Computer Graphics Midterm 01

A coordinate system

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

A point 𝒑 = (𝒙, 𝒚)

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

A 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 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

Vectors

are not associated with any particular location in space; the same vector may exist at different locations.

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) are often called _____

Pythagorean theorem

Given the length of the two (2) sides (x, y), you can determine the length/magnitude of a vector using the _____

A matrix (elements, subscripts)

is a rectangular array of values called _____ that are typically accessed by means of_____. The first subscript refers to the row number, while the second one refers to the column number, with the subscripts starting at 0.

The identity matrix

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

The transpose

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. This is known as _____

In 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 righthand side matrix.