COMP GRAPHICS MIDTERMS

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

• are not associated with any particular location in space

• may exist at different locations

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 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 (when a coordinate system is specified)

scalars

Individual numbers (that are not part of a point or 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

matrix is computed by interchanging its rows and columns.

scalar multiplication.

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

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.

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

2D rotation

a rotation transformation rotates vectors around the origin point

3D rotation

rotations are performed around a line rather than a point.

scaling factor

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

translation vector

• also called a shift vector,

• defines the distance to move an object’s coordinate

frustum or truncated pyramid

In a perspective projection, the shape of the viewable region is called _______ .

near and far distances

The shape of a frustum is defined by four (4) parameters

• refer to distances from the viewer (along the z-axis).

• These two set absolute bounds on what could potentially be seen by the viewer.

• Any points beyond this range will not be rendered.

• However, not everything between these bounds will be visible.

• larger angles of view correspond to larger frustums.

angle of view

The shape of a frustum is defined by four (4) parameters

• 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

aspect ratio

The shape of a frustum is defined by four (4) parameters

• defined as width divided by height

• 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