Copyright	(c) 2011 Brent Yorgey
License	BSD-style (see LICENSE)
Maintainer	byorgey@cis.upenn.edu
Safe Haskell	Safe
Language	Haskell2010

Data.AffineSpace.Point

Contents

Points
Reflection through a point

Description

A type for points (as distinct from vectors), with an appropriate AffineSpace instance.

Synopsis

newtype Point v = P v
unPoint :: Point v -> v
origin :: AdditiveGroup v => Point v
(*.) :: VectorSpace v => Scalar v -> Point v -> Point v
mirror :: AdditiveGroup v => Point v -> Point v
relative :: AffineSpace p => p -> (Diff p -> Diff p) -> p -> p
relative2 :: AffineSpace p => p -> (Diff p -> Diff p -> Diff p) -> p -> p -> p
relative3 :: AffineSpace p => p -> (Diff p -> Diff p -> Diff p -> Diff p) -> p -> p -> p -> p
reflectThrough :: AffineSpace p => p -> p -> p

Points

newtype Point v Source #

Point is a newtype wrapper around vectors used to represent points, so we don't get them mixed up. The distinction between vectors and points is important: translations affect points, but leave vectors unchanged. Points are instances of the AffineSpace class from Data.AffineSpace.

Constructors

P v

Instances

Functor Point Source #
Instance details Defined in Data.AffineSpace.Point Methods fmap :: (a -> b) -> Point a -> Point b Source # (<$) :: a -> Point b -> Point a Source #
Eq v => Eq (Point v) Source #
Instance details Defined in Data.AffineSpace.Point Methods (==) :: Point v -> Point v -> Bool Source # (/=) :: Point v -> Point v -> Bool Source #
Data v => Data (Point v) Source #
Instance details Defined in Data.AffineSpace.Point Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Point v -> c (Point v) Source # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Point v) Source # toConstr :: Point v -> Constr Source # dataTypeOf :: Point v -> DataType Source # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Point v)) Source # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Point v)) Source # gmapT :: (forall b. Data b => b -> b) -> Point v -> Point v Source # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Point v -> r Source # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Point v -> r Source # gmapQ :: (forall d. Data d => d -> u) -> Point v -> [u] Source # gmapQi :: Int -> (forall d. Data d => d -> u) -> Point v -> u Source # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Point v -> m (Point v) Source # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Point v -> m (Point v) Source # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Point v -> m (Point v) Source #
Ord v => Ord (Point v) Source #
Instance details Defined in Data.AffineSpace.Point Methods compare :: Point v -> Point v -> Ordering Source # (<) :: Point v -> Point v -> Bool Source # (<=) :: Point v -> Point v -> Bool Source # (>) :: Point v -> Point v -> Bool Source # (>=) :: Point v -> Point v -> Bool Source # max :: Point v -> Point v -> Point v Source # min :: Point v -> Point v -> Point v Source #
Read v => Read (Point v) Source #
Instance details Defined in Data.AffineSpace.Point Methods readsPrec :: Int -> ReadS (Point v) Source # readList :: ReadS [Point v] Source # readPrec :: ReadPrec (Point v) Source # readListPrec :: ReadPrec [Point v] Source #
Show v => Show (Point v) Source #
Instance details Defined in Data.AffineSpace.Point Methods showsPrec :: Int -> Point v -> ShowS Source # show :: Point v -> String Source # showList :: [Point v] -> ShowS Source #
AdditiveGroup v => AffineSpace (Point v) Source #
Instance details Defined in Data.AffineSpace.Point Associated Types type Diff (Point v) :: Type Source # Methods (.-.) :: Point v -> Point v -> Diff (Point v) Source # (.+^) :: Point v -> Diff (Point v) -> Point v Source #
type Diff (Point v) Source #
Instance details Defined in Data.AffineSpace.Point type Diff (Point v) = v

unPoint :: Point v -> v Source #

Convert a point p into the vector from the origin to p. This should be considered a "semantically unsafe" operation; think carefully about whether and why you need to use it. The recommended way to do this conversion would be to write (p .-. origin).

origin :: AdditiveGroup v => Point v Source #

The origin of the vector space v.

(*.) :: VectorSpace v => Scalar v -> Point v -> Point v Source #

Scale a point by a scalar.

mirror :: AdditiveGroup v => Point v -> Point v Source #

Reflect a point through the origin.

Reflection through a point

relative :: AffineSpace p => p -> (Diff p -> Diff p) -> p -> p Source #

Apply a transformation relative to the given point.

relative2 :: AffineSpace p => p -> (Diff p -> Diff p -> Diff p) -> p -> p -> p Source #

Apply a transformation relative to the given point.

relative3 :: AffineSpace p => p -> (Diff p -> Diff p -> Diff p -> Diff p) -> p -> p -> p -> p Source #

Apply a transformation relative to the given point.

reflectThrough :: AffineSpace p => p -> p -> p Source #

Mirror a point through a given point.