Slavomir Kaslev
On 11/29/06, Krasimir Angelov
wrote: It is possible of course but your definition doesn't correspond to any operation in the usual vector algebra. By the way how do you define (*)? Isn't it 3D vector multiplication?
(*) is per component multiplication, as it is in Cg/HLSL. For vector to vector, vector to matrix, etc. multiplication there is mul.
Cheers.
Hello, I have defined a class for vectors that I think can be interesting for you, althougt I do NOT use the Num class. I really like infix operators for vectors but using + * ... and so gets things confusing for me and have bad interaction with scalars. So I define infix operators <+> <-> <*> ... with an "<" or ">" on the side when a vector is spected, so (*>) is a scalar multiplication of a vector, (<*>) multiplication of two vectors, <.> dot product .... The class is named Vector, and I don't make distinction bewteen vectors and points. A minimalist instance of Vector class, can be defined by only two method functions, reduceComponent and combineComponent. reduceComponent is like a fold functions over the components of a vector, so for example the max component of a vector is defined as "maxComponent vec = reduceComponent (max) vec". combineComponent apply a function to every pair of components of two vectors, so an addition of two vectors is defined as "(<+>) a b = combineComponent (+) a b". Note that for Vector3 and Vector2 datatypes I define instances with reduceComponent and combineComponent, but for performance reasons I override default implementations of the most used operations. Here is the code, I hope that it makes clear what I have tried to explain. Please, feel free to criticize the code Fco. Javier Loma fjloma <at> andaluciajunta.es --begin code {-# OPTIONS_GHC -fglasgow-exts -fbang-patterns #-} module Data.Vectors where -- Use a Double for each component type VReal = Double --data Dimension = X | Y | Z | W deriving (Show, Read, Eq) data Vector3 = V3 !VReal !VReal !VReal deriving (Show, Read, Eq) class (Floating r, Ord r) => (Vector r) v | v -> r where -- minimun definition by reduceComponent and combineComponent reduceComponent :: (r -> r -> r) -> v -> r combineComponent :: (r -> r -> r) -> v -> v -> v (<+>) :: v -> v -> v (<+>) a b = combineComponent (+) a b (<->) :: v -> v -> v (<->) a b = combineComponent (-) a b (<*>) :: v -> v -> v (<*>) a b = combineComponent (*) a b () :: v -> v -> v () a b = combineComponent (/) a b (<.>) :: v -> v -> r a <.> b = reduceComponent (+) (combineComponent (*) a b) (<*) :: v -> r -> v a <* k = combineComponent (\x -> \_ -> x*k) a a ( r -> v a \_ -> x/k) a a (*>) :: r -> v -> v k *> vec = vec <* k normalize :: v -> v normalize vec = vec r vlength vec = sqrt(vec <.> vec) maxComponent :: v -> r maxComponent vec = reduceComponent (max) vec minComponent :: v -> r minComponent vec = reduceComponent (min) vec middle :: v -> v -> v middle a b = (a <+> b) v -> r distance a b = sqrt (distance2 a b) distance2 :: v -> v -> r distance2 a b = r <.> r where r = b <-> a instance Vector VReal Vector3 where reduceComponent f (V3 a1 a2 a3) = (f a1 (f a2 a3)) combineComponent f (V3 a1 a2 a3) (V3 b1 b2 b3) = V3 (f a1 b1) (f a2 b2) (f a3 b3) (!V3 a1 a2 a3) <+> (!V3 b1 b2 b3) = V3 (a1 + b1) (a2 + b2) (a3 + b3) (!V3 a1 a2 a3) <-> (!V3 b1 b2 b3) = V3 (a1 - b1) (a2 - b2) (a3 - b3) (!V3 a1 a2 a3) <*> (!V3 b1 b2 b3) = V3 (a1 * b1) (a2 * b2) (a3 * b3) (!V3 a1 a2 a3) (!V3 b1 b2 b3) = V3 (a1 / b1) (a2 / b2) (a3 / b3) (!V3 a1 a2 a3) <.> (!V3 b1 b2 b3) = a1 * b1 + a2 * b2 + a3 * b3 (!V3 a1 a2 a3) <* k = V3 (a1 * k) (a2 * k) (a3 * k) (!V3 a1 a2 a3) (V2 b1 b2 ) = a1 * b1 + a2 * b2 (V2 a1 a2 ) <* k = V2 (a1 * k) (a2 * k) (V2 a1 a2 )