diff --git a/Setup.lhs b/Setup.lhs new file mode 100644 --- /dev/null +++ b/Setup.lhs @@ -0,0 +1,6 @@ +#!/usr/bin/runhaskell +> module Main where +> import Distribution.Simple +> main :: IO () +> main = defaultMain + diff --git a/Vec-Transform.cabal b/Vec-Transform.cabal new file mode 100644 --- /dev/null +++ b/Vec-Transform.cabal @@ -0,0 +1,47 @@ +name: Vec-Transform +version: 1.0.0 +cabal-version: >=1.2.3 +build-type: Simple +license: BSD3 +license-file: "" +copyright: Tobias Bexelius +maintainer: Tobias Bexelius +build-depends: Vec -any, base ==4.1.0.0 +stability: +homepage: +package-url: +bug-reports: mailto:tobias_bexelius@hotmail.com +synopsis: Extends the Vec package with some 4x4 transform matrices +description: This package adds some 4x4 transform matrices to the Vec package, that is useful in graphics applications, such as those written with the GPipe package. + Specifically, it adds translation, scaling, rotation, perspective projection and orthogonal projection matrices. +category: Math, Graphics +author: Tobias Bexelius +tested-with: +data-files: +data-dir: "" +extra-source-files: +extra-tmp-files: +exposed-modules: Data.Vec.LinAlg.Transform3D +exposed: True +buildable: True +build-tools: +cpp-options: +cc-options: +ld-options: +pkgconfig-depends: +frameworks: +c-sources: +extensions: +extra-libraries: +extra-lib-dirs: +includes: +install-includes: +include-dirs: +hs-source-dirs: src +other-modules: +ghc-prof-options: +ghc-shared-options: +ghc-options: +hugs-options: +nhc98-options: +jhc-options: diff --git a/src/Data/Vec/LinAlg/Transform3D.hs b/src/Data/Vec/LinAlg/Transform3D.hs new file mode 100644 --- /dev/null +++ b/src/Data/Vec/LinAlg/Transform3D.hs @@ -0,0 +1,121 @@ +----------------------------------------------------------------------------- +-- +-- Module : Data.Vec.LinAlg.Transform3D +-- Copyright : Tobias Bexelius +-- License : BSD3 +-- +-- Maintainer : Tobias Bexelius +-- Stability : +-- Portability : +-- +-- | +-- Some 4x4 transformation matrices, using a right handed coordinate system. +-- These matrices are used by multiplying vectors from the right. +----------------------------------------------------------------------------- + +module Data.Vec.LinAlg.Transform3D ( + translation, + rotationX, + rotationY, + rotationZ, + rotationVec, + rotationEuler, + rotationQuat, + scaling, + perspective, + orthogonal, +) where +import Data.Vec + +-- | A 4x4 translation matrix +translation :: Num a => Vec3 a -> Mat44 a +translation = flip translate identity + +-- | A 4x4 rotation matrix for a rotation around the X axis +rotationX :: Floating a + => a -- ^ The angle in radians + -> Mat44 a +rotationX a = matFromList [1, 0, 0, 0, + 0, cos a, -sin a, 0, + 0, sin a, cos a, 0, + 0, 0, 0, 1] + +-- | A 4x4 rotation matrix for a rotation around the Y axis +rotationY :: Floating a + => a -- ^ The angle in radians + -> Mat44 a +rotationY a = matFromList [cos a, 0, sin a, 0, + 0, 1, 0, 0, + -sin a, 0, cos a, 0, + 0, 0, 0, 1] + +-- | A 4x4 rotation matrix for a rotation around the Z axis +rotationZ :: Floating a + => a -- ^ The angle in radians + -> Mat44 a +rotationZ a = matFromList [cos a, -sin a, 0, 0, + sin a, cos a, 0, 0, + 0, 0, 1, 0, + 0, 0, 0, 1] + +-- | A 4x4 rotation matrix for a rotation around an arbitrary normalized vector +rotationVec :: Floating a + => Vec3 a -- ^ The normalized vector around which the rotation goes + -> a -- ^ The angle in radians + -> Mat44 a +rotationVec (x:.y:.z:.()) a = + matFromList [x^2+(1-x^2)*c, x*y*(1-c)-z*s, x*z*(1-c)+y*s, 0, + x*y*(1-c)+z*s, y^2+(1-y^2)*c, y*z*(1-c)-x*s, 0, + x*z*(1-c)-y*s, y*z*(1-c)+x*s, z^2+(1-z^2)*c, 0, + 0, 0, 0, 1] + where c = cos a + s = sin a + +-- | A 4x4 rotation matrix from the euler angles yaw pitch and roll. Could be useful in e.g. +-- first person shooter games, +rotationEuler :: Floating a + => Vec3 a -- rotation around x, y and z respectively + -> Mat44 a +rotationEuler (x:.y:.z:.()) = rotationZ z `multmm` rotationY y `multmm` rotationX x + +-- | A 4x4 rotation matrix from a normalized quaternion. Useful for most free flying rotations, such as airplanes. +rotationQuat :: Num a + => Vec4 a -- ^ The quaternion with the real part (w) last + -> Mat44 a +rotationQuat (x:.y:.z:.w:.()) = + matFromList [1-2*y^2-2*z^2, 2*(x*y-z*w), 2*(x*z+y*w), 0, + 2*(x*y+z*w), 1-2*x^2-2*z^2, 2*(y*z-x*w), 0, + 2*(x*z-y*w), 2*(x*w+y*z), 1-2*x^2-2*y^2, 0, + 0, 0, 0, 1] + +-- | A 4x4 scaling matrix +scaling :: Num a => Vec3 a -> Mat44 a +scaling = diagonal . homPoint + +-- | A perspective projection matrix for a right handed coordinate system looking down negative z +perspective :: Floating a + => a -- ^ Near plane clipping distance + -> a -- ^ Far plane clipping distance + -> a -- ^ Field of view of the y axis, in radians + -> a -- ^ Aspect ratio, i.e. screen's width\/height + -> Mat44 a +perspective n f fovy aspect = matFromList [2*n/(r-l), 0, -(r+l)/(r-l), 0, + 0, 2*n/(t-b), (t+b)/(t-b), 0, + 0, 0, -(f+n)/(f-n), -2*f*n/(f-n), + 0,0,-1,0] + where + t = 2*n*tan(fovy/2) + b = -t + r = aspect*t + l = -r + +-- | An orthogonal projection matrix for a right handed coordinate system looking down negative z +orthogonal :: Fractional a + => a -- ^ Near plane clipping distance + -> a -- ^ Far plane clipping distance + -> Vec2 a -- ^ The size of the view (center aligned around origo) + -> Mat44 a +orthogonal n f (w:.h:.()) = matFromList [2/w, 0, 0, 0, + 0, 2/h, 0, 0, + 0, 0, 2/(f-n), -(f+n)/(f-n), + 0, 0, 0, 1]