1. A normal detection method for measuring a plurality of distances to a measurement subject using one or a plurality of distance detectors, and obtaining a normal vector on a measured surface of the measurement subject from the obtained measurement results, the method comprising: representing four or more measurement points on the measured surface at four or more measurement positions with three-dimensional coordinates from the four or more measurement positions where the one or the plurality of distance detectors measures the distances to the measurement subject, and four or more measurement results obtained by the one or the plurality of distance detectors at the four or more measurement positions; defining, as a first vector, a straight line connecting, on three-dimensional axes, a first measurement point measured at an arbitrary first measurement position among the four or more measurement positions by a distance detector and a second measurement point measured at a second measurement position different from the first measurement position; defining, as a second vector, a straight line connecting, on three-dimensional axes, the first measurement point and a third measurement point measured at a third measurement position different from the first measurement position and the second measurement position; obtaining a normal vector on the measured surface by determining an outer product of the first vector and the second vector; calculating a machining vector based on the obtained normal vector; and controlling position of a machining jig so that a central axis of the machining jig coincides with the calculated machining vector, wherein the first measurement position, the second measurement position, and the third measurement position are selected so that the area of a triangle made with three points of the first measurement position, the second measurement position, and the third measurement position becomes the largest among areas of triangles made with combinations of other three points of measurement positions.