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 | Safe |

Language | Haskell98 |

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

Build a look at view matrix

Build a matrix for a symmetric perspective-view frustum

Build an inverse perspective matrix

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

Build a perspective matrix per the classic `glFrustum`

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:

`>>>`

V4 (-1.0) (-1.0) (-1.0) 1.0`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`

:: 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