MIDTERM CGP

coordinate system

It is defined by an origin point and the orientation and scale of a set of coordinate axes.

point 𝒑=(𝒙,𝒚)

It refers to a location in space, specified relative to a coordinate system.

vector 𝒗=〈𝒎,𝒏〉

It 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 or tail

It is the point where the arrow begins.

Terminal point or head

It is the point where the arrow ends; indicates the result when the displacement has been applied to the initial point.

Length or magnitude

It 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 (when a coordinate system is specified) is said to be in ___________.

scalars

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

It is used determine the length/magnitude of a vector. ||𝒗||=√𝒙𝟐+𝒚𝟐

Pythagorean theorem

matrix

It is a rectangular array of values called elements.

elements

It is typically accessed by means of subscripts.

identity matrix

It contains all zeros, with ones along the diagonal.

transpose

The _____ of 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.

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.

first subscript

It refers to the row number.

second subscript

It refers to the column number.

geometric transformation

It 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.

scaling factor

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

translation vector

It is also called a shift vector, defines the distance to move an object’s coordinate.

Rotation

In 3D, there are three (3) types of rotation: x-axis rotation, y-axis rotation, and z-axis rotation.

frustum or truncated pyramid

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

near and far distances

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

angle of view

It measures how much of the scene is visible to the viewer.

aspect ratio

It is used to specify the shape of the frustum.

projection window

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