Abstract: A sampling point generating apparatus generates sampling points on an original curve even at gentle slope portions of the original curve and, according to the sampling points, provides a curve that closely approximates the original curve. To accomplish this function, the apparatus has a unit for drawing a straight line between the start and end points of the original curve; a unit for calculating errors between the coordinates of the original curve and the coordinates of the straight line; a unit for detecting extremal value points, where increase or decrease in the errors is reversed, according to the errors; and a unit for generating intermediate points among the extremal value points. The extremal value points and intermediate points are used as sampling points to provide a cubic curve that closely approximates the original curve.