LIC-R: Line Integral Convolution Revisited

We present a novel formulation of Line Integral Convolution (LIC), a fundamental method for visualizing vector fields in flow visualization. Our approach reinterprets the traditional LIC technique by leveraging a regularized, directional curvature flow along streamlines, utilizing material derivatives to achieve the desired convolution. By adopting an entirely Eulerian framework, our method eliminates the need for complex numerical integration and high-order interpolation schemes that are typically required in classical LIC algorithms. This shift not only simplifies the implementation of LIC, making it more accessible for both CPU and GPU architectures, but also significantly reduces the computational overhead. Despite these simplifications, our method maintains visual quality comparable to that of more traditional and computationally expensive approaches. Moreover, the discrete nature of our formulation makes it particularly well-suited for irregular grids and sparse data, broadening its applicability in practical settings. Through various experiments, we demonstrate that our algorithm delivers efficient and visually coherent results, offering an attractive alternative for dense flow visualization with reduced complexity.