Copyright	(C) Frank Staals
License	see the LICENSE file
Maintainer	Frank Staals
Safe Haskell	Safe-Inferred
Language	GHC2021

HGeometry.HyperPlane.NonVertical

Description

Non-vertical hyperplanes in d-dimensional space.

Synopsis

newtype NonVerticalHyperPlane d r where
- NonVerticalHyperPlane (Vector d r)
- pattern Plane :: r -> r -> r -> Plane r
asNonVerticalHyperPlane :: (HyperPlane_ hyperPlane d r, Fractional r, Eq r, 1 <= d) => hyperPlane -> Maybe (NonVerticalHyperPlane d r)
type Plane = NonVerticalHyperPlane 3
type Plane_ plane = NonVerticalHyperPlane_ plane 3
pattern Plane_ :: Plane_ plane r => r -> r -> r -> plane

Documentation

newtype NonVerticalHyperPlane d r Source #

A non-vertical Hyperplane described by ( x_d = a_d + sum_{i=1}^{d-1} a_i * x_i ) where $\langle a_1,..,a_d \rangle $ are the coefficients of te hyperplane.

e.g. the myLineAsNV defines the hyperplane (i.e. the line) described by

y = 2 + 1*x

Constructors

NonVerticalHyperPlane (Vector d r)

