Direct interactive visualization of locally refined spline volumes for scalar and vector fields
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We present a novel approach enabling interactive visualization of volumetric Locally Refined B-splines (LR-splines). To this end we propose a highly efficient algorithm for direct visualization of scalar and vector fields given by an LR-spline. For the case of scalar fields a volume rendering approach is designed, along with methods for the necessary adaptive sampling distance, on-the-fly trimming with a surface geometry given by a STereoLithography (STL)-file, and local volume illumination based on on-the-fly evaluation of the derivative of the underlying LR-spline function. For vector fields we design a two-stage algorithm consisting of the computation of stream lines with adaptive step size and their rendering with tubes. In both cases, the common basic ingredient to achieve interactive frame rates is an acceleration structure based on a k-d forest together with suitable data structures. The algorithms are designed to fully utilize modern graphics processing unit (GPU) capabilities. Important applications where LR-spline volumes emerge are given for instance by approximation of large-scale simulation and sensor data, and Isogeometric Analysis (IGA). For the first case -- approximation of large three dimensional point clouds with an associated field -- we provide an extension of the multilevel B-spline approximation (MBA) algorithm to the case of volumetric LR-splines. We showcase interactive rendering achieved by our approach on different representative use cases, stemming from simulations of wind flow around a telescope, Magnetic Resonance (MR) imaging of a human brain, and simulations of a fluidized bed used for mixing and coating particles in industrial processes.
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