This paper describes the results of basic studies on procedures for creating solid models of component geometry from two-dimensional orthographic projections. An interactive graphic program was developed to allow the input of three orthographic views of a component geometry by digitizing from a drawing. The views may contain straight lines and circular arcs, solid or dashed. No restrictions are placed on the order or direction of lines and arcs in any view. Using an extension of the Wesley-Markowski procedure, the program constructs a three-dimensional solid model of the object. When the projections are ambiguous, multiple solid models are produced. The solid model may contain planar, cylindrical, conical, spherical and toroidal surfaces. Topological information of the solid model is stored in a winged edge structure. Geometric information is stored as vertex coordinates and surface equations.

A system has been developed which utilizes variational geometry in the design and modification of mechanical parts. Three-dimensional constraints between characteristic points are used to define an object's geometry. Modification of geometry is accomplished by alteration of one or more constraints. A matrix method is used to determine the shape of the part by simultaneous solution of constraint equations. A method for increasing the speed and efficiency of the solution procedure is described. The method uses the relationships between the geometry and constraints to minimize the number of equations and variables to be solved.