diagrams-lib-1.4.2.3: Embedded domain-specific language for declarative graphics

Diagrams.Trace

Description

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

Synopsis

# Types

data Trace (v :: Type -> Type) n #

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).

Instances
 Show (Trace v n) Instance detailsDefined in Diagrams.Core.Trace MethodsshowsPrec :: Int -> Trace v n -> ShowS #show :: Trace v n -> String #showList :: [Trace v n] -> ShowS # Ord n => Semigroup (Trace v n) Traces form a semigroup with pointwise minimum as composition. Hence, if t1 is the trace for diagram d1, and e2 is the trace for d2, then e1 mappend e2 is the trace for d1 atop d2. Instance detailsDefined in Diagrams.Core.Trace Methods(<>) :: Trace v n -> Trace v n -> Trace v n #sconcat :: NonEmpty (Trace v n) -> Trace v n #stimes :: Integral b => b -> Trace v n -> Trace v n # Ord n => Monoid (Trace v n) Instance detailsDefined in Diagrams.Core.Trace Methodsmempty :: Trace v n #mappend :: Trace v n -> Trace v n -> Trace v n #mconcat :: [Trace v n] -> Trace v n # (Additive v, Ord n) => Traced (Trace v n) Instance detailsDefined in Diagrams.Core.Trace MethodsgetTrace :: Trace v n -> Trace (V (Trace v n)) (N (Trace v n)) # (Additive v, Num n) => Transformable (Trace v n) Instance detailsDefined in Diagrams.Core.Trace Methodstransform :: Transformation (V (Trace v n)) (N (Trace v n)) -> Trace v n -> Trace v n # (Additive v, Num n) => HasOrigin (Trace v n) Instance detailsDefined in Diagrams.Core.Trace MethodsmoveOriginTo :: Point (V (Trace v n)) (N (Trace v n)) -> Trace v n -> Trace v n # Wrapped (Trace v n) Instance detailsDefined in Diagrams.Core.Trace Associated Typestype Unwrapped (Trace v n) :: Type # Methods_Wrapped' :: Iso' (Trace v n) (Unwrapped (Trace v n)) # (Metric v, OrderedField n) => Alignable (Trace v n) # Instance detailsDefined in Diagrams.Align MethodsalignBy' :: (InSpace v0 n0 (Trace v n), Fractional n0, HasOrigin (Trace v n)) => (v0 n0 -> Trace v n -> Point v0 n0) -> v0 n0 -> n0 -> Trace v n -> Trace v n #defaultBoundary :: (V (Trace v n) ~ v0, N (Trace v n) ~ n0) => v0 n0 -> Trace v n -> Point v0 n0 #alignBy :: (InSpace v0 n0 (Trace v n), Fractional n0, HasOrigin (Trace v n)) => v0 n0 -> n0 -> Trace v n -> Trace v n # Rewrapped (Trace v n) (Trace v' n') Instance detailsDefined in Diagrams.Core.Trace type V (Trace v n) Instance detailsDefined in Diagrams.Core.Trace type V (Trace v n) = v type N (Trace v n) Instance detailsDefined in Diagrams.Core.Trace type N (Trace v n) = n type Unwrapped (Trace v n) Instance detailsDefined in Diagrams.Core.Trace type Unwrapped (Trace v n) = Point v n -> v n -> SortedList n

class (Additive (V a), Ord (N a)) => Traced a #

Traced abstracts over things which have a trace.

