Related papers: Hemispheroidal parameterization and harmonic decom…
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 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.…
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…
Spherical harmonics (SH) have been extensively used as a basis for analyzing the morphology of particles in granular mechanics. The use of SH is facilitated by mapping the particle coordinates onto a unit sphere, in practice often a…
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…
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 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…
This paper presents a spline-based parameterisation framework for plane graphs. The plane graph is characterised by a collection of curves forming closed loops that fence-off planar faces which have to be parameterised individually. Hereby,…
We use spherical cap harmonic (SCH) basis functions to analyse and reconstruct the morphology of scanned genus-0 rough surface patches with open edges. We first develop a novel one-to-one conformal mapping algorithm with minimal area…
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…
The parameterization of closed surfaces typically requires either multiple charts or a non-planar domain to achieve a seamless global mapping. In this paper, we propose a numerical framework for the seamless parameterization of genus-zero…
Harmonic decomposition of surfaces, such as spherical and spheroidal harmonics, is used to analyze morphology, reconstruct, and generate surface inclusions of particulate microstructures. However, obtaining high-quality meshes of…
With advances in technology, there has been growing interest in developing effective mapping methods for 3-dimensional objects in recent years. Volumetric parameterization for 3D solid manifolds plays an important role in processing 3D…
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…
Surface parameterizations have been widely applied to computer graphics and digital geometry processing. In this paper, we propose a novel stretch energy minimization (SEM) algorithm for the computation of equiareal parameterizations of…
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…
Tube-like surfaces are widely encountered in geometry processing, engineering structures, and medical anatomy, yet their intrinsic longitudinal and circumferential topology is not well preserved by conventional planar annular or rectangular…
We present a constructive approach for approximating the conformal map (uniformization) of a polyhedral surface to a canonical domain in the plane. The main tool is a characterization of convex spaces of quasiconformal simplicial maps and…
Surface parametrization is a crucial part in various fields, having applications in computer graphic, medical imaging, scientific computing and computational engineering. The majority of surface parametrization approaches are performed on…
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…