| Copyright | (c) 2014-2015 diagrams team (see LICENSE) |
|---|---|
| License | BSD-style (see LICENSE) |
| Maintainer | diagrams-discuss@googlegroups.com |
| Safe Haskell | None |
| Language | Haskell2010 |
Diagrams.LinearMap
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.
- newtype LinearMap v u n = LinearMap {
- lapply :: v n -> u n
- class LinearMappable a b where
- 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
- 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
Type for holding linear maps. Note that these are not affine transforms so
attemping apply a translation with LinearMap will likely produce incorrect
results.
class LinearMappable a b where
Class of things that have vectors that can be mapped over.
Methods
vmap :: (Vn a -> Vn b) -> a -> b
Apply a linear map to an object. If the map is not linear, behaviour will likely be wrong.
Instances
| (LinearMappable a b, (~) * r (Located b)) => LinearMappable (Located a) r | |
| (~) * r (FixedSegment u m) => LinearMappable (FixedSegment v n) r | |
| (Metric v, Metric u, OrderedField n, OrderedField m, (~) * r (Trail u m)) => LinearMappable (Trail v n) r | |
| (Metric v, Metric u, OrderedField n, OrderedField m, (~) * r (SegTree u m)) => LinearMappable (SegTree v n) r | |
| (Metric v, Metric u, OrderedField n, OrderedField m, (~) * r (Path u m)) => LinearMappable (Path v n) r | |
| LinearMappable (Point v n) (Point u m) | |
| (~) * r (Segment c u m) => LinearMappable (Segment c v n) r | |
| (~) * r (Offset c u m) => LinearMappable (Offset c v n) r | |
| (Metric v, Metric u, OrderedField n, OrderedField m, (~) * r (Trail' l u m)) => LinearMappable (Trail' l v n) r |
Applying linear maps
linmap :: (InSpace v n a, LinearMappable a b, N b ~ n) => LinearMap v (V b) n -> a -> b
Apply a linear map.
Affine maps
data AffineMap v u n
Affine linear maps. Unlike Transformation these do not have to be
invertible so we can map between spaces.
class (LinearMappable a b, N a ~ N b) => AffineMappable a b where
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
Affine map over an object. Has a default implimentation of only applying the linear map
Instances
| (LinearMappable a b, (~) * (N a) (N b), (~) * r (Located b)) => AffineMappable (Located a) r | |
| (Additive v, Num n, (~) * r (Point u n)) => AffineMappable (Point v n) r | |
| (~) * r (FixedSegment u n) => AffineMappable (FixedSegment v n) r | |
| (Metric v, Metric u, OrderedField n, (~) * r (Trail u n)) => AffineMappable (Trail v n) r | |
| (Metric v, Metric u, OrderedField n, (~) * r (SegTree u n)) => AffineMappable (SegTree v n) r | |
| (Metric v, Metric u, OrderedField n, (~) * r (Path u n)) => AffineMappable (Path v n) r | |
| (~) * r (Segment c u n) => AffineMappable (Segment c v n) r | |
| (~) * r (Offset c u n) => AffineMappable (Offset c v n) r | |
| (Metric v, Metric u, OrderedField n, (~) * r (Trail' l u n)) => AffineMappable (Trail' l v n) r |
Constructing affine maps
mkAffineMap :: (v n -> u n) -> u n -> AffineMap v u n
Make an affine map from a linear function and a translation.
toAffineMap :: Transformation v n -> AffineMap v v n