# View Volumes and General Projection Transformations

General Projection Transformations is the important topic of the Computer Graphics. Moreover, It is the Important subject of the Computer Science.

- Fig. View volume of parallel and perspective projection.
- Based on view window we can generate the different image of the same scene.
- A volume which appears on the display known as view volume.
- Given the specification of the view window, we can set up a view volume using the window boundaries.
- Only those objects within the view volume will appear in the generated display on an output device; all others clipped from the display.
- The size of the view volume depends on the size of the window, while the shape of the view volume depends on the type of projection to use to generate the display.
- Also, A finite view volume obtained by limiting the extent of the volume in the z
_{v} - This done by specifying positions for one or two additional boundary planes. These z
_{v}-boundary planes referred to as the**front plane**and**backplane**, or the**near plane**and the**far plane**, of the viewing volume. - Moreover, Orthographic parallel projections not affected by view-plane positioning because of the projection lines perpendicular to the view plane regardless of its location.
- Oblique projections may be affected by view-plane positioning, depending on how the projection direction to specified.
**General Parallel-Projection Transformation**

Here we will obtain transformation matrix for parallel projection which is applicable to both orthographic as well as oblique projection.

- Also, As shown in figure parallel projection is specified with a projection vector from the projection reference point to the view window.
- Now we will apply shear transformation so that view volume will convert into regular parallelepiped and projection vector will become parallel to normal vector N.

**General Perspective-Projection Transformations **

The General Projection Transformations reference point can located at any position in the viewing system, except on the view plane or between the front and back clipping planes.

Moreover, We can obtain the general perspective-projection transformation with the following two operations:

- Moreover, Shear the view volume so that the center line of the frustum is perpendicular to the view plane.
- Scale the view volume with a scaling factor that depends on 1/z .

A shear operation to align a general perspective view volume with the General Projection Transformations window shown in Figure.

**Related Terms**

Computer Graphics, Viewing Pipelines, Projections, Perspective Projection

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