Academic literature on the topic 'Trilinear Coordinates'

Abstract This paper describes a three-dimensional immersed boundary method (IBM) that facilitates the explicit resolution of complex terrain within the Weather Research and Forecasting (WRF) model. Two interpolation methods—trilinear and inverse distance weighting (IDW)—are used at the core of the IBM algorithm. This work expands on the previous two-dimensional IBM algorithm of Lundquist et al., which uses bilinear interpolation. Simulations of flow over a three-dimensional hill are performed with WRF’s native terrain-following coordinate and with both IB methods. Comparisons of flow fields from the three simulations show excellent agreement, indicating that both IB methods produce accurate results. IDW proves more adept at handling highly complex urban terrain, where the trilinear interpolation algorithm fails. This capability is demonstrated by using the IDW core to model flow in Oklahoma City, Oklahoma, from intensive observation period 3 (IOP3) of the Joint Urban 2003 field campaign. Flow in Oklahoma City is simulated concurrently with an outer domain with flat terrain using one-way nesting to generate a turbulent flow field. Results from the IBM-WRF simulation of IOP3 compare well with observations from the field campaign, as well as with results from an urban computational fluid dynamics code, Finite Element Model in 3-Dimensions and Massively Parallelized (FEM3MP), which used body-fitted coordinates. Using the FAC2 performance metric from Chang and Hanna, which is the fraction of predictions within a factor of 2 of observations, IBM-WRF achieves 100% and 71% for velocity predictions using cup and sonic anemometer observations, respectively. For the passive scalar, 53% of the model predictions meet the FAC5 (factor of 5) criteria.

A central task of computer vision is to automatically recognize objects in real-world scenes. The parameters defining image and object spaces can vary due to lighting conditions, camera calibration and viewing positions. It is therefore desirable to look for geometric properties of the object which remain invariant under such changes. In this paper we present geometric algebra as a complete framework for the theory and computation of projective invariants formed from points and lines in computer vision. We will look at the formation of 3D projective invariants from multiple images, show how they can be formed from image coordinates and estimated tensors (F, fundamental matrix and T, trilinear tensor) and give results on simulated and real data.

By exploiting favorable characteristics of a uniform cross-array, a passive localization algorithm of narrowband cyclostationary sources in the spherical coordinates (azimuth, elevation, and range) is proposed. Firstly, we construct a parallel factor (PARAFAC) analysis model by computing the third-order cyclic moment matrices of the properly chosen sensor outputs. Then, we analyze the uniqueness of the constructed model and obtain three-dimensional (3D) near-field parameters via trilinear alternating least squares regression (TALS). The investigated algorithm is well suitable for the localization of the near-field cyclostationary sources. In addition, it avoids the multidimensional search and pairing parameters. Results of computer simulations are carried out to confirm the satisfactory performance of the proposed method.