Declaring and Initializing Points

The most basic drawable object in 3DLDF is class Point. It is analogous to pair in Metafont. For example, in Metafont one can define a pair using the "z" syntax as follows:

     z0 = (1cm, 1cm);
     

There are other ways of defining pairs in Metafont (and MetaPost), but this is the usual way.

In 3DLDF, a Point is declared and initialized as follows:

     Point pt0(1, 2, 3);
     

This simple example demonstrates several differences between Metafont and 3DLDF. First of all, there is no analog in 3DLDF to Metafont's "z" syntax. If I want to have Points called "pt0", "pt1", "pt2", etc., then I must declare each of them to be a Point:

     Point pt0(10, 15, 2);
     Point pt1(13, 41, 5.5);
     Point pt2(62.9, 7.02, 8);
     

Alternatively, I could declare an array of Points:

     Point pt[3];
     

Now I can refer to pt[0], pt[1], and pt[2].

In the Metafont example, the x and y-coordinates of the pair z0 are specified using the unit of measurement, in this case, centimeters. This is currently not possible in 3DLDF. The current unit of measurement is stored in the static variable Point::measurement_units, which is a string. Its default value is "cm" for "centimeters". At present, it is best to stick with one unit of measurement for a drawing. After I've defined an input routine, 3DLDF should handle units of measurement in the same way that Metafont does.

Another difference is that the Points pt0, pt1, and pt2 have three coordinates, x, y, and z, whereas z0 has only two, x and y. Actually, the difference goes deeper than this. In Metafont, a pair has two parts, xpart and ypart, which can be examined by the user. In 3DLDF, a Point contains the following sets of coordinates:

     world_coordinates
     user_coordinates
     view_coordinates
     projective_coordinates
     

These are sets of 3-dimensional homogeneous coordinates, which means that they contain four coordinates: x, y, z, and w. Homogeneous coordinates are used in the affine and perspective transformations (see Transforms).

Currently, only world_coordinates and projective_coordinates are used in 3DLDF. The world_coordinates refer to the position of a Point in 3DLDF's basic, unchanging coordinate system. The projective_coordinates are the coordinates of the two-dimensional projection of the Point onto a plane. This projection is what is ultimately printed out or displayed on the computer screen. Please note, that when the coordinates of a Point are referred to in this manual, the world_coordinates are meant, unless otherwise stated.

Points can be declared and their values can be set in different ways.

     Point pt0;
     Point pt1(1);
     Point pt2(2.3, 52);
     Point pt3(4.5, 7, 13.205);
     

pt0 is declared without any arguments, i.e., using the default constructor, so the values of its x, y, and z-coordinates are all 0.

pt1 is declared and initialized with one argument for the x-coordinate, so its y and z-coordinates are initialized with the values of CURR_Y and CURR_Z respectively. The latter are static constant data members of class Point, whose values are 0 by default. They can be reset by the user, who should make sure that they have sensible values.

pt2 is declared and initialized with two arguments for its x and y-coordinates, so its z-coordinate is initialized to the value of CURR_Z. Finally, pt3 has an argument for each of its coordinates.

Please note that pt0 is constructed using a the default constructor, whereas the other Points are constructed using a constructor with one required argument (for the x-coordinate), and two optional arguments (for the y and z-coordinates). The default constructor always sets all the coordinates to 0, irrespective of the values of CURR_Y and CURR_Z.