The invention provides a shape member manufacturing apparatus and a shape member manufacturing method which aims at cutting and grinding a joint projection 8B formed when a plurality of shape members are joined together by welding or friction stir welding, in a short time with high accuracy. A first peripheral flange extends around at least a portion of the periphery of the outboard end of the first elongated tubular section. The slope of the ramp wave can be changed by changing the mirror ratio or the capacitance of a comparator as well as by changing the resistance of a DAC. In certain aspects, a normalized loss function f is utilized to determine a preferred construction among a plurality of iteratively generated selections.