Vector3

type alias Float3 =

Vec3 Float

type alias Vec3 a =

( a, a, a )

fromV2 : Vec2 a -> a -> Vec3 a

fromV2 (1,2) 3 == (1,2,3)

setX : a -> Vec3 a -> Vec3 a

setY : a -> Vec3 a -> Vec3 a

setZ : a -> Vec3 a -> Vec3 a

getX : Vec3 a -> a

getY : Vec3 a -> a

getZ : Vec3 a -> a

map : (a -> b) -> Vec3 a -> Vec3 b

map sqrt (1,4,9) == (1,2,3)

map2 : (a -> b -> c) -> Vec3 a -> Vec3 b -> Vec3 c

map2 (/) (4,9,12) (2,3,4) == (2,3,3)

foldl : (elem -> acc -> acc) -> acc -> Vec3 elem -> acc

foldl (*) 1 (2,4,1) == 8

foldr : (elem -> acc -> acc) -> acc -> Vec3 elem -> acc

foldr max 0 (1,12,-5) == 12

add : Float3 -> Float3 -> Float3

v + w

add (2,4,1) (3,-6,2) == (5,-2,3)

sub : Float3 -> Float3 -> Float3

v - w

sub (4,6,1) (3,-1,-4) == (1,7,5)

negate : Float3 -> Float3

-v

negate (2,-1,5) == (-2,1,-5)

scale : Float -> Float3 -> Float3

a*v

scale (1/2) (4,2,6) == (2,1,3)

divideBy : Float -> Float3 -> Float3

v/a

divideBy (1/2) (2,1,3) == (4,2,6)

dot : Float3 -> Float3 -> Float

v dot w

The dot product of two vectors. Also called scalar product or inner product.

It links the length and angle of two vectors.

v dot w = |v|*|w|*cos(phi)

dot (1,2,2) (3,3,2) == 1*3 + 2*3 + 2*2 == 13

cross : Float3 -> Float3 -> Float3

v cross w

The cross product of two vectors. Also called vector product.

v cross w is a vector that is perpendicular to both v and w and therefore normal to the plane containing them.

The length of v cross w is equal to the area of the parallelogram spanned by v and w.

|v cross w| = |v|*|w|*sin(phi)

cross (2,1,3) (4,5,-3) == (1*(-3) - 3*5, 3*4 - 2*(-3), 2*5 - 1*4) == (-18, 18, 6)

length : Float3 -> Float

The length of a vector. Also known as magnitude or norm.

|v| = sqrt(v dot v)

length (4,2,4) == sqrt (4^2+2^2+4^2) == 6

lengthSquared : Float3 -> Float

The squared length. This is cheaper to calculate, so if you only need to compare lengths you can use this instead of the length.

|v|^2 = v dot w

lengthSquared (3,4,1) == 3^2+4^2+1^2 == 26

normalize : Float3 -> Float3

Normalizes a vector. This will give you a unit vector (e.g. with length 1) in the same direction as v.

v/|v|

normalize (4,2,4) == (2/3,1/3,2/3)

directionFromTo : Float3 -> Float3 -> Float3

A unit vector pointing from v to w

(w - v)/|w - v|

directionFromTo (5,1,2) (9,3,6) == (2/3,1/3,2/3)

distance : Float3 -> Float3 -> Float

Calculates the distance from v to w.

|v - w| = |w - v|

distance (2,0,4) (0,4,0) == 6

distanceSquared : Float3 -> Float3 -> Float

The squared distance. This is slightly faster.

|v - w|^2

distanceSquared (3,0,2) (0,4,1) == 26

angle : Float3 -> Float3 -> Float

The angle between two vectors. The angle is in radians.

acos((v dot w)/(|v|*|w|))

angle (-1,-1,2) (2,2,2) == pi/2    -- or 90°

project : Float3 -> Float3 -> Float3

The projection of v onto w.

(v dot w)/|w| * w/|w|

project (2,1,0) (4,0,0) == (2,0,0)

reject : Float3 -> Float3 -> Float3

The rejection of v onto w. This is always perpendicular to the projection.

v - (project v w)

reject (2,1,0) (4,0,0) == (0,1,0)

Zinggi/elm-webgl-math/1.0.4

Vector3

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