Apparatus and methods to model the dimension and contour of a segment of piping to be installed between a pair of open ends of a piping circuit, are provided. A first backing plate of a first end of an exemplary apparatus is connected to a first flange of a piping circuit. A telescopic elongate linkage member is extended and a second backing plate of a second end of the apparatus is connected to a second flange of the piping circuit. Various measurements are taken, to include a rotational angular difference between the backing plate and a coaxial alignment disk coaxially located with the backing plate, an angular difference between a central axis of the backing plate and the main axis of a hinged yoke connected to the coaxial alignment disk, an angular difference between the main axis of the yoke and a longitudinal axis of the linkage member, and an amount of telescopic extension of the linkage member.