Abstract: This disclosure describes a method to verify the design of an article of manufacture that includes a software program executing on a workstation that executes the following steps: providing the shape of a first component and providing the shape of a second component; providing a boundary distance constraint; constructing a shape spectrum of the exterior boundary surface of closest approach associated with the shape of the first component, the shape of the second component, and the boundary distance constraint; verifying that the arrangement of the shape of the first component and the shape of the second component satisfy the boundary distance constraint; evaluating a subderivative of the shape spectrum of the exterior boundary surface of closest approach associated with the shape of the first component, the shape of the second component; where verifying that the boundary distance constraint is satisfied between the shape of the first component and the shape of the second component and when satisfied, the desi

Abstract: This disclosure describes a method to verify the design of an article of manufacture that includes a software program executing on a workstation that executes the following steps: providing the shape of a first component and providing the shape of a second component; providing a boundary distance constraint; constructing a shape spectrum of the exterior boundary surface of closest approach associated with the shape of the first component, the shape of the second component, and the boundary distance constraint; verifying that the arrangement of the shape of the first component and the shape of the second component satisfy the boundary distance constraint; evaluating a subderivative of the shape spectrum of the exterior boundary surface of closest approach associated with the shape of the first component, the shape of the second component; where verifying that the boundary distance constraint is satisfied between the shape of the first component and the shape of the second component and when satisfied, the desi

Abstract: This disclosure describes a method and design in producing the design of an article of manufacture that includes two or more components and the method satisfies the analytical representation of the boundary distance constraint between the shapes of the two components during the design. The disclosure includes providing a software program executing on a workstation that executes a number of steps that include: Providing the shape of a first component, the shape of a second component, and a boundary distance constraint. The disclosure includes the construction of a shape spectrum. The disclosure searches to find an arrangement of the shapes. The disclosure evaluates the boundary distance constraint to determine if the boundary distance constraint is satisfied. Further, the disclosure evaluates a subderivative of the shape spectrum. Additionally, the disclosure provides that the searching continues until the boundary distance constraint is satisfied, and when satisfied, the design is produced.