Interactive physically based modeling, simulation, and analysis of digitized real-world models are extremely challenging tasks. Physically based simulation approaches, such as finite element methods based on continuum mechanics, are computationally intensive, which makes them impractical for simulating and visualizing large-scale complex data in real-time. The introduction of geometric mapping in this research provides Euclidean parametric domain and regular structure inherent to complex geometric shapes, and provides efficient tools (such as GPU-based computation) to speed up the simulation process.
This research tackles the speed bottleneck of physical simulation and visualization of deformable models by exploring the relationship between conformal and harmonic geometric mapping with physically based simulation, and develops efficient algorithms that allow users to perform real-time physical simulation, collision detection, material modeling, and visualization of large-scale, complicated geometric data. In particular, efficient and robust algorithms are investigated to enable dynamic space & time adaptive physical deformation of thin-shells and volumetric objects, by exploiting novel numerical methods to solve PDEs/ ODEs on graphics hardware, based on surface and volumetric mappings. The PI investigates novel GPU-based hierarchical collision detection algorithms for deformable models, using multiresolution geometry images to represent the bounding deformation trees as dynamic textures in the graphics hardware, to efficiently detect both inter-objects collision and self-collision of deformable models during simulations. This research project also develops powerful GPU-based multiresolution modeling and parallel visualization methods to efficiently represent and render heterogeneous material properties of the simulated deformable models. This investigation has broad impacts on an array of applications spanning physical science, mechanical engineering, medicine, K-12 education, training, and entertainment.
Interactive physically based modeling and simulation of deformable models are extremely challenging tasks. Physically based approaches, such as finite element methods, are computationally intensive, which makes them impractical for modeling and simulating large-scale complex data in real-time. The introduction of geometric mapping in this research provides canonical parametric domain (Spherical, Euclidean, Hyperbolic domains) and regular structure (rectangles, polycubes, etc.) inherent to complex geometric shapes, and provides efficient tools (such as GPU-based computation) to speed up the modeling and simulation process. The first step of modeling and simulating real-world scanned objects in this project is to generate high-quality mesh of surfaces and volumes using Centroidal Voronoi Tessellation (CVT). The PI extended CVT from the traditional Euclidean and Spherical domains into the unexplored Hyperbolic domain. The PI and his students unified the treatment of CVT in these three different spaces, introduced the new CVT energy functions, and proved its convergence under CVT. The PI and his students computed CVT in three different universal covering spaces (Spherical, Euclidean, Hyperbolic spaces) of manifold surfaces (genus-0, genus-1, genus≥2) for uniform partitions and remeshing. One main challenge which prohibits the usage of CVT in real-time systems, such as collaborative shape deformation, is the difficulty to compute it efficiently. The PI and his students investigated and implemented the GPU-based parallel algorithms for CVT computation on surfaces which can achieve up to several hundred times faster performance than the fastest previous algorithms. To generate the mapping from complex surfaces and volumes to the regular structures, such as polycubes, the PI investigated and developed the quasi-conformal surface mapping and harmonic volume mapping. The quasi-conformal surface mapping guarantees the mapping between two surfaces of complicated topology to have as little angle distortion as possible. The harmonic volume mapping algorithm can be applied to massive volume data sets with various geometric primitives and topological types. Based on the regular parameterization of surfaces, the PI proposed to simulate thin-shell elastic deformation and crack propagation directly over point-sampled surfaces, based on the point-based global conformal parameterization. Such treatment provides both accurate meshless simulation and efficient discontinuity modeling for complex branching cracks. For physically based simulation of volumetric deformable models, modal analysis method is a dimensional reduction approach to speed-up the simulation efficiency. The co-rotational technique can be combined with modal analysis, i.e. using linear strain tensor in combination with modal rotation matrix, to handle large rotational deformation. In our research, the PI and his students showed that the same technique can be used for simulating rigid bodies except for the difference that only the first six eigenvectors are used as the spectral bases for the rigid parts. Thus the PI integrated both deformable and rigid body simulation into a unified spectral framework, and show that the proposed hybrid simulation system is both effective and efficient, and can handle large-scaled tetrahedral meshes in real-time. Deformable 3D models provide an excellent platform for collaborative interactive applications where remote users can carry out manipulations on the same virtual object. Streaming deformations of complex 3D objects over networks arising from a user's manipulations is a challenging task. The PI and his students developed an interactive collaboration framework that supports real-time streaming of 3D deformations over networks. This framework offers users from remote locations to manipulate the same 3D model and share its deformation in real-time. This investigation has broader impacts on an array of applications spanning from medical physics, radiation oncology, to communication disorder. The GPU-based deformable models can be used to provide a real-time solution for tracking daily lung tumor position in CT scanned images, based on the PI’s collaboration with UT Southwestern Medical Center at Dallas. The PI and his students investigated novel GPU-based fast digital reconstructed radiograph (DRR) generation algorithm and image correlation algorithms to locate the tumor in every on-line generated CT image. The PI also collaborated with Callier Center for Communication Disorder at UT-Dallas, on applying our real-time physics-based deformable model to the human tongue modeling and visualization. The PI’s preliminary results show that the physics-based deformation framework has significant potential to unveil the characteristic tongue deformation patterns between different speakers, as well as the different syllables produced from the same speaker. The features of the deformation patterns are important to study the divergences of individual human subjects (e.g. native/foreign language, gender, or pathological abnormality of the speakers). The investigation results in this proposal have been integrated into both undergraduate and graduate curriculum that the PI is teaching at UT-Dallas. Two new courses – "Geometric Modeling and Processing" and "Physics-Based Modeling and Simulation", were developed for the graduate students at UT-Dallas. Besides the postdoc and graduate students who were directly involved in this project, four undergraduate students were supported from the REU supplements and received rigorous research training in related fields of physics-based modeling, computer graphics, and virtual reality.
