New method for the display of three-dimensional vector fields

The paper starts by reviewing the limitations of the existing methods of display of vector fields with particular reference to electromagnetic fields. A new method of display is then proposed which uses an arrow of fixed proportions to display the magnitude and direction of the vector field at each point at which it is known. The arrow head has thickness and the whole arrow is scaled in proportion to the strength of the field so that the orientation perpendicular to the plane of the paper is indicated by the body of the head and foreshortening of the image. The method is illustrated with some computer-generated diagrams. The computer program draws an arrow in the spacially correct position where the vector field is specified by three perpendicular components, having first scaled the arrow to the largest vector magnitude in the field. The system was devised particularly to display the results of finite element analysis of electromagnetic fields, but as an example, it is also used to display the electric and magnetic fields inside rectangular waveguide which have been calculated analytically. It will have applications in all branches of engineering and science where calculations give numerical values of field vectors.