Beads-on-String Model for Virtual Rectum Surgery Simulation

A beads-on-string model is proposed to handle the deformation and collision of the rectum in virtual surgery simulation. The idea is firstly inspired by the observation of the similarity in shape shared by a rectum with regular bulges and a string of beads. It is beneficial to introduce an additional layer of beads, which provides an interface to map the deformation of centreline to the associated mesh in an elegant manner and a bounding volume approximation in collision handling. Our approach is carefully crafted to achieve high computational efficiency and retain its physical basis. It can be implemented for real time surgery simulation application

Shape manipulation using physically based wire deformations

This paper develops an efficient, physically based shape manipulation technique. It defines a 3D model with profile curves, and uses spine curves generated from the profile curves to control the motion and global shape of 3D models. Profile and spine curves are changed into profile and spine wires by specifying proper material and geometric properties together with external forces. The underlying physics is introduced to deform profile and spine wires through the closed form solution to ordinary differential equations for axial and bending deformations. With the proposed approach, global shape changes are achieved through manipulating spine wires, and local surface details are created by deforming profile wires. A number of examples are presented to demonstrate the applications of our proposed approach in shape manipulation

Барицентрические координаты Пуассона — Римана

The article deals with the problem of finding barycentric coordinates for arbitrary, simply connected, closed, discrete regions that are defined in and . Barycentric coordinates are given by a set of scalar parameters that unambiguously define a point of the affine space inside a simply connected, closed, discrete region through a specified point basis, which is given by the vertices of the region. Barycentriс coordinates being defined for the simply connected, closed, discrete region are harmonic and satisfy the properties of affine invariance, positive definiteness and equality to unit. The solution is based on the Riemann theorem on the uniqueness of conformal mapping and the Poisson integral formula for the ball. The paper shows the examples of approximation of the potential inside arbitrary, simply connected, closed, discrete regions using the proposed method, compared with the approximation using the finite element method.В статье выполнено решение задачи нахождения барицентрических координат для произвольных односвязных замкнутых дискретных областей, заданных в и . Барицентрические координаты задаются набором скалярных параметров, однозначно определяющих точку аффинного пространства внутри односвязной замкнутой дискретной области через заданный точечный базис. Точечный базис задается вершинами односвязной замкнутой дискретной области. Определяемые барицентрические координаты для односвязной замкнутой дискретной области являются гармоническими и удовлетворяют свойствам аффинной инвариантности, положительной определенности и равенстве единице. Решение основано на теореме Римана о единственности конформного отображения и интегральной формуле Пуассона для шара. Приведены примеры аппроксимации потенциала внутри произвольных односвязных замкнутых дискретных областей по предложенному методу в сравнении с аппроксимацией методом конечных элементов

Mean value coordinates–based caricature and expression synthesis

We present a novel method for caricature synthesis based on mean value coordinates (MVC). Our method can be applied to any single frontal face image to learn a specified caricature face pair for frontal and 3D caricature synthesis. This technique only requires one or a small number of exemplar pairs and a natural frontal face image training set, while the system can transfer the style of the exemplar pair across individuals. Further exaggeration can be fulfilled in a controllable way. Our method is further applied to facial expression transfer, interpolation, and exaggeration, which are applications of expression editing. Additionally, we have extended our approach to 3D caricature synthesis based on the 3D version of MVC. With experiments we demonstrate that the transferred expressions are credible and the resulting caricatures can be characterized and recognized

Transfinite mean value interpolation in general dimension

AbstractMean value interpolation is a simple, fast, linearly precise method of smoothly interpolating a function given on the boundary of a domain. For planar domains, several properties of the interpolant were established in a recent paper by Dyken and the second author, including: sufficient conditions on the boundary to guarantee interpolation for continuous data; a formula for the normal derivative at the boundary; and the construction of a Hermite interpolant when normal derivative data is also available. In this paper we generalize these results to domains in arbitrary dimension