Vector Operations

Builders

Operation	r2	r3	r4	rn
Create a vector	`r2(x0, x1)`	`r3(x0, x1, x2)`	`r4(x0, x1, x2, x3)`	`rn(...)`
Create a zero vector	`r2_zero()`	`r3_zero()`	`r4_zero()`	`rn_zero(n)`
Clone/copy a vector	`r2_clone(v, [vout])`	`r3_clone(v, [vout])`	`r4_clone(v, [vout])`	`rn_clone(v, [vout])`

Operation	r2	r3	r4	rn
Vector addition	`r2_add(v1, v2, [vout])`	`r3_add(v1, v2, [vout])`	`r4_add(v1, v2, [vout])`	`rn_add(v1, v2, [vout])`
Vector subtraction	`r2_subtract(v1, v2, [vout])`	`r3_subtract(v1, v2, [vout])`	`r4_subtract(v1, v2, [vout])`	`rn_subtract(v1, v2, [vout])`
Scalar multiplication	`r2_scale(v, r, [vout])`	`r3_scale(v, r, [vout])`	`r4_scale(v, r, [vout])`	`rn_scale(v, r, [vout])`
Dot product	`r2_dot(v1, v2)`	`r3_dot(v1, v2)`	`r4_dot(v1, v2)`	`rn_dot(v1, v2)`
Cross product	N/A	`r3_cross(v1, v2, [vout])`	N/A	N/A

Operation	r2	r3	r4	rn
Unit vector	`r2_unit(v, [vout])`	`r3_unit(v, [vout])`	`r4_unit(v, [vout])`	`rn_unit(v, [vout])`
Linear Interpolation	`r2_lerp(v1, v2, amount, [vout])`	`r3_lerp(v1, v2, amount, [vout])`	`r4_lerp(v1, v2, amount, [vout])`	`rn_lerp(v1, v2, amount, [vout])`
Vector Projection	`r2_proj(v1, v2, [vout])`	`r3_proj(v1, v2, [vout])`	`r4_proj(v1, v2, [vout])`	`rn_proj(v1, v2, [vout])`
Vector Rejection	`r2_rej(v1, v2, [vout])`	`r3_rej(v1, v2, [vout])`	`r4_rej(v1, v2, [vout])`	`rn_rej(v1, v2, [vout])`

Operation	r2	r3	r4	rn
Euclidean norm	`r2_norm(v)`	`r3_norm(v)`	`r4_norm(v)`	`rn_norm(v)`
Manhattan norm	`r2_1norm(v)`	`r3_1norm(v)`	`r4_1norm(v)`	`rn_1norm(v)`
Maximum norm	`r2_maxnorm(v)`	`r3_maxnorm(v)`	`r4_maxnorm(v)`	`rn_maxnorm(v)`
Euclidean distance	`r2_dist(v1, v2)`	`r3_dist(v1, v2)`	`r4_dist(v1, v2)`	`rn_dist(v1, v2)`
Manhattan distance	`r2_1dist(v1, v2)`	`r3_1dist(v1, v2)`	`r4_1dist(v1, v2)`	`rn_1dist(v1, v2)`

String format: Each entry is written with 14 decimal digits, separated by commas.
Base64 format: Each entry is written as a 64-bit float to the buffer, then encoded as base64.

Operation	r2	r3	r4	rn
Encode to string	`r2_encode_string(v)`	`r3_encode_string(v)`	`r4_encode_string(v)`	`rn_encode_string(v)`
Decode from string	`r2_decode_string(str, [vout])`	`r3_decode_string(str, [vout])`	`r4_decode_string(str, [vout])`	`rn_decode_string(str, [vout])`
Encode to base64	`r2_encode_base64(v)`	`r3_encode_base64(v)`	`r4_encode_base64(v)`	`rn_encode_base64(v)`
Decode from base64	`r2_decode_base64(enc, [vout])`	`r3_decode_base64(enc, [vout])`	`r4_decode_base64(enc, [vout])`	`rn_decode_base64(enc, n, [vout])`

These functions take the form r2_IN_OUT(v, [vout]).

Name	Name Code (IN/OUT)	Component 0	Component 1
Rectangular	`rec`	`x` (pixels)	`y` (pixels)
GameMaker Polar	`gmp`	`len` (pixels)	`dir` (degrees, counter-clockwise from right with downward y axis)
Polar	`pol`	`r` (pixels)	`theta` (radians, counter-clockwise from right with upward y axis)

These functions take the form r3_IN_OUT(v, [vout]).

Name	Name Code (IN/OUT)	Component 0	Component 1	Component 2
Rectangular	`rec`	`x` (pixels)	`y` (pixels)	`z` (pixels)
Cylindrical	`cyl`	`rho` (pixels)	`phi` (radians)	`z` (pixels)
Spherical	`sph`	`rho` (pixels)	`phi` (radians, azimuth)	`theta` (radians, declination)

These constants allow you to semantically access vector entries.