Minimal complete definition

getTrace

Instances
 Traced b => Traced [b] Instance detailsDefined in Diagrams.Core.Trace MethodsgetTrace :: [b] -> Trace (V [b]) (N [b]) # Traced b => Traced (Set b) Instance detailsDefined in Diagrams.Core.Trace MethodsgetTrace :: Set b -> Trace (V (Set b)) (N (Set b)) # Traced t => Traced (TransInv t) Instance detailsDefined in Diagrams.Core.Trace MethodsgetTrace :: TransInv t -> Trace (V (TransInv t)) (N (TransInv t)) # (RealFloat n, Ord n) => Traced (CSG n) # Instance detailsDefined in Diagrams.ThreeD.Shapes MethodsgetTrace :: CSG n -> Trace (V (CSG n)) (N (CSG n)) # (RealFloat n, Ord n) => Traced (Frustum n) # Instance detailsDefined in Diagrams.ThreeD.Shapes MethodsgetTrace :: Frustum n -> Trace (V (Frustum n)) (N (Frustum n)) # (Fractional n, Ord n) => Traced (Box n) # Instance detailsDefined in Diagrams.ThreeD.Shapes MethodsgetTrace :: Box n -> Trace (V (Box n)) (N (Box n)) # OrderedField n => Traced (Ellipsoid n) # Instance detailsDefined in Diagrams.ThreeD.Shapes MethodsgetTrace :: Ellipsoid n -> Trace (V (Ellipsoid n)) (N (Ellipsoid n)) # (Traced a, Num (N a)) => Traced (Located a) # The trace of a Located a is the trace of the a, translated to the location. Instance detailsDefined in Diagrams.Located MethodsgetTrace :: Located a -> Trace (V (Located a)) (N (Located a)) # (Traced a, Traced b, SameSpace a b) => Traced (a, b) Instance detailsDefined in Diagrams.Core.Trace MethodsgetTrace :: (a, b) -> Trace (V (a, b)) (N (a, b)) # Traced b => Traced (Map k b) Instance detailsDefined in Diagrams.Core.Trace MethodsgetTrace :: Map k b -> Trace (V (Map k b)) (N (Map k b)) # (Additive v, Ord n) => Traced (Trace v n) Instance detailsDefined in Diagrams.Core.Trace MethodsgetTrace :: Trace v n -> Trace (V (Trace v n)) (N (Trace v n)) # (Additive v, Ord n) => Traced (Point v n) 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). Instance detailsDefined in Diagrams.Core.Trace MethodsgetTrace :: Point v n -> Trace (V (Point v n)) (N (Point v n)) # # Instance detailsDefined in Diagrams.TwoD.Segment MethodsgetTrace :: FixedSegment V2 n -> Trace (V (FixedSegment V2 n)) (N (FixedSegment V2 n)) # RealFloat n => Traced (Trail V2 n) # Instance detailsDefined in Diagrams.TwoD.Path MethodsgetTrace :: Trail V2 n -> Trace (V (Trail V2 n)) (N (Trail V2 n)) # RealFloat n => Traced (Path V2 n) # Instance detailsDefined in Diagrams.TwoD.Path MethodsgetTrace :: Path V2 n -> Trace (V (Path V2 n)) (N (Path V2 n)) # # Instance detailsDefined in Diagrams.BoundingBox MethodsgetTrace :: BoundingBox V3 n -> Trace (V (BoundingBox V3 n)) (N (BoundingBox V3 n)) # RealFloat n => Traced (BoundingBox V2 n) # Instance detailsDefined in Diagrams.BoundingBox MethodsgetTrace :: BoundingBox V2 n -> Trace (V (BoundingBox V2 n)) (N (BoundingBox V2 n)) # # Instance detailsDefined in Diagrams.TwoD.Segment MethodsgetTrace :: Segment Closed V2 n -> Trace (V (Segment Closed V2 n)) (N (Segment Closed V2 n)) # (Metric v, OrderedField n, Semigroup m) => Traced (QDiagram b v n m) Instance detailsDefined in Diagrams.Core.Types MethodsgetTrace :: QDiagram b v n m -> Trace (V (QDiagram b v n m)) (N (QDiagram b v n m)) # (OrderedField n, Metric v, Semigroup m) => Traced (Subdiagram b v n m) Instance detailsDefined in Diagrams.Core.Types MethodsgetTrace :: Subdiagram b v n m -> Trace (V (Subdiagram b v n m)) (N (Subdiagram b v n m)) #

# Diagram traces

trace :: (Metric v, OrderedField n, Semigroup m) => Lens' (QDiagram b v n m) (Trace v n) #

Lens onto the Trace of a QDiagram.

setTrace :: (OrderedField n, Metric v, Semigroup m) => Trace v n -> QDiagram b v n m -> QDiagram b v n m #

Replace the trace of a diagram.

withTrace :: (InSpace v n a, Metric v, OrderedField n, Monoid' m, Traced a) => a -> QDiagram b v n m -> QDiagram b v n m #

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

# Querying traces

traceV :: (n ~ N a, Num n, Traced a) => Point (V a) n -> V a n -> a -> Maybe (V a n) #

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 :: (n ~ N a, Traced a, Num n) => Point (V a) n -> V a n -> a -> Maybe (Point (V a) n) #

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 :: (n ~ N a, Num n, Traced a) => Point (V a) n -> V a n -> a -> Maybe (V a n) #

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 :: (n ~ N a, Num n, Traced a) => Point (V a) n -> V a n -> a -> Maybe (Point (V a) n) #

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.)

# Subdiagram traces

boundaryFrom :: (OrderedField n, Metric v, Semigroup m) => Subdiagram b v n m -> v n -> Point v n #

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 :: (Metric v, OrderedField n, Semigroup m) => Subdiagram b v n m -> v n -> Maybe (Point v n) #

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.