3D Computer Graphics

As opposed to 2D, 3D uses an additional coordinate Z. X and Y are used in 2D but Z is used in 3D. The entertainment, gaming, and computer-aided design industries rely on 3D graphics. This field of research is constantly evolving.

Furthermore, 3D graphics components are now included in nearly every personal computer, and although traditionally used for graphics-intensive software like games, they are increasingly found in other applications.

Parallel Projection

The parallel projection ignores the z-coordinate and extends parallel lines from each vertex of the object until they intersect the view plane. Instead of specifying the center of projection, a parallel projection specifies a direction.

Parallel projection involves an infinite distance from the center of projection to the project plane. In this type of projection, we connect the projected vertices with line segments that correspond to the connections on the original object.

Although parallel projection is less realistic, it is good for precise measurements. In this type of projection, parallel lines remain parallel, but angles are not preserved. The following hierarchy illustrates various parallel projection types.

Orthographic Projection

An orthographic projection has a projection direction normal to the plane's projection. Orthographic projections can be categorized into three types.

Front Projection
Top Projection
Side Projection
Oblique Projection

In oblique projection, the direction of projection is not normal to the projection of plane. We can view objects more clearly in oblique projection than in orthographic projection.

Oblique projections are classified as Cavalier and Cabinet. Cavalier projections make an angle of 45° with the projection plane. In Cavalier projection, the projection of a line parallel to the view plane has the same length as the line itself. A cavalier projection has equal foreshortening factors for all three principal directions.

An angle of 63.4° is made between the projection plane and the Cabinet projection. Cabinet projection projects lines perpendicular to the viewing surface at a distance of 12 times their real length. Fig. 1* shows both projections.

Isometric Projections

Axonometric orthographic projections are those that show more than one side of an object. An axonometric projection is an isometric projection in which the projection plane intersects each coordinate axis in the model coordinate system at an equal distance. Parallelism of lines is preserved in this projection, but angles are not preserved. (*)

Perspective Projection

As the distance from the center of projection to the project plane is finite, the size of the object varies inversely with distance, which gives a more realistic look.

The distance and angle of the projection are unpreserved and parallel lines are not preserved. All of them converge at a single point called a center of projection or projection reference point. Below is a chart that illustrates three types of perspective projections.

One-point perspective projections are straightforward to draw.
Two-point perspective projections give a better sense of depth.
Drawing a three-point perspective projection is the most challenging.

Here are the three types of perspective projection.

Translation

Three-dimensional translation involves the transfer of the Z coordinate along with the X and Y coordinates. It is similar to 2D translation. Translation involves moving an object.

The following figure shows the effect of translation −

A point can be translated in 3D by adding translation coordinate (tx,ty,tz) to the original coordinate X,Y,Z to get the new coordinate X′,Y′,Z′.

$T = [\begin{matrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ t_{x} & t_{y} & t_{z} & 1 \end{matrix}]$