text: Although the input vector field and the result image are discretized, it pays to look at it from a continuous viewpoint. Let  be the vector field given in some domain . Although the input vector field is typically discretized, we regard the field  as defined in every point of , i.e. we assume an interpolation. Streamlines, or more generally field lines, are tangent to the vector field in each point. They end either at the boundary of  or at critical points where . For the sake of simplicity, in the following critical points and boundaries are ignored. A field line , parametrized by arc length , is defined as . Let  be the field line that passes through the point  for . Then the image gray value at  is set to
  where  is the convolution kernel,  is the noise image, and  is the length of field line segment that is followed.
   has to be computed for each pixel in the LIC image. If carried out naively, this is quite expensive. First, the field lines have to be computed using a numerical method for solving ordinary differential equations, like a Runge–Kutta method, and then for each pixel the convolution along a field line segment has to be calculated.
  The output image will normally be colored in some way. Typically some scalar field in  is used, like the vector length, to determine the hue, while the gray-scale LIC image determines the brightness of the color.
  Different choices of convolution kernels and random noise produce different textures: for example pink noise produces a cloudy pattern where areas of higher flow stand out as smearing, suitable for weather visualization. Further refinements in the convolution can improve the quality of the image.