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

Safe Haskell | None |

"Traces", aka embedded raytracers, for finding points on the edge of a diagram. See Diagrams.Core.Trace for internal implementation details.

- data Trace v
- class (Ord (Scalar (V a)), VectorSpace (V a)) => Traced a
- trace :: (InnerSpace v, HasLinearMap v, OrderedField (Scalar v), Semigroup m) => Lens' (QDiagram b v m) (Trace v)
- setTrace :: (OrderedField (Scalar v), InnerSpace v, HasLinearMap v, Semigroup m) => Trace v -> QDiagram b v m -> QDiagram b v m
- withTrace :: (HasLinearMap (V a), Traced a, OrderedField (Scalar (V a)), InnerSpace (V a), Monoid' m) => a -> QDiagram b (V a) m -> QDiagram b (V a) m
- traceV :: Traced a => Point (V a) -> V a -> a -> Maybe (V a)
- traceP :: Traced a => Point (V a) -> V a -> a -> Maybe (Point (V a))
- maxTraceV :: Traced a => Point (V a) -> V a -> a -> Maybe (V a)
- maxTraceP :: Traced a => Point (V a) -> V a -> a -> Maybe (Point (V a))
- boundaryFrom :: (HasLinearMap v, OrderedField (Scalar v), InnerSpace v, Semigroup m) => Subdiagram b v m -> v -> Point v
- boundaryFromMay :: (HasLinearMap v, OrderedField (Scalar v), Semigroup m, InnerSpace v) => Subdiagram b v m -> v -> Maybe (Point v)

# Types

data Trace v

Every diagram comes equipped with a *trace*. Intuitively, the
trace for a diagram is like a raytracer: given a line
(represented as a base point and a direction), the trace computes
the distance from the base point along the line to the first
intersection with the diagram. The distance can be negative if
the intersection is in the opposite direction from the base
point, or infinite if the ray never intersects the diagram.
Note: to obtain the distance to the *furthest* intersection
instead of the *closest*, just negate the direction vector and
then negate the result.

Note that the output should actually be interpreted not as an
absolute distance, but as a multiplier relative to the input
vector. That is, if the input vector is `v`

and the returned
scalar is `s`

, the distance from the base point to the
intersection is given by `s * magnitude v`

.

Action Name (Trace v) | |

Show (Trace v) | |

Ord (Scalar v) => Semigroup (Trace v) | |

Ord (Scalar v) => Monoid (Trace v) | |

(Ord (Scalar v), VectorSpace v) => Traced (Trace v) | |

HasLinearMap v => Transformable (Trace v) | |

VectorSpace v => HasOrigin (Trace v) | |

(InnerSpace v, OrderedField (Scalar v)) => Alignable (Trace v) | |

(~ * (Scalar v) s, ~ * (Scalar v') s', ~ * s s') => Wrapped (Point v -> v -> PosInf s) (Point v' -> v' -> PosInf s') (Trace v) (Trace v') | |

Wrapped (DUALTree (DownAnnots v) (UpAnnots b v m) () (QDiaLeaf b v m)) (DUALTree (DownAnnots v') (UpAnnots b' v' m') () (QDiaLeaf b' v' m')) (QDiagram b v m) (QDiagram b' v' m') |

class (Ord (Scalar (V a)), VectorSpace (V a)) => Traced a

`Traced`

abstracts over things which have a trace.

Traced b => Traced [b] | |

Traced b => Traced (Set b) | |

(Ord (Scalar v), VectorSpace v) => Traced (Trace v) | |

Traced t => Traced (TransInv t) | |

(Ord (Scalar v), VectorSpace v) => Traced (Point v) | The trace of a single point is the empty trace, |

Traced a => Traced (Located a) | The trace of a |

Traced (FixedSegment R2) | |

Traced (Trail R2) | |

Traced (Path R2) | |

(Traced a, Traced b, ~ * (V a) (V b)) => Traced (a, b) | |

Traced b => Traced (Map k b) | |

Traced (Segment Closed R2) | |

(HasLinearMap v, VectorSpace v, Ord (Scalar v), InnerSpace v, Semigroup m, Fractional (Scalar v), Floating (Scalar v)) => Traced (QDiagram b v m) | |

(OrderedField (Scalar v), HasLinearMap v, InnerSpace v, Semigroup m) => Traced (Subdiagram b v m) |

# Diagram traces

trace :: (InnerSpace v, HasLinearMap v, OrderedField (Scalar v), Semigroup m) => Lens' (QDiagram b v m) (Trace v)

Get the trace of a diagram.

setTrace :: (OrderedField (Scalar v), InnerSpace v, HasLinearMap v, Semigroup m) => Trace v -> QDiagram b v m -> QDiagram b v m

Replace the trace of a diagram.

withTrace :: (HasLinearMap (V a), Traced a, OrderedField (Scalar (V a)), InnerSpace (V a), Monoid' m) => a -> QDiagram b (V a) m -> QDiagram b (V a) mSource

Use the trace from some object as the trace for a diagram, in place of the diagram's default trace.

# Querying traces

traceV :: Traced a => Point (V a) -> V a -> a -> Maybe (V a)

Compute the vector from the given point to the boundary of the
given object in the given direction, or `Nothing`

if there is no
intersection.

traceP :: Traced a => Point (V a) -> V a -> a -> Maybe (Point (V a))

Given a base point and direction, compute the closest point on
the boundary of the given object, or `Nothing`

if there is no
intersection in the given direction.

maxTraceV :: Traced a => Point (V a) -> V a -> a -> Maybe (V a)

Like `traceV`

, but computes a vector to the *furthest* point on
the boundary instead of the closest.

maxTraceP :: Traced a => Point (V a) -> V a -> a -> Maybe (Point (V a))

Like `traceP`

, but computes the *furthest* point on the boundary
instead of the closest.

# Subdiagram traces

boundaryFrom :: (HasLinearMap v, OrderedField (Scalar v), InnerSpace v, Semigroup m) => Subdiagram b v m -> v -> Point vSource

Compute the furthest point on the boundary of a subdiagram,
beginning from the location (local origin) of the subdiagram and
moving in the direction of the given vector. If there is no such
point, the origin is returned; see also `boundaryFromMay`

.

boundaryFromMay :: (HasLinearMap v, OrderedField (Scalar v), Semigroup m, InnerSpace v) => Subdiagram b v m -> v -> Maybe (Point v)Source

Compute the furthest point on the boundary of a subdiagram,
beginning from the location (local origin) of the subdiagram and
moving in the direction of the given vector, or `Nothing`

if
there is no such point.