libm3/src/geometry/Trapezoid.i3

 Copyright (C) 1992, Digital Equipment Corporation                         
 All rights reserved.                                                      
 See the file COPYRIGHT for a full description.                            
                                                                           
 Trapezoid.def, coded July 87 by Scott Seligman 
 Last modified on Tue Feb 11 16:25:00 PST 1992 by muller     
      modified on Tue Dec 17 13:11:39 PST 1991 by mhb        
      modified on Mon Nov  4 19:52:51 PST 1991 by gnelson    
      modified on Mon Sep  7 19:11:20 1987 by seligman       

<*PRAGMA LL*>

 A Trapezoid.T represents a set of points lying in a quadrilateral
   whose north and south edges are horizontal and whose west and east
   edges have arbitrary non-horizontal slopes.  For example, a diagonal 
   line can be represented as a tall skinny trapezoid.  


INTERFACE Trapezoid;

IMPORT Point;

TYPE
  T = RECORD
    vlo, vhi: INTEGER;
    m1, m2: Rational;
    p1, p2: Point.T;
  END;
  Rational = RECORD n, d: INTEGER END;

 For a trapezoid tr, 


\medskip\bulletitem tr.vlo and tr.vhi are the v coordinates of its north and south edges, respectively;


\medskip\bulletitem tr.m1 and tr.m2 are the slopes of its west and east edges, respectively, as (delta v) / (delta h). A denominator
of zero represents an infinite slope; i.e., a vertical
edge. A numerator of zero is illegal. 


\medskip\bulletitem tr.p1 and tr.p2 are points on the infinite lines
that extend the west and east edges, respectively.  


\medskip
Trapezoids are closed on the north and west edges, open on the
south and east edges, closed on the northwest corner, and open on
the other corners. 


A Rational q represents the rational number q.n/q.d. 




PROCEDURE FromEdges (y1, p1, q1: INTEGER;
                     y2, p2, q2: INTEGER): T;

 Return a trapezoid whose vertices are (p1, y1), (q1, y1),
   (p2, y2), and (q2, y2). The altitude of the trapezoid must be
   non-zero. 

PROCEDURE FromVertices (READONLY p1, p2, q1, q2: Point.T): T;

 Return a trapezoid from four vertices. The p1 and p2 vertices
   must have the same y-coordinates, as must the q1 and q2 vertices. 
   Furthermore, the altitude of the trapezoid must be non-zero. 

PROCEDURE FromTriangle (READONLY a, b, c: Point.T): T;

 Return a trapezoid from the vertices of a triangle. One of the sides of
   the triangle must be parallel to the x-axis, and the triangle's altitude
   must be non-zero. 

END Trapezoid.