Fast and resolution independent line integral convolution

Line Integral Convolution (LIC) is a powerful technique for generating striking images and animations from vector data. Introduced in 1993, the method has rapidly found many application areas, ranging from computer arts to scientific visualization. Based upon locally filtering an input texture along a curved stream line segment in a vector field, it is able to depict directional information at high spatial resolutions. We present a new method for computing LIC images, which minimizes the total number of stream lines to be computed and thereby reduces computational costs by an order of magnitude compared to the original algorithm. Our methods utilizes fast, error-controlled numerical integrators. Decoupling the characteristic lengths in vector field grid, input texture and output image, it allows to compute filtered images at arbitrary resolution. This feature is of great significance in computer animation as well as in scientific visualization, where it can be used to explore vector data by smoothly enlarging structure of details. We also present methods for improved texture animation, employing constant filter kernels only. To obtain an optimal motion effect, spatial decay of correlation between intensities of distant pixels in the output image has to be controlled. This is achieved by blending different phase shifted box filter animations and by adaptively rescaling the contrast of the output frames.

[1]  Nelson L. Max,et al.  Flow volumes for interactive vector field visualization , 1993, Proceedings Visualization '93.

[2]  E. Hairer,et al.  Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems , 1993 .

[3]  Lisa K. Forssell.  Visualizing flow over curvilinear grid surfaces using line integral convolution , 1994, Proceedings Visualization '94.

[4]  Paul Haeberli,et al.  Paint by numbers: abstract image representations , 1990, SIGGRAPH.

[5]  Nancy J. Nersessian,et al.  Faraday’s Field Concept , 1985 .

[6]  Lambertus Hesselink,et al.  Visualizing vector field topology in fluid flows , 1991, IEEE Computer Graphics and Applications.

[7]  Jeffrey P. M. Hultquist,et al.  Interactive numerical flow visualization using stream surfaces , 1996 .

[8]  Ken Perlin,et al.  [Computer Graphics]: Three-Dimensional Graphics and Realism , 2022 .

[9]  Alan H. Karp,et al.  A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides , 1990, TOMS.

[10]  Frits H. Post,et al.  Visualization of turbulent flow with particles , 1993, Proceedings Visualization '93.

[11]  Peter Deuflhard,et al.  Numerische Mathematik II , 1994 .

[12]  Jarke J. van Wijk.  Rendering surface-particles , 1992, Proceedings Visualization '92.

[13]  Brian Cabral,et al.  Imaging vector fields using line integral convolution , 1993, SIGGRAPH.

[14]  J. van Wijk,et al.  Spot noise texture synthesis for data visualization , 1991, SIGGRAPH.

[15]  F. A. Seiler,et al.  Numerical Recipes in C: The Art of Scientific Computing , 1989 .

[16]  Kwan-Liu Ma,et al.  Virtual Smoke: an interactive 3D flow visualization technique , 1992, Proceedings Visualization '92.

[17]  Ernst Hairer,et al.  Solving Ordinary Differential Equations I: Nonstiff Problems , 2009 .

[18]  J. Dormand,et al.  High order embedded Runge-Kutta formulae , 1981 .

[19]  William H. Press,et al.  The Art of Scientific Computing Second Edition , 1998 .