Vector Primer

From Tech Artists Wiki

Jump to: navigation, search

THIS IS PLACEHOLDER FOR NOW, PLEASE CONTRIBUTE

Contents

Mathematical application

A 2D vector in the Coordinate plane, showing the position of point A with coordinates (2,3).
A 2D vector in the Coordinate plane, showing the position of point A with coordinates (2,3).

Definition

A vector is a type of data that has both a magnitude (or length) and direction. There are vectors for every dimension of space (2D, 3D, etc).

Vectors are written in coordinates. The most common in the Cartesian XYZ coordinates you're used to, but there are others, such as the polar(2D), cylindrical(3D) or spherical(3D) coordinate systems.

Vectors are represented graphically as an arrow.

Vector vs scalar

Scalars are the normal numbers you're used to, like "7". Scalars are used to represent values without direction(i.e. age, luminescence, radius).

Dimension

3d application

Definition

Vectors can be confusing, because in graphics they are used to represent completely different ideas. A vector can be used to represent a location in space (i.e. vertex, UV coordinate), OR it can purely represent direction (i.e. normal, tangent). Sometimes even colors are referred to as vectors, even though they do not technically fit the definition.

Magnitude

The magnitude of a vector is it's "length". For a location in space, the magnitude would be the distance from the origin (or it's pivot point). Some vectors do not have a magnitude (or more accurately, they always have a magnitude of 1), such as normals. These vectors are "normalized".

Direction

Types of Vectors

Points & Locations

Points in space, such as Vertices, UV points, pivots points, and object locations can all be represented with vectors. These vectors usually start at the origin, and "point" to the location of the object.

Directional Vectors

Vector math

A 3D Vector "a" is shown in black.  The coordinate axis are in R,G,B, and the component vectors of "a" are in gray.
A 3D Vector "a" is shown in black. The coordinate axis are in R,G,B, and the component vectors of "a" are in gray.

Coordinate systems

Component Vectors

The Origin

The zero vector (0,0,0). This is the "center" of your coordinate system. In "world space", this is the same for every object, and is usually represented in 3D programs with a grid (the origin is at the center of the grid).

Multiplication by a Scalar

Negation

Addition/Subtraction

Vecotor Multiplication

Dot Product

Cross Product

Magnitude/Distance

Normalization

Projection

Personal tools