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

Graphics.Rendering.Diagrams defines the core library of primitives forming the basis of an embedded domain-specific language for describing and rendering diagrams.

The `Bounds`

module defines a data type and type class for functional
bounding regions.

- newtype Bounds v = Bounds {}
- class (InnerSpace (V b), OrderedField (Scalar (V b))) => Boundable b where
- diameter :: Boundable a => V a -> a -> Scalar (V a)
- radius :: Boundable a => V a -> a -> Scalar (V a)
- boundaryV :: Boundable a => V a -> a -> V a
- boundary :: Boundable a => V a -> a -> Point (V a)
- boundaryFrom :: Boundable a => Point (V a) -> V a -> a -> Point (V a)
- class (Fractional s, Floating s, Ord s, AdditiveGroup s) => OrderedField s

# Bounding regions

Every diagram comes equipped with a bounding function.
Intuitively, the bounding function for a diagram tells us the
minimum distance we have to go in a given direction to get to a
(hyper)plane entirely containing the diagram on one side of
it. Formally, given a vector `v`

, it returns a scalar `s`

such
that

- for every vector
`u`

with its endpoint inside the diagram, if the projection of`u`

onto`v`

is`s' *^ v`

, then`s' <= s`

. -
`s`

is the smallest such scalar.

This could probably be expressed in terms of a Galois connection; this is left as an exercise for the reader.

Essentially, bounding functions are a functional representation of (a conservative approximation to) convex bounding regions. The idea for this representation came from Sebastian Setzer; see http://byorgey.wordpress.com/2009/10/28/collecting-attributes/#comment-2030.

Show (Bounds v) | |

(Ord (Scalar v), AdditiveGroup (Scalar v)) => Monoid (Bounds v) | Bounding functions form a monoid, with the constantly zero
function ( |

(InnerSpace v, AdditiveGroup (Scalar v), Fractional (Scalar v)) => HasOrigin (Bounds v) | The local origin of a bounding function is the point with respect to which bounding queries are made, i.e. the point from which the input vectors are taken to originate. |

(HasLinearMap v, InnerSpace v, Floating (Scalar v), AdditiveGroup (Scalar v)) => Transformable (Bounds v) | |

(InnerSpace v, OrderedField (Scalar v)) => Boundable (Bounds v) |

class (InnerSpace (V b), OrderedField (Scalar (V b))) => Boundable b whereSource

`Boundable`

abstracts over things which can be bounded.

getBounds :: b -> Bounds (V b)Source

Given a boundable object, compute a functional bounding region
for it. For types with an intrinsic notion of "local
origin", the bounding function will be based there. Other
types (e.g. `Trail`

) may have some other default reference
point at which the bounding function will be based; their
instances should document what it is.

Boundable b => Boundable [b] | |

(OrderedField (Scalar v), InnerSpace v) => Boundable (Point v) | |

(InnerSpace v, OrderedField (Scalar v)) => Boundable (Bounds v) | |

(HasLinearMap v, InnerSpace v, OrderedField (Scalar v)) => Boundable (AnnDiagram b v m) |

# Utility functions

diameter :: Boundable a => V a -> a -> Scalar (V a)Source

Compute the diameter of a boundable object along a particular vector.

radius :: Boundable a => V a -> a -> Scalar (V a)Source

Compute the radius (1/2 the diameter) of a boundable object along a particular vector.

boundaryV :: Boundable a => V a -> a -> V aSource

Compute the vector from the local origin to a separating hyperplane in the given direction.

boundary :: Boundable a => V a -> a -> Point (V a)Source

Compute the point on the boundary in the given direction.
Caution: this point is only valid in the local vector space of
the `Boundable`

object. If you want to compute boundary points
of things which are subparts of a larger diagram (and hence
embedded within a different vector space), you must use
`boundaryFrom`

instead.

boundaryFrom :: Boundable a => Point (V a) -> V a -> a -> Point (V a)Source

`boundaryFrom o v a`

computes the point along the boundary of `a`

in the direction of `v`

, assuming that `a`

's local origin is
located at the point `o`

of the vector space we care about.

# Miscellaneous

class (Fractional s, Floating s, Ord s, AdditiveGroup s) => OrderedField s Source

When dealing with bounding regions we often want scalars to be an ordered field (i.e. support all four arithmetic operations and be totally ordered) so we introduce this class as a convenient shorthand.

(Fractional s, Floating s, Ord s, AdditiveGroup s) => OrderedField s |