An N-dimensional algorithm to draw contour lines over triangular elements

In the process of solving electromagnetic boundary-value problems by means of numerical methods, such as the finite element method (FEM) or the boundary element method (BEM), the postprocessing phase is of great importance. In this phase graphical restitutions (contour lines or vector fields) have to be drawn and integral parameters (capacitances, fluxes, forces) have to be computed. A simple algorithm is presented to draw accurate contour lines over triangular elements of high order and with curved sides, in a 2D or 3D space. The algorithm, applicable both to FEM and BEM, is based on the regular decomposition of the standard triangle into smaller ones on the sides of which the points of the contour lines are interpolated. An optimized "pursuing" procedure is utilized to draw the resulting broken line approximating the contour line. An extension to quadrangular finite elements is also given.