by parameter t being zero at b 0 and 1 at b 2 with intermediate points described by r t 1 u2212 t 2 b 0 2 t 1 u2212 t b 1 t 2 b 2 differentiating this gives the derivative vector r u2032 which gives the slope of the curve r u2032 t 2 t u2212 1 b 0 1 u2212 2 t b 1 tb 2 when the three points are not in a plane then r t is a space curve rather than a parabola in asap the three coordinate triplets mentioned are those of the three defining point vectors b 0 b 1 and b 2 ray fan 141 of fig1 has the width necessary to achieve the desired illumination level at the center of the target and in short throw lighting this is less than what the led would do by itself this means the central part of the illumination lens must demagnify the source which is why the lens center is has a diverging optical power with negative focal length in fact the very function of lens center 140 is to provide the proper size of source image of which ray fan 141 is a cross section for the target center x t 0 inherent to short throw illumination lenses is that this target center source image is smaller.