Distance Computation between Convex Objects using Axis-Aligned Bounding-Box in Virtual Environment Application

Performing collision detection between convex objects in virtual environment simulation is one of vital problems in computer visualization research area. Given a set of two or more colliding objects, in order to determine the exact point of contact between object we need to undergo various high computation algorithm. In this paper, we describes our current work of determining the precise contact by measuring the distance between near colliding objects in order to maintain the accuracy and improve the speed of collision detection algorithm. Common method determine the distance by checking for vertices and edges point between objects in brute force condition. Compared to our method, by given set of objects in virtual environment world, we find the closest point between near colliding objects and bound the potential colliding area with an Axis-Aligned Bounding-Box. Then, we approximate the distance by measuring the distance of the box itself and hence recognize potential colliding area faster than the common method. Our method proven to most effective and efficient for narrow phase collision detection by removing unnecessary testing and reduced computational cost

Model-reduced variational fluid simulation

We present a model-reduced variational Eulerian integrator for incompressible fluids, which combines the efficiency gains of dimension reduction, the qualitative robustness of coarse spatial and temporal resolutions of geometric integrators, and the simplicity of sub-grid accurate boundary conditions on regular grids to deal with arbitrarily-shaped domains. At the core of our contributions is a functional map approach to fluid simulation for which scalar- and vector-valued eigenfunctions of the Laplacian operator can be easily used as reduced bases. Using a variational integrator in time to preserve liveliness and a simple, yet accurate embedding of the fluid domain onto a Cartesian grid, our model-reduced fluid simulator can achieve realistic animations in significantly less computational time than full-scale non-dissipative methods but without the numerical viscosity from which current reduced methods suffer. We also demonstrate the versatility of our approach by showing how it easily extends to magnetohydrodynamics and turbulence modeling in 2D, 3D and curved domains

View-Dependent Multiscale Fluid Simulation

Fluid flows are highly nonlinear and nonstationary, with turbulence occurring and developing at different length and time scales. In real-life observations, the multiscale flow generates different visual impacts depending on the distance to the viewer. We propose a new fluid simulation framework that adaptively allocates computational resources according to the viewer's position. First, a 3D empirical mode decomposition scheme is developed to obtain the velocity spectrum of the turbulent flow. Then, depending on the distance to the viewer, the fluid domain is divided into a sequence of nested simulation partitions. Finally, the multiscale fluid motions revealed in the velocity spectrum are distributed nonuniformly to these view-dependent partitions, and the mixed velocity fields defined on different partitions are solved separately using different grid sizes and time steps. The fluid flow is solved at different spatial-temporal resolutions, such that higher frequency motions closer to the viewer are solved at higher resolutions and vice versa. The new simulator better utilizes the computing power, producing visually plausible results with realistic fine-scale details in a more efficient way. It is particularly suitable for large scenes with the viewer inside the fluid domain. Also, as high-frequency fluid motions are distinguished from low-frequency motions in the simulation, the numerical dissipation is effectively reduced