or a black line and this would make the image confusing for the user with minimum arc interpolation as depicted in fig1 b the interpolation direction is along the minimum distance from a to b when they are arranged as depicted in a circular manner so the value of a rises up until it reaches maximum intensity then flips the sign and then moves from the highest blue value to the value of b finally fig1 c depicts the sign value mapping interpolation of the present invention on the left the two values a and b are shown in the grey shaded box where they are placed at the respective intensities independent of the sign in the box on the right the values a and b are placed according to the direction positive or negative which is depicted as either red or blue the interpolation is carried out separately in contrast to minimum arc interpolation the intensity of either value is never below or above the actual value of a or b the direction sign change is determined by nearest neighbour filtering so the point of turn is always in the middle of the ab region fig2 shows mathematical graphs depicting the various interpolation methods as shown in fig1 fig2 a and fig2 b show normal and minimum arc interpolation whereas fig2 c 1 and 2 c 2 show the interpolations according to the present invention where fig2 c 1 shows the interpolation according to the first embodiment and fig2 c 2 shows the interpolation according to the second embodiment in the first embodiment which is depicted in fig2 c 1 the sign is determined by nearest neighbour filtering i e the.