Computer Graphics Midterm 02

A geometric transformation

refers to a change applied to an object in terms of size, orientation, or position.

1. Scaling:

The object's dimensions are either expanded or compressed to change its size.

2. Translation:

The object is moved to another position or location on the screen. All coordinates of the points defining an entity are modified by adding the same vector quantity.

3. Rotation:

The object is moved around a fixed point at a given angle

In 2D,

a rotation transformation rotates vectors around the origin point.

In 3D,

rotations are performed around a line rather than a point.

The scaling factor

is used to determine whether the size of an object will be increased or reduced.

A translation vector,

also called a shift vector, defines the distance to move an object's coordinate. You can determine the new coordinates of an object after translation by creating a 4x4 matrix

sine, cosine

Given the initial x, y, z coordinates of an object and the rotation angle, you can determine the new coordinates by creating 4x4 matrices with combinations of the _____ and _____ functions.

frustum

In a perspective projection, the shape of the viewable region is called a _____ or truncated pyramid.

The near and far distances

refer to distances from the viewer (along the z-axis). These two set absolute bounds on what could potentially be seen by the viewer.

The angle of view

measures how much of the scene is visible to the viewer. It is defined as the angle between the top and bottom planes of the frustum

The aspect ratio

is used to specify the shape of the frustum,

projection window:

a flat rectangular region in space corresponding to the rendered image that will be displayed on the computer screen. The _____ corresponds to the smaller rectangular side of the frustum, the side nearest to the origin.