CGP (midterms)

Coordinate system

Defined by an origin point and the orientation and the 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 displacement

Displacement

An amount of change in each coordinate and is typically drawn as an arrow pointing along the direction of displacement

Initial point or tail

The point where the arrow begins

Terminal point or head

The point where the arrow ends; indicates the result when the displacement has been applied to the initial point

Length or magnitude

The distance between the initial and terminal point 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

Pythagorean theorem

Used to determine the length/magnitude of a vector

Matrix

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

Identity matrix

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

Transpose of a matrix

Computed by interchanging its rows and columns

Scalar multiplication

You can multiply a scalar by each element of the matrix using the dot operator

Matrix multiplication

You can only multiply matrices if the number of columns on the left hand side is equal to the number of rows on the right hand side of the matrix

Geometric transformation

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

Scaling

The objects dimension are either expanded or compressed to change its size

Translation

The object is moved to another position or location on the screen

Rotation

The object is moved around a fixed point at a given angle; in 2d it rotates vectors around the origin point; in 3d it rotates vectors around a line

Scaling factor

Used to determine whether the size of an object will increase or decrease; if greater than 1 = increased; if less than 1 = decreased

Translation vector (shift vector)

Defines the distance to move an object's coordinate

Sine and 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 or truncated pyramid

The shape of the viewable region in a perspective projection

Near and far distances

Refers to the distance from the viewer (along the z-axis)

Angle of view

Measures how much of the scene is visible to the viewer

Aspect ratio

Used to specify the shape of the frustum

Projection window

A flat rectangular region in space corresponding to the rendered image