Guodong Rong

Spectral mesh deformation

In this paper, we present a novel spectral method for mesh deformation based on manifold harmonics transform. The eigenfunctions of the Laplace–Beltrami operator give orthogonal bases for parameterizing the space of functions defined on the surfaces. The geometry and motion of the original irregular meshes can be compactly encoded using the low-frequency spectrum of the manifold harmonics. Using the spectral method, the size of the linear deformation system can be significantly reduced to achieve interactive computational speed for manipulating large triangle meshes. Our experimental results demonstrate that only a small spectrum is needed to achieve undistinguishable deformations for large triangle meshes. The spectral mesh deformation approach shows great performance improvement on computational speed over its spatial counterparts.

GPU-Assisted Computation of Centroidal Voronoi Tessellation

Centroidal Voronoi tessellations (CVT) are widely used in computational science and engineering. The most commonly used method is Lloyds method, and recently the L-BFGS method is shown to be faster than Lloyds method for computing the CVT. However, these methods run on the CPU and are still too slow for many practical applications. We present techniques to implement these methods on the GPU for computing the CVT on 2D planes and on surfaces, and demonstrate significant speedup of these GPU-based methods over their CPU counterparts. For CVT computation on a surface, we use a geometry image stored in the GPU to represent the surface for computing the Voronoi diagram on it. In our implementation a new technique is proposed for parallel regional reduction on the GPU for evaluating integrals over Voronoi cells.

Optimal surface deployment problem in wireless sensor networks

Sensor deployment is a fundamental issue in a wireless sensor network, which often dictates the overall network performance. Previous studies on sensor deployment mainly focused on sensor networks on 2D plane or in 3D volume. In this paper, we tackle the problem of optimal sensor deployment on 3D surfaces, aiming to achieve the highest overall sensing quality. In general, the reading of a sensor node exhibits unreliability, which often depends on the distance between the sensor and the target to be sensed, as observed in a wide range of applications. Therefore, with a given set of sensors, a sensor network offers different accuracy in data acquisition when the sensors are deployed in different ways in the Field of Interest (FoI). We formulate this optimal surface deployment problem in terms of sensing quality by introducing a general function to measure the unreliability of monitored data in the entire sensor network. We present its optimal solution and propose a series of algorithms for practical implementation. Extensive simulations are conducted on various 3D mountain surface models to demonstrate the effectiveness of the proposed algorithms.

Hyperbolic centroidal Voronoi tessellation

The centroidal Voronoi tessellation (CVT) has found versatile applications in geometric modeling, computer graphics, and visualization. In this paper, we extend the concept of the CVT from Euclidean space to hyperbolic space. A novel hyperbolic CVT energy is defined, and the relationship between minimizing this energy and the hyperbolic CVT is proved. We also show by our experimental results that the hyperbolic CVT has the similar property as its Euclidean counterpart where the sites are uniformly distributed according to given density values. Two algorithms -- Lloyds algorithm and the L-BFGS algorithm -- are adopted to compute the hyperbolic CVT, and the convergence of Lloyds algorithm is proved. As an example of the application, we utilize the hyperbolic CVT to compute uniform partitions and high-quality remeshing results for high-genus (genus>1) surfaces.

Centroidal Voronoi tessellation in universal covering space of manifold surfaces

The centroidal Voronoi tessellation (CVT) has found versatile applications in geometric modeling, computer graphics, and visualization, etc. In this paper, we first extend the concept of CVT from Euclidean space to spherical space and hyperbolic space, and then combine all of them into a unified framework - the CVT in universal covering space. The novel spherical and hyperbolic CVT energy functions are defined, and the relationship between minimizing the energy and the CVT is proved. We also show by our experimental results that both spherical and hyperbolic CVTs have the similar property as their Euclidean counterpart where the sites are uniformly distributed with respect to given density values. As an example of the application, we utilize the CVT in universal covering space to compute uniform partitions and high-quality remeshing results for genus-0, genus-1, and high-genus (genus>1) surfaces.

Streaming 3D shape deformations in collaborative virtual environment

Collaborative virtual environment has been limited on static or rigid 3D models, due to the difficulties of real-time streaming of large amounts of data that is required to describe motions of 3D deformable models. Streaming shape deformations of complex 3D models arising from a remote users manipulations is a challenging task. In this paper, we present a framework based on spectral transformation that encodes surface deformations in a frequency format to successfully meet the challenge, and demonstrate its use in a distributed virtual environment. Our research contributions through this framework include: i) we reduce the data size to be streamed for surface deformations since we stream only the transformed spectral coefficients and not the deformed model; ii) we propose a mapping method to allow models with multi-resolutions to have the same deformations simultaneously; iii) our streaming strategy can tolerate loss without the need for special handling of packet loss. Our system guarantees real-time transmission of shape deformations and ensures the smooth motions of 3D models. Moreover, we achieve very effective performance over real Internet conditions as well as a local LAN. Experimental results show that we get low distortion and small delays even when surface deformations of large and complicated 3D models are streamed over lossy networks.

Real-time hybrid solid simulation: spectral unification of deformable and rigid materials

Realistic character animation requires elaborate rigging built on top of high quality 3D models. Sophisticated anatomically based rigs are often the choice of visual effect studios where life-like animation of CG characters is the primary objective. However, rigging a character with a muscular-skeletal system is very involving and time-consuming process, even for professionals. Although, there have been recent research efforts to automate either all or some parts of the rigging process, the complexity of anatomically based rigging nonetheless opens up new research challenges. We propose a new method to automate anatomically based rigging that transfers an existing rig of one character to another. The method is based on a data interpolation in the surface and volume domain, where various rigging elements can be transferred between different models. As it only requires a small number of corresponding input feature points, users can produce highly detailed rigs for a variety of desired character with ease. Copyright

Generalized Voronoi Diagram Computation on GPU

We study the problem of using the GPU to compute the generalized Voronoi diagram (GVD) for higher-order sites, such as line segments and curves. This problem has applications in many fields, including computer animation, pattern recognition and so on. A number of methods have been proposed that use the GPU to speed up the computation of the GVD. The jump flooding algorithm (to be called JFA) is such an efficient GPU-based method that is particularly suitable for computing the ordinary Voronoi diagram of point sites. We improve the jump flooding algorithm and apply it to computing the GVD. Specifically, instead of directly propagating the complete information of a site (i.e. the coordinates or other geometric parameters) as in the original JFA, we store the site information in a 1-D texture, and propagate only the IDs, which are short integers, of the sites in another 2D texture to generate the Voronoi diagram. This simple strategy avoids storing redundant data and leads to considerately more accurate computation of the GVD with much less memory than using the original JFA, with only moderate increase of the running time.

Spectral simulation of hybrid bodies with deformable and rigid materials

We presents a spectral approach to simulate hybrid objects with deformable and rigid materials in real time. This framework is able to handle large-scale model under the help of GPUs parallel computation.