal mappings have widespread applications in imaging science, computer vision and computer graphics, such as surface registration, segmentation, remeshing, and texture map compression. While various conformal and…
We study numerical computation of conformal invariants of domains in the complex plane. In particular, we provide an algorithm for computing the conformal capacity of a condenser. The algorithm applies for wide kind of geometries: domains…
Mapping a shape to some parametric domain is a fundamental tool in graphics and scientific computing. In practice, a map between two shapes is commonly represented by two meshes with same connectivity and different embedding. The standard…
We use conformal maps to study a free boundary problem for a two-fluid electromechanical system, where the interface between the fluids is determined by the combined effects of electrostatic forces, gravity and surface tension. The free…
A conformal flattening maps a curved surface to the plane without distorting angles---such maps have become a fundamental building block for problems in geometry processing, numerical simulation, and computational design. Yet existing…
We present a strongly-coupled immersed-boundary method for flow-structure interaction problems involving thin deforming bodies. The method is stable for arbitrary choices of solid-to-fluid mass ratios and for large body motions. As with…