Maintainer | diagrams-discuss@googlegroups.com |
---|---|

Safe Haskell | None |

Transformations specific to three dimensions, with a few generic transformations (uniform scaling, translation) also re-exported for convenience.

- aboutX :: Angle -> T3
- aboutY :: Angle -> T3
- aboutZ :: Angle -> T3
- rotationAbout :: Direction d => P3 -> d -> Angle -> T3
- pointAt :: Direction d => d -> d -> d -> T3
- pointAt' :: R3 -> R3 -> R3 -> T3
- scalingX :: Double -> T3
- scalingY :: Double -> T3
- scalingZ :: Double -> T3
- scaleX :: (Transformable t, V t ~ R3) => Double -> t -> t
- scaleY :: (Transformable t, V t ~ R3) => Double -> t -> t
- scaleZ :: (Transformable t, V t ~ R3) => Double -> t -> t
- scaling :: (HasLinearMap v, Fractional (Scalar v)) => Scalar v -> Transformation v
- scale :: (Transformable t, Fractional (Scalar (V t)), Eq (Scalar (V t))) => Scalar (V t) -> t -> t
- translationX :: Double -> T3
- translateX :: (Transformable t, V t ~ R3) => Double -> t -> t
- translationY :: Double -> T3
- translateY :: (Transformable t, V t ~ R3) => Double -> t -> t
- translationZ :: Double -> T3
- translateZ :: (Transformable t, V t ~ R3) => Double -> t -> t
- translation :: HasLinearMap v => v -> Transformation v
- translate :: (Transformable t, HasLinearMap (V t)) => V t -> t -> t
- reflectionX :: T3
- reflectX :: (Transformable t, V t ~ R3) => t -> t
- reflectionY :: T3
- reflectY :: (Transformable t, V t ~ R3) => t -> t
- reflectionZ :: T3
- reflectZ :: (Transformable t, V t ~ R3) => t -> t
- reflectionAbout :: P3 -> R3 -> T3
- reflectAbout :: (Transformable t, V t ~ R3) => P3 -> R3 -> t -> t
- onBasis :: T3 -> ((R3, R3, R3), R3)

# Rotation

Like `aboutZ`

, but rotates about the X axis, bringing positive y-values
towards the positive z-axis.

Like `aboutZ`

, but rotates about the Y axis, bringing postive
x-values towards the negative z-axis.

Create a transformation which rotates by the given angle about a line parallel the Z axis passing through the local origin. A positive angle brings positive x-values towards the positive-y axis.

The angle can be expressed using any type which is an
instance of `Angle`

. For example, ```
aboutZ (1/4 @@
```

, `turn`

)`aboutZ (tau/4 @@ `

, and `rad`

)```
aboutZ (90 @@
```

all represent the same transformation, namely, a
counterclockwise rotation by a right angle. For more general rotations,
see `deg`

)`rotationAbout`

.

Note that writing `aboutZ (1/4)`

, with no type annotation, will
yield an error since GHC cannot figure out which sort of angle
you want to use.

:: Direction d | |

=> P3 | origin of rotation |

-> d | direction of rotation axis |

-> Angle | angle of rotation |

-> T3 |

`rotationAbout p d a`

is a rotation about a line parallel to `d`

passing through `p`

.

pointAt :: Direction d => d -> d -> d -> T3Source

`pointAt about initial final`

produces a rotation which brings
the direction `initial`

to point in the direction `final`

by first
panning around `about`

, then tilting about the axis perpendicular
to initial and final. In particular, if this can be accomplished
without tilting, it will be, otherwise if only tilting is
necessary, no panning will occur. The tilt will always be between
± /4 turn.

pointAt' :: R3 -> R3 -> R3 -> T3Source

pointAt' has the same behavior as `pointAt`

, but takes vectors
instead of directions.

# Scaling

scalingX :: Double -> T3Source

Construct a transformation which scales by the given factor in the x direction.

scalingY :: Double -> T3Source

Construct a transformation which scales by the given factor in the y direction.

scalingZ :: Double -> T3Source

Construct a transformation which scales by the given factor in the z direction.

scaleX :: (Transformable t, V t ~ R3) => Double -> t -> tSource

Scale a diagram by the given factor in the x (horizontal)
direction. To scale uniformly, use `scale`

.

scaleY :: (Transformable t, V t ~ R3) => Double -> t -> tSource

Scale a diagram by the given factor in the y (vertical)
direction. To scale uniformly, use `scale`

.

scaleZ :: (Transformable t, V t ~ R3) => Double -> t -> tSource

Scale a diagram by the given factor in the z direction. To scale
uniformly, use `scale`

.

scaling :: (HasLinearMap v, Fractional (Scalar v)) => Scalar v -> Transformation v

Create a uniform scaling transformation.

scale :: (Transformable t, Fractional (Scalar (V t)), Eq (Scalar (V t))) => Scalar (V t) -> t -> t

Scale uniformly in every dimension by the given scalar.

# Translation

translationX :: Double -> T3Source

Construct a transformation which translates by the given distance in the x direction.

translateX :: (Transformable t, V t ~ R3) => Double -> t -> tSource

Translate a diagram by the given distance in the x direction.

translationY :: Double -> T3Source

Construct a transformation which translates by the given distance in the y direction.

translateY :: (Transformable t, V t ~ R3) => Double -> t -> tSource

Translate a diagram by the given distance in the y direction.

translationZ :: Double -> T3Source

Construct a transformation which translates by the given distance in the z direction.

translateZ :: (Transformable t, V t ~ R3) => Double -> t -> tSource

Translate a diagram by the given distance in the y direction.

translation :: HasLinearMap v => v -> Transformation v

Create a translation.

translate :: (Transformable t, HasLinearMap (V t)) => V t -> t -> t

Translate by a vector.

# Reflection

Construct a transformation which flips a diagram across x=0, i.e. sends the point (x,y,z) to (-x,y,z).

reflectX :: (Transformable t, V t ~ R3) => t -> tSource

Flip a diagram across x=0, i.e. send the point (x,y,z) to (-x,y,z).

Construct a transformation which flips a diagram across y=0, i.e. sends the point (x,y,z) to (x,-y,z).

reflectY :: (Transformable t, V t ~ R3) => t -> tSource

Flip a diagram across y=0, i.e. send the point (x,y,z) to (x,-y,z).

Construct a transformation which flips a diagram across z=0, i.e. sends the point (x,y,z) to (x,y,-z).

reflectZ :: (Transformable t, V t ~ R3) => t -> tSource

Flip a diagram across z=0, i.e. send the point (x,y,z) to (x,y,-z).

reflectionAbout :: P3 -> R3 -> T3Source

`reflectionAbout p v`

is a reflection across the plane through
the point `p`

and normal to vector `v`

.

reflectAbout :: (Transformable t, V t ~ R3) => P3 -> R3 -> t -> tSource

`reflectAbout p v`

reflects a diagram in the line determined by
the point `p`

and the vector `v`

.