Safe Haskell	Safe-Inferred
Language	Haskell2010

Geomancy.Vector

Synopsis

class VectorSpace v a | v -> a where
- zeroVector :: v
- (*^) :: a -> v -> v
- (^/) :: v -> a -> v
- (^+^) :: v -> v -> v
- (^-^) :: v -> v -> v
- negateVector :: v -> v
- dot :: v -> v -> a
- norm :: v -> a
- normalize :: v -> v
(^*) :: VectorSpace v a => v -> a -> v
quadrance :: VectorSpace v a => v -> a
lerp :: (VectorSpace v a, Num a) => v -> v -> a -> v
lerpClip :: (VectorSpace v a, Ord a, Num a) => v -> v -> a -> v

Documentation

class VectorSpace v a | v -> a where #

Vector space type relation.

A vector space is a set (type) closed under addition and multiplication by a scalar. The type of the scalar is the field of the vector space, and it is said that v is a vector space over a.

The encoding uses a type class |VectorSpace| v a, where v represents the type of the vectors and a represents the types of the scalars.

Minimal complete definition

zeroVector, (*^), (^+^), dot

Methods

zeroVector :: v #

Vector with no magnitude (unit for addition).

(*^) :: a -> v -> v infixr 9 #

Multiplication by a scalar.

(^/) :: v -> a -> v infixl 9 #

Division by a scalar.

(^+^) :: v -> v -> v infixl 6 #

Vector addition

(^-^) :: v -> v -> v infixl 6 #

Vector subtraction

negateVector :: v -> v #

Vector negation. Addition with a negated vector should be same as subtraction.

dot :: v -> v -> a infix 7 #

Dot product (also known as scalar or inner product).

For two vectors, mathematically represented as a = a1,a2,...,an and b = b1,b2,...,bn, the dot product is a . b = a1*b1 + a2*b2 + ... + an*bn.

Some properties are derived from this. The dot product of a vector with itself is the square of its magnitude (norm), and the dot product of two orthogonal vectors is zero.

norm :: v -> a #

Vector's norm (also known as magnitude).

For a vector represented mathematically as a = a1,a2,...,an, the norm is the square root of a1^2 + a2^2 + ... + an^2.

normalize :: v -> v #

Return a vector with the same origin and orientation (angle), but such that the norm is one (the unit for multiplication by a scalar).

