Rectangles

A Rectangle can be constructed in the x-z plane by specifying a center Point, the width, and the height:

     Rectangle r(origin, 2, 3);
     r.draw();
     

Fig. 27.

Three additional arguments can be used to specify rotation about the x, y, and z-axes respectively:

     Rectangle r(origin, 2, 3, 30, 45, 15);
     r.draw();
     

Fig. 28.

If a Point p other than the origin is specified as the center of the Rectangle, the latter is first created in the x-z plane, centered about the origin, as above. Then, any rotations specified are performed. Finally, the Rectangle is shifted such that its center comes to lie at p:

     Point p0(.5, 1, 3);
     Rectangle r(p0, 4, 2, 30, 30, 30);
     r.draw();
     

Fig. 29.

This constructor has a corresponding setting function:

     Rectangle r;
     for (int i = 0; i < 180; i += 30)
       {
         r.set(origin, 4, 2, i);
         r.draw();
       }
     

Fig. 30.

Rectangles can also be specified using four Points as arguments, whereby they must be ordered so that they are contiguous in the resulting Rectangle:

     Point pt[4];
     pt[0].shift(-1, -2);
     pt[2] = pt[1] = pt[0];
     pt[1].rotate(180);
     pt[3] = pt[1];
     pt[2] *= pt[3].rotate(0, 180);
     Rectangle r(pt[0], pt[2], pt[3], pt[1]);
     r.draw();
     

Fig. 31.

This constructor checks whether the Point arguments are coplanar, however, it does not check whether they are really the corners of a valid rectangle; the user, or the code that calls this function, must ensure that they are. In the following example, r, although not rectangular, is a Rectangle, as far as 3DLDF is concerned:

     pt[0].shift(0, -1);
     pt[3].shift(0, 1);
     Rectangle q(pt[0], pt[2], pt[3], pt[1]);
     q.draw();
     

Fig. 32.

This constructor is not really intended to be used directly, but should mostly be called from within other functions, that should ensure that the arguments produce a rectangular Rectangle. There is also no guarantee that transformations or other functions called on Rectangle, Circle, or other classes representing geometric figures won't cause them to become non-rectangular, non-circular, or otherwise irregular. Sometimes, this might even be desirable. I plan to add the function Rectangle::is_rectangular() soon, so that users can test Rectangles for rectangularity.