Nonlinear.Projective.Hom3

Functions for working with 3-dimensional homogeneous coordinates. This includes 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

Adapted from Linear.Projection

Documentation

m43_to_m44 :: Num a => M43 a -> M44 a

Convert from a 4x3 matrix to a 4x4 matrix, extending it with the [ 0 0 0 1 ] column vector

vector :: Num a => V3 a -> V4 a

Convert a 3-dimensional affine vector into a 4-dimensional homogeneous vector, i.e. sets the w coordinate to 0.

point :: Num a => V3 a -> V4 a

Convert a 3-dimensional affine point into a 4-dimensional homogeneous vector, i.e. sets the w coordinate to 1.

normalizePoint :: Fractional a => V4 a -> V3 a

Convert 4-dimensional projective coordinates to a 3-dimensional point. This operation may be denoted, euclidean [x:y:z:w] = (x/w, y/w, z/w) where the projective, homogeneous, coordinate [x:y:z:w] is one of many associated with a single point (x/w, y/w, z/w).

m33_to_m44 :: Num a => M33 a -> M44 a

Convert a 3x3 matrix to a 4x4 matrix extending it with 0's in the new row and column.

translation :: (Vec t, R3 t, R4 v) => Lens' (t (v a)) (V3 a)

Extract the translation vector (first three entries of the last column) from a 3x4 or 4x4 matrix.

mkTransformationMat :: Num a => M33 a -> V3 a -> M44 a

Build a transformation matrix from a rotation matrix and a translation vector.

mkTransformation :: Num a => Quaternion a -> V3 a -> M44 a

Build a transformation matrix from a rotation expressed as a Quaternion and a translation vector.

lookAt

Arguments

:: Floating a

=> V3 a

Eye

-> V3 a

Center

-> V3 a

Up

-> M44 a

Build a look at view matrix

perspective

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

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

frustum

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

Arguments

:: Floating a

=> a

Left

-> a

Right

-> a

Bottom

-> a

Top

-> a

Near

-> a

Far

-> M44 a

infinitePerspective

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

Arguments

:: Floating a

=> a

FOV (y direction, in radians)

-> a

Aspect Ratio

-> a

Near plane

-> M44 a

ortho

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

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