Instances

Instances details

VectorSpace Vec2 Float Source #
Instance details Defined in Geomancy.Vec2 Methods zeroVector :: Vec2 # (*^) :: Float -> Vec2 -> Vec2 # (^/) :: Vec2 -> Float -> Vec2 # (^+^) :: Vec2 -> Vec2 -> Vec2 # (^-^) :: Vec2 -> Vec2 -> Vec2 # negateVector :: Vec2 -> Vec2 # dot :: Vec2 -> Vec2 -> Float # norm :: Vec2 -> Float # normalize :: Vec2 -> Vec2 #
VectorSpace Packed Float Source #
Instance details Defined in Geomancy.Vec3 Methods zeroVector :: Packed # (*^) :: Float -> Packed -> Packed # (^/) :: Packed -> Float -> Packed # (^+^) :: Packed -> Packed -> Packed # (^-^) :: Packed -> Packed -> Packed # negateVector :: Packed -> Packed # dot :: Packed -> Packed -> Float # norm :: Packed -> Float # normalize :: Packed -> Packed #
VectorSpace Vec3 Float Source #
Instance details Defined in Geomancy.Vec3 Methods zeroVector :: Vec3 # (*^) :: Float -> Vec3 -> Vec3 # (^/) :: Vec3 -> Float -> Vec3 # (^+^) :: Vec3 -> Vec3 -> Vec3 # (^-^) :: Vec3 -> Vec3 -> Vec3 # negateVector :: Vec3 -> Vec3 # dot :: Vec3 -> Vec3 -> Float # norm :: Vec3 -> Float # normalize :: Vec3 -> Vec3 #
VectorSpace Vec4 Float Source #
Instance details Defined in Geomancy.Vec4 Methods zeroVector :: Vec4 # (*^) :: Float -> Vec4 -> Vec4 # (^/) :: Vec4 -> Float -> Vec4 # (^+^) :: Vec4 -> Vec4 -> Vec4 # (^-^) :: Vec4 -> Vec4 -> Vec4 # negateVector :: Vec4 -> Vec4 # dot :: Vec4 -> Vec4 -> Float # norm :: Vec4 -> Float # normalize :: Vec4 -> Vec4 #
VectorSpace Double Double	Vector space instance for `Double`s, with `Double` scalars.
Instance details Defined in Data.VectorSpace Methods zeroVector :: Double # (*^) :: Double -> Double -> Double # (^/) :: Double -> Double -> Double # (^+^) :: Double -> Double -> Double # (^-^) :: Double -> Double -> Double # negateVector :: Double -> Double # dot :: Double -> Double -> Double # norm :: Double -> Double # normalize :: Double -> Double #
VectorSpace Float Float	Vector space instance for `Float`s, with `Float` scalars.
Instance details Defined in Data.VectorSpace Methods zeroVector :: Float # (*^) :: Float -> Float -> Float # (^/) :: Float -> Float -> Float # (^+^) :: Float -> Float -> Float # (^-^) :: Float -> Float -> Float # negateVector :: Float -> Float # dot :: Float -> Float -> Float # norm :: Float -> Float # normalize :: Float -> Float #
(Eq a, Floating a) => VectorSpace (a, a) a	Vector space instance for pairs of `Floating` point numbers.
Instance details Defined in Data.VectorSpace Methods zeroVector :: (a, a) # (*^) :: a -> (a, a) -> (a, a) # (^/) :: (a, a) -> a -> (a, a) # (^+^) :: (a, a) -> (a, a) -> (a, a) # (^-^) :: (a, a) -> (a, a) -> (a, a) # negateVector :: (a, a) -> (a, a) # dot :: (a, a) -> (a, a) -> a # norm :: (a, a) -> a # normalize :: (a, a) -> (a, a) #
(Eq a, Floating a) => VectorSpace (a, a, a) a	Vector space instance for triplets of `Floating` point numbers.
Instance details Defined in Data.VectorSpace Methods zeroVector :: (a, a, a) # (*^) :: a -> (a, a, a) -> (a, a, a) # (^/) :: (a, a, a) -> a -> (a, a, a) # (^+^) :: (a, a, a) -> (a, a, a) -> (a, a, a) # (^-^) :: (a, a, a) -> (a, a, a) -> (a, a, a) # negateVector :: (a, a, a) -> (a, a, a) # dot :: (a, a, a) -> (a, a, a) -> a # norm :: (a, a, a) -> a # normalize :: (a, a, a) -> (a, a, a) #
(Eq a, Floating a) => VectorSpace (a, a, a, a) a	Vector space instance for tuples with four `Floating` point numbers.
Instance details Defined in Data.VectorSpace Methods zeroVector :: (a, a, a, a) # (*^) :: a -> (a, a, a, a) -> (a, a, a, a) # (^/) :: (a, a, a, a) -> a -> (a, a, a, a) # (^+^) :: (a, a, a, a) -> (a, a, a, a) -> (a, a, a, a) # (^-^) :: (a, a, a, a) -> (a, a, a, a) -> (a, a, a, a) # negateVector :: (a, a, a, a) -> (a, a, a, a) # dot :: (a, a, a, a) -> (a, a, a, a) -> a # norm :: (a, a, a, a) -> a # normalize :: (a, a, a, a) -> (a, a, a, a) #
(Eq a, Floating a) => VectorSpace (a, a, a, a, a) a	Vector space instance for tuples with five `Floating` point numbers.
Instance details Defined in Data.VectorSpace Methods zeroVector :: (a, a, a, a, a) # (*^) :: a -> (a, a, a, a, a) -> (a, a, a, a, a) # (^/) :: (a, a, a, a, a) -> a -> (a, a, a, a, a) # (^+^) :: (a, a, a, a, a) -> (a, a, a, a, a) -> (a, a, a, a, a) # (^-^) :: (a, a, a, a, a) -> (a, a, a, a, a) -> (a, a, a, a, a) # negateVector :: (a, a, a, a, a) -> (a, a, a, a, a) # dot :: (a, a, a, a, a) -> (a, a, a, a, a) -> a # norm :: (a, a, a, a, a) -> a # normalize :: (a, a, a, a, a) -> (a, a, a, a, a) #

(^*) :: VectorSpace v a => v -> a -> v Source #

quadrance :: VectorSpace v a => v -> a Source #

lerp :: (VectorSpace v a, Num a) => v -> v -> a -> v Source #

lerpClip :: (VectorSpace v a, Ord a, Num a) => v -> v -> a -> v Source #