### Table 3: Summary of a collection of physically-based deformable models.

"... In PAGE 12: ... Tables 2 and 3 list some of the previous developments in this area (including those for AORs and HORs), and their main technical char- acteristics. After a summary of empirical deformable models (Table 2), we brie y examine several major physically-based models ( Table3 ). We then consider techniques for rendering deformation directly.... In PAGE 12: ... Finally we give an overview of defor- mation techniques in the context of a particular application, namely surgical simulation, where SOR deformation could potentially play a major role. As shown in Table3 , physically-based models are usually de ned on mesh-based data representations. In some appli- cations, such as surgical simulation, it has been common to add analytical information (e.... In PAGE 13: ... For this reason, there have been many physically-based models proposed for deformation. As shown in Table3 , almost all physically-based mod- els are associated with a mesh data representation, typi- cally with triangular or rectangular elements for surfaces and tetrahedral or hexahedral elements for solids or volumes. In most applications involving SORs, such data representations can be extracted or reconstructed from SORs using the tech- niques discussed in Section 4.... ..."

### Table 2: Summary of a collection of example deformable models.

"... In PAGE 12: ... these include those techniques that operate directly on DSORs, as well as those involve geometric rep- resentations extracted from DSORs. Table2 lists a collection of previous developments in this area, and their main tech- nical characteristics. After a summary of non-physically- based deformable models, we brie y examine several ma- jor physically-based models that have been deployed for de- forming DSORs.... In PAGE 14: ...2. Physically-based Models As shown in Table2 , almost all physically-based models are associated with a mesh data representation, typically with triangular or rectangular elements for surfaces and tetrahe- dral or hexahedral elements for solids or volumes. In most applications involving DSORs, such data representations can be extracted or reconstructed from DSORs using the tech- niques discussed in Section 4.... ..."

### Table 2: Physics-based tracking problem: Free and Fixed Parameters

2006

### Table 5.1: Comparison of different physically based deformable model approaches. Accuracy determines how closely the behaviour of the simulated model matches the behaviour of the real world object.

2006

### Table 2. Quasiphysical and Physically Based Hydrological Modelsa

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### Table 1.1: An overview of the algorithms presented in the publications that make up this thesis. Publication [P1] presents a theoretical framework for precomputed light transport (PLT). Publications [P2] and [P3] describe interactive techniques for global illumination and shadows on deformable objects, respectively, while Publication [P4] presents a physically-based soft shadow algorithm for off-line use.

### Table 2: Di erent possible cases for C = AB. to nodes so that it is consistent with the distribution of the vectors, as we describe below. We call such matrix distributions physically based if the layout of the vectors which induce the distribution of A to nodes is consistent with where an application would naturally want them. We will use the abbreviation PBMD for Physically Based Matrix Distribution. We now describe the distribution of the vectors, x and y, to nodes, after which we will show how the matrix distribution is induced (derived) by this vector distribution. Let us assume x and y are of length n and m, respectively. We will distribute these vectors using a distribution block size of bdistr. For simplicity assume n = Nbdistr and m = Mbdistr. Partition x and y so that

"... In PAGE 4: ... Given the operation C = AB there are three dimensions: m, n, and k, where C is m n, A is m k and B is k n. In a typical use, each of these dimensions can be either large or small, leading to the di erent shapes given in Table2 . In our model, we will use a di erent cost for each shape, as indicated in the table.... In PAGE 8: ... We show that di erent blockings of the operands lead to di erent algorithms, each of which can be built from a simple parallel matrix-matrix multiplication kernel. These kernels themselves can be recognized as the special cases in Table2 where one or more of the dimensions are small. The kernels can be separated into two groups.... In PAGE 16: ....1.2 Computation Ultimately, it is the performance of the local 64 bit matrix-matrix multiplication implemen- tation that determines the asymptotic performance rate that can be achieved. Notice that our algorithms inherently operate on matrices and panels, and thus the performance for the di erent cases in Table2 where quot;small quot; is taken to equal the algorithmic blocking size needs to be determined. In our preliminary performance tests, we chose the algorithmic blocking size to equal 128, which has, in the past, given us reasonable performance for a wide range of algorithms.... ..."

### Table 1. Performance of new (1+1)-ES and IFEP finding parameters for a physics-based model of colon colouration. Number of samples = 45.

2004

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### Table 3 Heterogeneous lofting examples with hetero-material profile curves Index Profile curves Lofted surfaces Description

2006

"... In PAGE 6: ....2.2. Heterogeneous material profile curves/surfaces However, to make the heterogeneous lofting more flexible, we can bypass this iso-material constraint and use hetero- material profile curves/surfaces, as shown in Table3 . These two examples are corresponding to examples in Table 1.... In PAGE 13: ...model in (a) Table3 case 1, (b) Table 3 case 2. homogeneous Lagrange element.... In PAGE 13: ... In the above case studies, for the sake of comparison with analytical solutions, we chose examples of relatively simple geometrical shape. However, our approach could be applied to more complicated cases, for example, the applications to the models in Table3 , as shown in Fig. 14.... ..."

### Table 2: MAV design variables

2001

"... In PAGE 2: ... The simulated environment consists of physics-based models of the key aspects of the MAV design space, as shown in Table 1. The design variables used for the first generation MAV optimization study are shown in Table2 . The objective function was to maximize the endurance of the MAV.... ..."

Cited by 21