Quadrangulating a Mesh using Laplacian Eigenvectors

نویسندگان

  • Shen Dong
  • Peer-Timo Bremer
  • Michael Garland
  • Valerio Pascucci
  • John C. Hart
چکیده

Resampling raw surface meshes is one of the most fundamental operations used by nearly all digital geometry processing systems. The vast majority of work in the past has focused on triangular remeshing; the equally important problem of resampling surfaces with quadrilaterals has remained largely unaddressed. Despite the relative lack of attention, the need for quality quadrangular resampling methods is of central importance in a number of important areas of graphics. Quadrilaterals are the preferred primitive in many cases, such as Catmull-Clark subdivision surfaces, fluid dynamics, and texture atlasing. We propose a fundamentally new approach to the problem of quadrangulating manifold polygon meshes. By applying a Morsetheoretic analysis to the eigenvectors of the mesh Laplacian, we have developed an algorithm that can correctly quadrangulate any manifold, no matter its genus. Because of the properties of the Laplacian operator, the resulting quadrangular patches are wellshaped and arise directly from intrinsic properties of the surface, rather than from arbitrary heuristics. We demonstrate that this quadrangulation of the surface provides a base complex that is wellsuited to semi-regular remeshing of the initial surface into a fully conforming mesh composed exclusively of quadrilaterals.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Quadrangulating a Mesh using Laplacian Eigenvectors

Resampling raw surface meshes is one of the most fundamental operations used by nearly all digital geometry processing methods. While the majority of work in the past has focused on triangular remeshing, the problem of resampling surfaces with quadrilaterals is at least as important. Quadrilaterals are the preferred primitive in many cases, such as Catmull-Clark subdivision surfaces, fluid dyna...

متن کامل

Mesh Segmentation Using Laplacian Eigenvectors and Gaussian Mixtures

In this paper a new completely unsupervised mesh segmentation algorithm is proposed, which is based on the PCA interpretation of the Laplacian eigenvectors of the mesh and on parametric clustering using Gaussian mixtures. We analyse the geometric properties of these vectors and we devise a practical method that combines single-vector analysis with multiple-vector analysis. We attempt to charact...

متن کامل

Watermarking 3D Polygonal Meshes in the Mesh Spectral Domain

Digital watermarking embeds a structure called watermark into the target data, such as image and 3D polygonal models. The watermark can be used, for example, to enforce copyright and to detect tampering. This paper presents a new robust watermarking method that adds watermark into a 3D polygonal mesh in the mesh’s spectral domain. The algorithm computes spectra of the mesh by using eigenvalue d...

متن کامل

On the Optimality of Spectral Compression of Meshes

Spectral compression of triangle meshes has shown good results in practice, but there has been little or no theoretical support for the optimality of this compression. We show that for certain classes of geometric mesh models, spectral decomposition using the eigenvectors of the symmetric Laplacian of the connectivity graph is equivalent to principal component analysis. The key component of the...

متن کامل

Spectral Geometry Processing with Manifold Harmonics

We present a new method to convert the geometry of a mesh into frequency space. The eigenfunctions of the Laplace-Beltrami operator are used to define Fourier-like function basis and transform. Since this generalizes the classical Spherical Harmonics to arbitrary manifolds, the basis functions will be called Manifold Harmonics. It is well known that the eigenvectors of the discrete Laplacian de...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2005