Copyright	(C) 2015 Edward Kmett
License	BSD-style (see the file LICENSE)
Maintainer	Edward Kmett <ekmett@gmail.com>
Stability	experimental
Portability	non-portable
Safe Haskell	None
Language	Haskell2010

Linear.Projection

Description

Common projection matrices: e.g. perspective/orthographic transformation matrices.

Analytically derived inverses are also supplied, because they can be much more accurate in practice than computing them through general purpose means

Synopsis

lookAt :: (Epsilon a, Floating a) => V3 a -> V3 a -> V3 a -> M44 a
perspective :: Floating a => a -> a -> a -> a -> M44 a
inversePerspective :: Floating a => a -> a -> a -> a -> M44 a
infinitePerspective :: Floating a => a -> a -> a -> M44 a
inverseInfinitePerspective :: Floating a => a -> a -> a -> M44 a
frustum :: Floating a => a -> a -> a -> a -> a -> a -> M44 a
inverseFrustum :: Floating a => a -> a -> a -> a -> a -> a -> M44 a
ortho :: Fractional a => a -> a -> a -> a -> a -> a -> M44 a
inverseOrtho :: Fractional a => a -> a -> a -> a -> a -> a -> M44 a

Documentation

lookAt Source #

Arguments

:: (Epsilon a, Floating a)
=> V3 a	Eye
-> V3 a	Center
-> V3 a	Up
-> M44 a

Build a look at view matrix

perspective Source #

Arguments

:: Floating a
=> a	FOV (y direction, in radians)
-> a	Aspect ratio
-> a	Near plane
-> a	Far plane
-> M44 a

Build a matrix for a symmetric perspective-view frustum

inversePerspective Source #

Arguments

:: Floating a
=> a	FOV (y direction, in radians)
-> a	Aspect ratio
-> a	Near plane
-> a	Far plane
-> M44 a

Build an inverse perspective matrix

infinitePerspective Source #

Arguments

:: Floating a
=> a	FOV (y direction, in radians)
-> a	Aspect Ratio
-> a	Near plane
-> M44 a

Build a matrix for a symmetric perspective-view frustum with a far plane at infinite

inverseInfinitePerspective Source #

Arguments

:: Floating a
=> a	FOV (y direction, in radians)
-> a	Aspect Ratio
-> a	Near plane
-> M44 a

frustum Source #

Arguments

:: Floating a
=> a	Left
-> a	Right
-> a	Bottom
-> a	Top
-> a	Near
-> a	Far
-> M44 a

Build a perspective matrix per the classic glFrustum arguments.

inverseFrustum Source #

Arguments

:: Floating a
=> a	Left
-> a	Right
-> a	Bottom
-> a	Top
-> a	Near
-> a	Far
-> M44 a

ortho Source #

Arguments

:: Fractional a
=> a	Left
-> a	Right
-> a	Bottom
-> a	Top
-> a	Near
-> a	Far
-> M44 a

Build an orthographic perspective matrix from 6 clipping planes. This matrix takes the region delimited by these planes and maps it to normalized device coordinates between [-1,1]

This call is designed to mimic the parameters to the OpenGL glOrtho call, so it has a slightly strange convention: Notably: the near and far planes are negated.

Consequently:

ortho l r b t n f !* V4 l b (-n) 1 = V4 (-1) (-1) (-1) 1
ortho l r b t n f !* V4 r t (-f) 1 = V4 1 1 1 1

Examples:

>>> ortho 1 2 3 4 5 6 !* V4 1 3 (-5) 1
V4 (-1.0) (-1.0) (-1.0) 1.0

>>> ortho 1 2 3 4 5 6 !* V4 2 4 (-6) 1
V4 1.0 1.0 1.0 1.0

inverseOrtho Source #

Arguments

:: Fractional a
=> a	Left
-> a	Right
-> a	Bottom
-> a	Top
-> a	Near
-> a	Far
-> M44 a

Build an inverse orthographic perspective matrix from 6 clipping planes