Modulelinear-1.22Haskell2010

Linear.Projection

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

9 values

Packagelinear-1.22
Exports9
LanguageHaskell2010
LicenceBSD-3-Clause
SourceProjection.hs

valuelookAt

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

Build a look at view matrix

valueperspective

:: 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

valueinversePerspective

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

Build an inverse perspective matrix

valueinfinitePerspective

:: 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

valueinverseInfinitePerspective

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

valuefrustum

:: 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.

valueinverseFrustum

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

valueortho

:: 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:

Example1 expression

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

Example1 expression

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

valueinverseOrtho

:: 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