10 research outputs found
A fast numerical solver for local barycentric coordinates
The local barycentric coordinates (LBC), proposed in Zhang et al (2014), demonstrate good locality and can be used for local control on function value interpolation and shape deformation. However, it has no closed- form expression and must be computed by solving an optimization problem, which can be time-consuming especially for high-resolution models. In this paper, we propose a new technique to compute LBC efficiently. The new solver is developed based on two key insights. First, we prove that the non-negativity constraints in the original LBC formulation is not necessary, and can be removed without affecting the solution of the optimization problem. Furthermore, the removal of this constraint allows us to reformulate the computation of LBC as a convex constrained optimization for its gradients, followed by a fast integration to recover the coordinate values. The reformulated gradient optimization problem can be solved using ADMM, where each step is trivially parallelizable and does not involve global linear system solving, making it much more scalable and efficient than the original LBC solver. Numerical experiments verify the effectiveness of our technique on a large variety of models
Nonnegative moment coordinates on finite element geometries
In this paper, we introduce new generalized barycentric coordinates (coined
as {\em moment coordinates}) on nonconvex quadrilaterals and convex hexahedra
with planar faces. This work draws on recent advances in constructing
interpolants to describe the motion of the Filippov sliding vector field in
nonsmooth dynamical systems, in which nonnegative solutions of signed matrices
based on (partial) distances are studied. For a finite element with
vertices (nodes) in , the constant and linear reproducing
conditions are supplemented with additional linear moment equations to set up a
linear system of equations of full rank , whose solution results in the
nonnegative shape functions. On a simple (convex or nonconvex) quadrilateral,
moment coordinates using signed distances are identical to mean value
coordinates. For signed weights that are based on the product of distances to
edges that are incident to a vertex and their edge lengths, we recover
Wachspress coordinates on a convex quadrilateral. Moment coordinates are also
constructed on a convex hexahedra with planar faces. We present proofs in
support of the construction and plots of the shape functions that affirm its
properties
Nonnegative moment coordinates on finite element geometries
In this paper, we introduce new generalized barycentric coordinates (coined as moment coordinates) on convex and nonconvex quadrilaterals and convex hexahedra with planar faces. This work draws on recent advances in constructing interpolants to describe the motion of the Filippov sliding vector field in nonsmooth dynamical systems, in which nonnegative solutions of signed matrices based on (partial) distances are studied. For a finite element with vertices (nodes) in , the constant and linear reproducing conditions are supplemented with additional linear moment equations to set up a linear system of equations of full rank , whose solution results in the nonnegative shape functions. On a simple (convex or nonconvex) quadrilateral, moment coordinates using signed distances are identical to mean value coordinates. For signed weights that are based on the product of distances to edges that are incident to a vertex and their edge lengths, we recover Wachspress coordinates on a convex quadrilateral. Moment coordinates are also constructed on a convex hexahedra with planar faces. We present proofs in support of the construction and plots of the shape functions that affirm its properties
A Revisit of Shape Editing Techniques: from the Geometric to the Neural Viewpoint
3D shape editing is widely used in a range of applications such as movie
production, computer games and computer aided design. It is also a popular
research topic in computer graphics and computer vision. In past decades,
researchers have developed a series of editing methods to make the editing
process faster, more robust, and more reliable. Traditionally, the deformed
shape is determined by the optimal transformation and weights for an energy
term. With increasing availability of 3D shapes on the Internet, data-driven
methods were proposed to improve the editing results. More recently as the deep
neural networks became popular, many deep learning based editing methods have
been developed in this field, which is naturally data-driven. We mainly survey
recent research works from the geometric viewpoint to those emerging neural
deformation techniques and categorize them into organic shape editing methods
and man-made model editing methods. Both traditional methods and recent neural
network based methods are reviewed