{-
Michael Chen
CS429 Final Project

A "demo" quality 3D renderer implemented in Haskell.  Do note that this
renderer is limited to drawing a model in a window, and rotating the model.

Rotating the model is "painful" because this is running as interpreted 
Haskell.
-}

module Vec3d where

type Vector2 = (Float, Float)

{- 
Whoa!  What's Happening here?  This is done because translations in
3d have to be done this way, or you'll mess up the perspective and
stuff.  Just keep "w" blank 
-}
type Vector3 = (Float, Float, Float)

{-
Get the length of a vector
-}
vecLength3 :: Vector3 -> Float
vecLength3 (x,y,z) = sqrt (x*x + y*y + z*z)

{-
Add two vectors
-}
add3 :: Vector3 -> Vector3 -> Vector3
add3 (aX,aY,aZ) (bX,bY,bZ) = (aX+bX, aY+bY, aZ+bZ)
add2 :: Vector2 -> Vector2 -> Vector2
add2 (aX,aY) (bX,bY) = (aX+bX,aY+bY)

{-
generate the dot product of two vectors
-}
dot3 :: Vector3 -> Vector3 -> Float
dot3 (aX,aY,aZ) (bX,bY,bZ) = aX*bX + aY*bY + aZ*bZ
dot2 :: Vector2 -> Vector2 -> Float
dot2 (aX,aY) (bX,bY) = aX*bX + aY*bY

{-
Get the cross product of two vectors
-}
cross3 :: Vector3 -> Vector3 -> Vector3
cross3 (aX,aY,aZ) (bX,bY,bZ) = (aY*bZ-bY*aZ,bX*aZ-aX*bZ,aX*bY-bX*aY)

{-
Multiply a float to a vector
-}
mult3 :: Float -> Vector3 -> Vector3
mult3 f (x,y,z) = (f*x, f*y, f*z)

{-
transform a vector3 to vector2.  IE, transform the point from 3d coord to
2d coord while maintaining perspective, etc.
-}
protoVec3To2 :: Float -> Vector3 -> Vector2
protoVec3To2 g (aX,aY,aZ) =  (aX * scale, aY * scale)
  where scale = g / aZ

deriveVec3To2 :: Float -> (Vector3 -> Vector2)
deriveVec3To2 g = protoVec3To2 g

{-
Calculate the projection of v1 onto v2
-}
projectVec3 :: Vector3 -> Vector3 -> Vector3
projectVec3 v1 v2 = (v1 `dot3` v2) `mult3` v2