The present invention is in the field of manufacturing, processing and design, and also packaging. Nesting is the process of placing objects together with minimal spaces between them. The invention is described below in two forms. The first form, set forth in Part I below, is directed to methods and systems for nesting of two dimensional (2D) objects in a target plane. The second form, set forth in Part II below, is directed to methods and systems for nesting three dimensional (3D) objects in a target volume. The specific details of the preferred embodiments are set forth in those respective parts.

Two curved arch rib supports are provided with a pre-shaped flexible membrane cover attached to the ribs; the ends of the ribs are hinged on a common locus at base supports. When erected, a saddle shaped roof is formed to which contoured end walls may be added. Additional modules may be joined to the structure so formed, by applying a pre-shaped and independent fabric membrane or cable net attached by rings to only each of the two structure base pivot axles. A catenary cable and web belt stress concentrator connect each ring to its opposite on each separate structure. The cable and web are of pre-set length and are shorter than the perimeter of the outer chord of the beam. Alternatively, for joining a plurality of the saddle shaped structures, geodetic stress concentrators may be added to enhance and maintain the shape and performance of the cable net, thus stabilizing and drawing pre-stress or wind reactions from the membrane and facilitating their efficient flow to the ground anchors in purely tensile forces.

A computer-based system and method is provided for positioning a cutter tool to an edge of a solid model in a computer aided manufacturing environment. A shortest distance and direction required to position the machine tool cutter to the edge of the solid model is determined. Edges are defined as three dimensional space curves. The machine tool cutter is defined as a convex envelope. Using the space curve definition, the cutter location, and the center axis of rotation for the cutter, computations are executed to determine a directional vector and distance such that moving the cutter along the vector for the prescribed distance will cause it to be in contact with the curve. Adjustments are available which cause the cutter to travel to offsets from the curve, including aligning the front of the cutter to the curve, the end of the cutter on the curve, or the back of the cutter past the curve.

A light-weight portable structure having a plurality of planar panels joined together to form a dome-shaped structure. The generally trapezoidal-shaped panels have arcuate side edges instead of linear side edges in order to create the proper tension and cause the flexible panels to form the desired dome structure. The individual panels are joined together by H-shaped connectors extending the full side length of the panels. The side edges of the panels are fitted with a U-shaped locking caps before being inserted into the connectors. The caps of adjacent side panels are inserted into the open ends of the H-shaped connectors and are held in place by the connectors. As the panels are connected in series standing upright on the base edges of the panels, the cumulative forces used to insert the panels causes the partial structure to curve in a spiral manner. The spiral is unwound and the panels are pushed out at the base of the panels to form the circular shape of the structure and to connect the two free ends of the series of panels. This process transfers forces towards the narrower, top edge of the panels, which causes the panels and connectors to bend towards the center of the structure to form a dome.

A geodesic structure comprising convex-concave elements. The elements are easily manufactured, simple shapes that can be assembled randomly to form a geodesic structure, such as a dome. The geodesic structure can also be used to make flat maps of spherical bodies, exhibiting very little distortion.