Imaging vector field using SMP images

This paper presents a new concept of texture image method for displaying divergent-free vector field on surfaces, sine modulated potential (SMP) map. A scalar potential for such vector field is first defined. Field vectors are then mapped to a grayscale image through its scalar potential modulated with a sine function. The image visualizes a soft appearance of flux tubes instead of flux lines, whose orientation and width reflect the direction and amplitude of field vectors respectively. Animated SMP images can identify the exact "flow" direction inside each flux tube for the vector field at a specific moment, which is often missed in other visualization techniques. SMP images can also be animated for visualization of time-varying field, in which the variation of the field in space and the variation with time can be revealed simultaneously.