Computer Graphics Programming Midterm Reviewer

Coordinate System

Is defined by an origin point and the orientation and scale of a set of coordinate axes

Point

p = (x, y) refers to a location in space, specified relative to a coordinate system

Vector

v = (m, n) refers to a displacement, an amount of change in each coordinate and is typically drawn as an arrow pointing along the direction of displacement.

Initial point

Also known as tail, this is the point where the arrow begins

Terminal point

Also known as head, the point where the arrow ends; indicates the result when the displacement has been applied to the initial point.

Length

Also known as magnitude, this is the distance between the initial and terminal points of the vector; can be calculated from the components of the vector

Standard position

A vector whose initial point is located at the origin

Scalars

Individual numbers (that are not part of a point or vector

Matrix

A rectangular array of values called elements that are typicall accessed by means of subscripts

Identity Matrix

Contains all zeros, with ones along the diagonal. Any point or matrix multiplied by this is unchanged

Transpose

A matrix is computed by interchanging its rows and columns

Scalar Multiplication

You can multiply a scalar by each element of the matrix using the dot operator. This is known as scalar multiplication

Matrix Multiplication

You can only multiply matrices if the number of columns on the left-hand side matrix is equal to the number of rows on the right-hand side matrix. To multiply matrices, multiply the element of each row of the first matrix by the elements of each column in the second matrix. Then, add the products

Geometric Transformation

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

Scaling

The object’s dimensions are either expanded or compressed to change its size. A matrix can also be used to move points towards or away from the origin. By scaling relative to the origin, all coordinates of the points defining an entity are multiplied by the same factor

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.

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 performend around a line rather than a point

Scaling Factor

Is used to determine whether the side of an object will be increased or reduced. A scaling factor greater than 1 implies that the objects size will be increased. If the scaling factor is less than 1, the object size will be reduced.

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 4×4 matrix.

Rotation

Give the initial x, y, z coordinates of an object and the rotation angle, you can determine the new coordinates by creating 4×4 matrices with combinations of the sine and cosine functions

Frustum

The shape of the viewable region, or truncated pyramid.

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.

Projection Window

A flat rectangular region in space corresponding to the rendered image that will be displayed on the computer screen.