Copyright	(c) 2014-2015 diagrams team (see LICENSE)
License	BSD-style (see LICENSE)
Maintainer	diagrams-discuss@googlegroups.com
Safe Haskell	Safe-Inferred
Language	Haskell2010

Diagrams.LinearMap

Contents

Linear maps
- Applying linear maps
Affine maps
- Constructing affine maps

Description

Linear maps. Unlike Transformations these are not restricted to the same space. In practice these are used for projections in Diagrams.ThreeD.Projection. Unless you want to work with projections you're probably better off using Transform.

Currently only path-like things can be projected. In the future we hope to support projecting diagrams.

Synopsis

newtype LinearMap v u n = LinearMap {
- lapply :: v n -> u n
}
class LinearMappable a b where
- vmap :: (Vn a -> Vn b) -> a -> b
linmap :: (InSpace v n a, LinearMappable a b, N b ~ n) => LinearMap v (V b) n -> a -> b
data AffineMap v u n = AffineMap (LinearMap v u n) (u n)
class (LinearMappable a b, N a ~ N b) => AffineMappable a b where
- amap :: (Additive (V a), Foldable (V a), Additive (V b), Num (N b)) => AffineMap (V a) (V b) (N b) -> a -> b
mkAffineMap :: (v n -> u n) -> u n -> AffineMap v u n
toAffineMap :: Transformation v n -> AffineMap v v n

Linear maps

newtype LinearMap v u n Source #

Type for holding linear maps. Note that these are not affine transforms so attemping apply a translation with LinearMap will likely produce incorrect results.

Constructors

LinearMap
Fields lapply :: v n -> u n

class LinearMappable a b where Source #

Class of things that have vectors that can be mapped over.

Methods

vmap :: (Vn a -> Vn b) -> a -> b Source #

Apply a linear map to an object. If the map is not linear, behaviour will likely be wrong.

Instances

Instances details

(LinearMappable a b, r ~ Located b) => LinearMappable (Located a) r Source #
Instance details Defined in Diagrams.LinearMap Methods vmap :: (Vn (Located a) -> Vn r) -> Located a -> r Source #
(Metric v, Metric u, OrderedField n, OrderedField m, r ~ Path u m) => LinearMappable (Path v n) r Source #
Instance details Defined in Diagrams.LinearMap Methods vmap :: (Vn (Path v n) -> Vn r) -> Path v n -> r Source #
r ~ FixedSegment u m => LinearMappable (FixedSegment v n) r Source #
Instance details Defined in Diagrams.LinearMap Methods vmap :: (Vn (FixedSegment v n) -> Vn r) -> FixedSegment v n -> r Source #
(Metric v, Metric u, OrderedField n, OrderedField m, r ~ SegTree u m) => LinearMappable (SegTree v n) r Source #
Instance details Defined in Diagrams.LinearMap Methods vmap :: (Vn (SegTree v n) -> Vn r) -> SegTree v n -> r Source #
(Metric v, Metric u, OrderedField n, OrderedField m, r ~ Trail u m) => LinearMappable (Trail v n) r Source #
Instance details Defined in Diagrams.LinearMap Methods vmap :: (Vn (Trail v n) -> Vn r) -> Trail v n -> r Source #
LinearMappable (Point v n) (Point u m) Source #
Instance details Defined in Diagrams.LinearMap Methods vmap :: (Vn (Point v n) -> Vn (Point u m)) -> Point v n -> Point u m Source #
r ~ Offset c u m => LinearMappable (Offset c v n) r Source #
Instance details Defined in Diagrams.LinearMap Methods vmap :: (Vn (Offset c v n) -> Vn r) -> Offset c v n -> r Source #
r ~ Segment c u m => LinearMappable (Segment c v n) r Source #
Instance details Defined in Diagrams.LinearMap Methods vmap :: (Vn (Segment c v n) -> Vn r) -> Segment c v n -> r Source #
(Metric v, Metric u, OrderedField n, OrderedField m, r ~ Trail' l u m) => LinearMappable (Trail' l v n) r Source #
Instance details Defined in Diagrams.LinearMap Methods vmap :: (Vn (Trail' l v n) -> Vn r) -> Trail' l v n -> r Source #

Applying linear maps

linmap :: (InSpace v n a, LinearMappable a b, N b ~ n) => LinearMap v (V b) n -> a -> b Source #

Apply a linear map.

Affine maps

data AffineMap v u n Source #

Affine linear maps. Unlike Transformation these do not have to be invertible so we can map between spaces.

Constructors

AffineMap (LinearMap v u n) (u n)

class (LinearMappable a b, N a ~ N b) => AffineMappable a b where Source #

Minimal complete definition

Nothing

Methods

amap :: (Additive (V a), Foldable (V a), Additive (V b), Num (N b)) => AffineMap (V a) (V b) (N b) -> a -> b Source #

Affine map over an object. Has a default implimentation of only applying the linear map

Instances

Instances details

(LinearMappable a b, N a ~ N b, r ~ Located b) => AffineMappable (Located a) r Source #
Instance details Defined in Diagrams.LinearMap Methods amap :: AffineMap (V (Located a)) (V r) (N r) -> Located a -> r Source #
(Metric v, Metric u, OrderedField n, r ~ Path u n) => AffineMappable (Path v n) r Source #
Instance details Defined in Diagrams.LinearMap Methods amap :: AffineMap (V (Path v n)) (V r) (N r) -> Path v n -> r Source #
r ~ FixedSegment u n => AffineMappable (FixedSegment v n) r Source #
Instance details Defined in Diagrams.LinearMap Methods amap :: AffineMap (V (FixedSegment v n)) (V r) (N r) -> FixedSegment v n -> r Source #
(Metric v, Metric u, OrderedField n, r ~ SegTree u n) => AffineMappable (SegTree v n) r Source #
Instance details Defined in Diagrams.LinearMap Methods amap :: AffineMap (V (SegTree v n)) (V r) (N r) -> SegTree v n -> r Source #
(Metric v, Metric u, OrderedField n, r ~ Trail u n) => AffineMappable (Trail v n) r Source #
Instance details Defined in Diagrams.LinearMap Methods amap :: AffineMap (V (Trail v n)) (V r) (N r) -> Trail v n -> r Source #
(Additive v, Num n, r ~ Point u n) => AffineMappable (Point v n) r Source #
Instance details Defined in Diagrams.LinearMap Methods amap :: AffineMap (V (Point v n)) (V r) (N r) -> Point v n -> r Source #
r ~ Offset c u n => AffineMappable (Offset c v n) r Source #
Instance details Defined in Diagrams.LinearMap Methods amap :: AffineMap (V (Offset c v n)) (V r) (N r) -> Offset c v n -> r Source #
r ~ Segment c u n => AffineMappable (Segment c v n) r Source #
Instance details Defined in Diagrams.LinearMap Methods amap :: AffineMap (V (Segment c v n)) (V r) (N r) -> Segment c v n -> r Source #
(Metric v, Metric u, OrderedField n, r ~ Trail' l u n) => AffineMappable (Trail' l v n) r Source #
Instance details Defined in Diagrams.LinearMap Methods amap :: AffineMap (V (Trail' l v n)) (V r) (N r) -> Trail' l v n -> r Source #

Constructing affine maps

mkAffineMap :: (v n -> u n) -> u n -> AffineMap v u n Source #

Make an affine map from a linear function and a translation.

toAffineMap :: Transformation v n -> AffineMap v v n Source #