...where X, Y, and Z are the point 3-D coordinates, and W is the 'weight', and is used to normalise the result after an operation, multiplying each element by 1/W so that W ends equal to 1.[X, Y, Z, W]

Points can be moved around by matric multiplication with 4X4
*transformation matrices*. Multiplying a vector with a matric
produces a new vector, which is the transformed point. Standard
transformation matrices are:

Transformation matrices can be combined by multiplying them together, so a single matrix can be use to shift, rotate, and scale a point in a single operation. Other 3-D operations using vectors are also frequently used, such as to determine intersection points or the reflection of light rays.Identity (does not transform point): [ 1 0 0 0 ] [ 0 1 0 0 ] [ 0 0 1 0 ] [ 0 0 0 1 ] Translate (move along X, Y, Z axes): [ 1 0 0 0 ] [ 0 1 0 0 ] [ 0 0 1 0 ] [ Tx Ty Tz 1 ] Scale (translate to larger or smaller coordinates): [ Sx 0 0 0 ] [ 0 Sy 0 0 ] [ 0 0 Sz 0 ] [ 0 0 0 1 ] Rotate (around X, Y, or Z axis by angle U): Axis X: Axis Y: Axix Z: [ 1 0 0 0 ] [cosU 0 -sinU 0 ] [cosU sinU 0 0 ] [ 0 cosU sinU 0 ] [ 0 1 0 0 ] [-sinU cosU 0 0 ] [ 0-sinU cosU 0 ] [sinU 0 cosU 0 ] [ 0 0 1 0 ] [ 0 0 0 1 ] [ 0 0 0 1 ] [ 0 0 0 1 ] Perspective (d is the distance of "eye" behind "screen"): [ 1 0 0 0 ] [ 0 1 0 0 ] [ 0 0 1 0 ] [ 0 0 1/d 0 ]

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