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Wolf of eTc group / Scene
Projection.
The mathematical basis of
images of three-dimensional objects on the screen
is to design objects on
two-dimensional plane of the monitor screen.
We consider three ways of designing
objects:
1. Dimetricheskaya projection.
x '= y-x * c;
y '= z-x * c;
where x, y, z - three-dimensional coordinates of a point
in space, and x ', y' - two-dimensional
coordinates on the screen. c -
coefficient which is equal to:
c = sqrt (2) / 2; c = 0.707106781;
{Sqrt-square root}
2. Isometric projection.
x '= (y-x) * c1;
y '= z-(x + y) / 2;
where x, y, z - three-dimensional coordinates of a point
in space, and x ', y' - two-dimensional
coordinates on the screen.
c1 = sqrt (3) / 2; c = 0.866025404;
3. The view from the camera.
y z
/
/
/
x
/
*
/
* - The location of the camera.
Projecting in this location
camera in three dimensions, will
following form:
x '= x * camera / (x + camera);
y '= y * camera / (z + camera);
where x, y, z - three-dimensional coordinates of a point
in space, and x ', y' - two-dimensional
coordinates on the screen.
camera - camera distance from the beginning
coordinates.
Naturally all of these modified
coordinates x 'and y' must be put to
coordinates of the center of the screen:
x '= x' + x_size / 2;
y '= y' + y_size / 2;
where x_size - the width of the screen, and y_size -
height.
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