| Copyright | (c) 2012 diagrams-core team (see LICENSE) |
|---|---|
| License | BSD-style (see LICENSE) |
| Maintainer | diagrams-discuss@googlegroups.com |
| Safe Haskell | None |
| Language | Haskell2010 |
Diagrams.Core.Trace
Description
diagrams-core 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.
- data SortedList a
- mkSortedList :: Ord a => [a] -> SortedList a
- getSortedList :: SortedList a -> [a]
- onSortedList :: Ord b => ([a] -> [b]) -> SortedList a -> SortedList b
- unsafeOnSortedList :: ([a] -> [b]) -> SortedList a -> SortedList b
- newtype Trace v = Trace {
- appTrace :: Point v -> v -> SortedList (Scalar v)
- mkTrace :: (Point v -> v -> SortedList (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))
- getRayTrace :: (Traced a, Num (Scalar (V a))) => a -> Trace (V a)
- rayTraceV :: (Traced a, Num (Scalar (V a))) => Point (V a) -> V a -> a -> Maybe (V a)
- rayTraceP :: (Traced a, Num (Scalar (V a))) => Point (V a) -> V a -> a -> Maybe (Point (V a))
- maxRayTraceV :: (Traced a, Num (Scalar (V a))) => Point (V a) -> V a -> a -> Maybe (V a)
- maxRayTraceP :: (Traced a, Num (Scalar (V a))) => Point (V a) -> V a -> a -> Maybe (Point (V a))
SortedList
data SortedList a Source
A newtype wrapper around a list which maintains the invariant
that the list is sorted. The constructor is not exported; use
the smart constructor mkSortedList (which sorts the given list)
instead.
Instances
| Ord a => Monoid (SortedList a) |
|
| Ord a => Semigroup (SortedList a) |
|
mkSortedList :: Ord a => [a] -> SortedList a Source
A smart constructor for the SortedList type, which sorts the
input to ensure the SortedList invariant.
getSortedList :: SortedList a -> [a] Source
Project the (guaranteed sorted) list out of a SortedList
wrapper.
onSortedList :: Ord b => ([a] -> [b]) -> SortedList a -> SortedList b Source
Apply a list function to a SortedList. The function need not
result in a sorted list; the result will be sorted before being
rewrapped as a SortedList.
unsafeOnSortedList :: ([a] -> [b]) -> SortedList a -> SortedList b Source
Apply an order-preserving list function to a SortedList. No
sorts or checks are done.
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 and a direction vector), the trace computes a sorted list of signed distances from the base point to all intersections of the line with the boundary of the diagram.
Note that the outputs are not absolute distances, but multipliers
relative to the input vector. That is, if the base point is p
and direction vector is v, and one of the output scalars is
s, then there is an intersection at the point p .+^ (s *^ v).
Constructors
| Trace | |
Fields
| |
Instances
| Action Name (Trace v) | |
| Show (Trace v) | |
| Ord (Scalar v) => Monoid (Trace v) | |
| Ord (Scalar v) => Semigroup (Trace v) | |
| Wrapped (Trace v) | |
| VectorSpace v => HasOrigin (Trace v) | |
| HasLinearMap v => Transformable (Trace v) | |
| (Ord (Scalar v), VectorSpace v) => Traced (Trace v) | |
| Rewrapped (Trace v) (Trace v') | |
| type Unwrapped (Trace v) = Point v -> v -> SortedList (Scalar v) | |
| type V (Trace v) = v |
Traced class
class (Ord (Scalar (V a)), VectorSpace (V a)) => Traced a where Source
Traced abstracts over things which have a trace.
Instances
| Traced b => Traced [b] | |
| Traced b => Traced (Set b) | |
| (Ord (Scalar v), VectorSpace v) => Traced (Point v) | The trace of a single point is the empty trace, i.e. the one which returns no intersection points for every query. Arguably it should return a single finite distance for vectors aimed directly at the given point, 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). |
| Traced t => Traced (TransInv t) | |
| (Ord (Scalar v), VectorSpace v) => Traced (Trace v) | |
| (Traced a, Traced b, (~) * (V a) (V b)) => Traced (a, b) | |
| Traced b => Traced (Map k b) | |
| (OrderedField (Scalar v), HasLinearMap v, InnerSpace v, Semigroup m) => Traced (Subdiagram b v m) | |
| (HasLinearMap v, VectorSpace v, Ord (Scalar v), InnerSpace v, Semigroup m, Fractional (Scalar v), Floating (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 p to the "smallest"
boundary intersection along the given vector v. The
"smallest" boundary intersection is defined as the one given by
p .+^ (s *^ v) for the smallest (most negative) value of
s. Return Nothing if there is no intersection. See also
traceP.
See also rayTraceV which uses the smallest positive
intersection, which is often more intuitive behavior.
traceP :: Traced a => Point (V a) -> V a -> a -> Maybe (Point (V a)) Source
Compute the "smallest" boundary point along the line determined
by the given point p and vector v. The "smallest" boundary
point is defined as the one given by p .+^ (s *^ v) for
the smallest (most negative) value of s. Return Nothing if
there is no such boundary point. See also traceV.
See also rayTraceP which uses the smallest positive
intersection, which is often more intuitive behavior.
maxTraceV :: Traced a => Point (V a) -> V a -> a -> Maybe (V a) Source
Like traceV, but computes a vector to the "largest" boundary
point instead of the smallest. (Note, however, the "largest"
boundary point may still be in the opposite direction from the
given vector, if all the boundary points are, as in the third
example shown below.)
maxTraceP :: Traced a => Point (V a) -> V a -> a -> Maybe (Point (V a)) Source
Like traceP, but computes the "largest" boundary point
instead of the smallest. (Note, however, the "largest" boundary
point may still be in the opposite direction from the given
vector, if all the boundary points are.)
rayTraceV :: (Traced a, Num (Scalar (V a))) => Point (V a) -> V a -> a -> Maybe (V a) Source
Compute the vector from the given point to the closest boundary
point of the given object in the given direction, or Nothing if
there is no such boundary point (as in the third example
below). Note that unlike traceV, only positive boundary
points are considered, i.e. boundary points corresponding to a
positive scalar multiple of the direction vector. This is
intuitively the "usual" behavior of a raytracer, which only
considers intersections "in front of" the camera. Compare the
second example diagram below with the second example shown for
traceV.
rayTraceP :: (Traced a, Num (Scalar (V a))) => Point (V a) -> V a -> a -> Maybe (Point (V a)) Source
Compute the boundary point on an object which is closest to the
given base point in the given direction, or Nothing if there is
no such boundary point. Note that unlike traceP, only positive
boundary points are considered, i.e. boundary points
corresponding to a positive scalar multiple of the direction
vector. This is intuitively the "usual" behavior of a raytracer,
which only considers intersection points "in front of" the
camera.
