Method employing sequential two-dimensional geometry for producing shells for fabrication by a rapid prototyping system

A method for operating a system to fabricate a three dimensional object from a computer-generated specification of a solid S, the computer-generated specification of the solid S being oriented in an xyz-coordinate frame and having a height along the z-axis, comprising the steps of:

• (a) preprocessing the computer-generated specification of S, the step of preprocessing including the steps of,
• for each face f.sub.i lying on a boundary of the solid S, constructing a bounding z-axis interval I.sub.i =[z.sub.imin, Z.sub.max ];
• for all i, constructing an enlarged interval I.sub.i +=[z.sub.imin -t, z.sub.imax +t], where t is a thickness of a shell of S;
• and
• storing the enlarged intervals I+ for subsequent access;
• (b) searching the stored enlarged intervals to determine a specification of one slice of the shell of S, including the steps of,
• initializing a set of primitive slices .PI.=NULL;
• and
• for each interval I.sub.i + that contains a query point z.sub.q that overlaps with a query interval I.sub.q, adding P.andgate.{CL(f.sub.i .sym.B.sub.t)} to H.PI., where P is a slice plane, c1 indicates a closure, and B.sub.t is an open ball of radius t;
• (c) merging the set of primitive slices by performing a union of all of the primitive slices in .PI. to obtain .SIGMA.;
• and
• (d) returning (P.andgate.S).andgate..SIGMA. as the specification of one slice of the shell of S, including providing the specification of the one slice of the shell of S to a material deposition means for fabricating portion of the object in accordance with the specification of the one slice;
• and
• (e) thereafter operating the system to deposit material by said material deposition means to fabricate a portion of the object in accordance with the specification of the one slice.