Maintainer | diagrams-discuss@googlegroups.com |
---|---|
Safe Haskell | None |
Diagrams defines the core library of primitives forming the basis of an embedded domain-specific language for describing and rendering diagrams.
The Trace
module defines a data type and type class for
"traces", aka functional boundaries, essentially corresponding to
embedding a raytracer with each diagram.
- newtype Trace v = Trace {}
- inTrace :: ((Point v -> v -> PosInf (Scalar v)) -> Point v -> v -> PosInf (Scalar v)) -> Trace v -> Trace v
- mkTrace :: (Point v -> v -> PosInf (Scalar v)) -> Trace v
- class (Ord (Scalar (V a)), VectorSpace (V a)) => Traced a where
- 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))
Traces
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 + 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
.
Show (Trace v) | |
Ord (Scalar v) => Monoid (Trace v) | |
Ord (Scalar v) => Semigroup (Trace v) | |
(VectorSpace (V (Trace v)), VectorSpace v) => HasOrigin (Trace v) | |
(HasLinearMap (V (Trace v)), HasLinearMap v) => Transformable (Trace v) | |
(Ord (Scalar (V (Trace v))), VectorSpace (V (Trace v)), Ord (Scalar v), VectorSpace v) => Traced (Trace v) | |
Newtype (QDiagram b v m) (DUALTree (DownAnnots v) (UpAnnots b v m) () (Prim b v)) |
inTrace :: ((Point v -> v -> PosInf (Scalar v)) -> Point v -> v -> PosInf (Scalar v)) -> Trace v -> Trace vSource
Traced class
class (Ord (Scalar (V a)), VectorSpace (V a)) => Traced a whereSource
Traced
abstracts over things which have a trace.
(Ord (Scalar (V [b])), VectorSpace (V [b]), Traced b) => Traced [b] | |
(Ord (Scalar (V (Set b))), VectorSpace (V (Set b)), Traced b) => Traced (Set b) | |
(Ord (Scalar (V (Point v))), VectorSpace (V (Point v)), Ord (Scalar v), VectorSpace v) => Traced (Point v) | The trace of a single point is the empty trace, i.e. the one which returns positive infinity for every query. Arguably it should return a finite distance for vectors aimed directly at the given point and infinity for everything else, but due to floating-point inaccuracy this is problematic. Note that the envelope for a single point is *not* the empty envelope (see Diagrams.Core.Envelope). |
(Ord (Scalar (V (Trace v))), VectorSpace (V (Trace v)), Ord (Scalar v), VectorSpace v) => Traced (Trace v) | |
(Ord (Scalar (V (a, b))), VectorSpace (V (a, b)), Traced a, Traced b, ~ * (V a) (V b)) => Traced (a, b) | |
(Ord (Scalar (V (Map k b))), VectorSpace (V (Map k b)), Traced b) => Traced (Map k b) | |
(Ord (Scalar (V (Subdiagram b v m))), VectorSpace (V (Subdiagram b v m)), Ord (Scalar v), VectorSpace v, HasLinearMap v) => Traced (Subdiagram b v m) | |
(Ord (Scalar (V (QDiagram b v m))), VectorSpace (V (QDiagram b v m)), HasLinearMap v, VectorSpace v, Ord (Scalar v)) => Traced (QDiagram b v m) |
Computing with traces
traceV :: Traced a => Point (V a) -> V a -> a -> Maybe (V a)Source
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))Source
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.