Patent Document ID: 5481658
Application ID: 08124156
Patent Status: 1

Claim One:
1. A method of digitally determining and displaying a line that passes through a set of K boxes of a display image in a computer system, the boxes defined by box data vertex values defined with respect to a coordinate system and stored in memory of the computer system, such that the line passes through display image surfaces of each box in the set and thereby comprises a transversal line of the display image, the method comprising the steps producing a transformed set of digital box data vertex values comprising three-tuples (x.sub.1, x.sub.2, x.sub.3) in the computer memory that define respective vertex values of the K boxes relative to axes D.sub.1, D.sub.2, and D.sub.3 of the coordinate system such that the tuple position corresponding to a vertex value of a box is denoted either a.sub.i or b.sub.i, i=1, 2, 3 by a central processor unit of the computer system, where a vertex value of a box is denoted as an "a" if it is the minimum value of the box data vertex values along a respective D axis and the vertex value is denoted as a "b" if it is the maximum value of the box data vertex values along a respective D axis; producing a partition set in the computer memory comprising all three-tuples determined by the central processor unit as having elements selected from the set {+, 0, -} such that each three-tuple element corresponds to a partition subset I.sub.+, I.sub.0, or I.sub.- ; producing a set of linear inequality equations stored in the computer memory by the central processing unit that specify a set of line conditions comprising (1) for all the K boxes and for every digital box data vertex value that is an element of the partition subset I.sub.0, the maximum value of a box vertex value a; is less than or equal to the minimum value of a box vertex value b.sub.i for each box K, (2) for every i that is an element of the partition subset I.sub.+, all box data vertex values x.sub.i are greater than zero and for every i that is an element of the partition subset I.sub.-, the x.sub.i are less than zero, (3) for all i and j that are elements of the partition subset I.sub.+ and for all the boxes K, the difference of the product a.sub.i x.sub.i and a box data vertex value y.sub.i is less than or equal to the difference of b.sub.j x.sub.j and y.sub.j, (4) for all i and j that are elements of the partition subset I.sub.- and for all the K boxes, the difference of the product a.sub.i x.sub.i and a box data value y.sub.i is greater than or equal to the difference of b.sub.j x.sub.j and y.sub.j, (5) for every i that is an element of the partition subset I.sub.+ and for every J that is an element of the partition subset I.sub.- and for all of the K boxes, the difference of the product b.sub.i x.sub.i and the box data vertex value y.sub.i is greater than or equal to the difference of b.sub.j x.sub.j and y.sub.j and also the difference of the product a.sub.j x.sub.j and the box data vertex value y.sub.j is greater than or equal to the difference of a.sub.x x.sub.i and y.sub.i ; producing a resultant solution comprising two three-tuples R=(r.sub.1, r.sub.2, r.sub.3) and S=(s.sub.1, s.sub.2, s.sub.3) in the computer memory that are determined by the central processor unit of the computer system to satisfy the line conditions and thereby determine the transversal line; producing a central processor unit parametric representation of the transversal line determined by R and S in a form defined by an equation u+tv, where u and v are vectors and t is a scalar variable with respect to the coordinate system; producing a display signal determined by the central processing unit as corresponding to the resultant solution and the parametric representation of the transversal line and set of boxes; and displaying a plurality of objects and display signal simultaneously on a two-dimensional display of the computer system.