Bundled Patterns

pattern Plane :: r -> r -> r -> Plane r

Constructs a Plane in R^3 for the equation z = ax + by + c

Instances

Instances details

Foldable (Vector d) => Foldable (NonVerticalHyperPlane d) Source #
Instance details Defined in HGeometry.HyperPlane.NonVertical Methods fold :: Monoid m => NonVerticalHyperPlane d m -> m # foldMap :: Monoid m => (a -> m) -> NonVerticalHyperPlane d a -> m # foldMap' :: Monoid m => (a -> m) -> NonVerticalHyperPlane d a -> m # foldr :: (a -> b -> b) -> b -> NonVerticalHyperPlane d a -> b # foldr' :: (a -> b -> b) -> b -> NonVerticalHyperPlane d a -> b # foldl :: (b -> a -> b) -> b -> NonVerticalHyperPlane d a -> b # foldl' :: (b -> a -> b) -> b -> NonVerticalHyperPlane d a -> b # foldr1 :: (a -> a -> a) -> NonVerticalHyperPlane d a -> a # foldl1 :: (a -> a -> a) -> NonVerticalHyperPlane d a -> a # toList :: NonVerticalHyperPlane d a -> [a] # null :: NonVerticalHyperPlane d a -> Bool # length :: NonVerticalHyperPlane d a -> Int # elem :: Eq a => a -> NonVerticalHyperPlane d a -> Bool # maximum :: Ord a => NonVerticalHyperPlane d a -> a # minimum :: Ord a => NonVerticalHyperPlane d a -> a # sum :: Num a => NonVerticalHyperPlane d a -> a # product :: Num a => NonVerticalHyperPlane d a -> a #
Traversable (Vector d) => Traversable (NonVerticalHyperPlane d) Source #
Instance details Defined in HGeometry.HyperPlane.NonVertical Methods traverse :: Applicative f => (a -> f b) -> NonVerticalHyperPlane d a -> f (NonVerticalHyperPlane d b) # sequenceA :: Applicative f => NonVerticalHyperPlane d (f a) -> f (NonVerticalHyperPlane d a) # mapM :: Monad m => (a -> m b) -> NonVerticalHyperPlane d a -> m (NonVerticalHyperPlane d b) # sequence :: Monad m => NonVerticalHyperPlane d (m a) -> m (NonVerticalHyperPlane d a) #
Functor (Vector d) => Functor (NonVerticalHyperPlane d) Source #
Instance details Defined in HGeometry.HyperPlane.NonVertical Methods fmap :: (a -> b) -> NonVerticalHyperPlane d a -> NonVerticalHyperPlane d b # (<$) :: a -> NonVerticalHyperPlane d b -> NonVerticalHyperPlane d a #
(Read r, Has_ Vector_ d r) => Read (NonVerticalHyperPlane d r) Source #
Instance details Defined in HGeometry.HyperPlane.NonVertical Methods readsPrec :: Int -> ReadS (NonVerticalHyperPlane d r) # readList :: ReadS [NonVerticalHyperPlane d r] # readPrec :: ReadPrec (NonVerticalHyperPlane d r) # readListPrec :: ReadPrec [NonVerticalHyperPlane d r] #
(Show r, Foldable (Vector d)) => Show (NonVerticalHyperPlane d r) Source #
Instance details Defined in HGeometry.HyperPlane.NonVertical Methods showsPrec :: Int -> NonVerticalHyperPlane d r -> ShowS # show :: NonVerticalHyperPlane d r -> String # showList :: [NonVerticalHyperPlane d r] -> ShowS #
NFData (Vector d r) => NFData (NonVerticalHyperPlane d r) Source #
Instance details Defined in HGeometry.HyperPlane.NonVertical Methods rnf :: NonVerticalHyperPlane d r -> () #
Eq (Vector d r) => Eq (NonVerticalHyperPlane d r) Source #
Instance details Defined in HGeometry.HyperPlane.NonVertical Methods (==) :: NonVerticalHyperPlane d r -> NonVerticalHyperPlane d r -> Bool # (/=) :: NonVerticalHyperPlane d r -> NonVerticalHyperPlane d r -> Bool #
Ord (Vector d r) => Ord (NonVerticalHyperPlane d r) Source #
Instance details Defined in HGeometry.HyperPlane.NonVertical Methods compare :: NonVerticalHyperPlane d r -> NonVerticalHyperPlane d r -> Ordering # (<) :: NonVerticalHyperPlane d r -> NonVerticalHyperPlane d r -> Bool # (<=) :: NonVerticalHyperPlane d r -> NonVerticalHyperPlane d r -> Bool # (>) :: NonVerticalHyperPlane d r -> NonVerticalHyperPlane d r -> Bool # (>=) :: NonVerticalHyperPlane d r -> NonVerticalHyperPlane d r -> Bool # max :: NonVerticalHyperPlane d r -> NonVerticalHyperPlane d r -> NonVerticalHyperPlane d r # min :: NonVerticalHyperPlane d r -> NonVerticalHyperPlane d r -> NonVerticalHyperPlane d r #
(MkHyperPlaneConstraints d r, Fractional r, Eq r, 2 <= d) => ConstructableHyperPlane_ (NonVerticalHyperPlane d r) d r Source #
Instance details Defined in HGeometry.HyperPlane.NonVertical Associated Types type HyperPlaneFromEquationConstraint (NonVerticalHyperPlane d r) d r Source # Methods hyperPlaneFromEquation :: Vector (d + 1) r -> NonVerticalHyperPlane d r Source # fromPointAndNormal :: (Point_ point d r, Num r) => point -> Vector d r -> NonVerticalHyperPlane d r Source #
(MkHyperPlaneConstraints d r, 2 <= d) => HyperPlane_ (NonVerticalHyperPlane d r) d r Source #
Instance details Defined in HGeometry.HyperPlane.NonVertical Methods evalHyperPlaneEquation :: (Num r, Point_ point d r) => NonVerticalHyperPlane d r -> point -> r Source # hyperPlaneEquation :: NonVerticalHyperPlane d r -> Vector (d + 1) r Source # normalVector :: NonVerticalHyperPlane d r -> Vector d r Source # onHyperPlane :: (Point_ point d r, Eq r, Num r) => point -> NonVerticalHyperPlane d r -> Bool Source # onSideTest :: (Point_ point d r, Ord r, Num r) => point -> NonVerticalHyperPlane d r -> Ordering Source #
(MkHyperPlaneConstraints d r, (1 + (d - 1)) ~ d, Num r, 2 <= d) => NonVerticalHyperPlane_ (NonVerticalHyperPlane d r) d r Source #
Instance details Defined in HGeometry.HyperPlane.NonVertical Methods evalAt :: (Num r, 1 <= d, Point_ point (d - 1) r) => point -> NonVerticalHyperPlane d r -> r Source # hyperPlaneCoefficients :: Lens' (NonVerticalHyperPlane d r) (Vector d r) Source #
type Dimension (NonVerticalHyperPlane d r) Source #
Instance details Defined in HGeometry.HyperPlane.NonVertical type Dimension (NonVerticalHyperPlane d r) = d
type NumType (NonVerticalHyperPlane d r) Source #
Instance details Defined in HGeometry.HyperPlane.NonVertical type NumType (NonVerticalHyperPlane d r) = r
type HyperPlaneFromEquationConstraint (NonVerticalHyperPlane d r) d r Source #
Instance details Defined in HGeometry.HyperPlane.NonVertical type HyperPlaneFromEquationConstraint (NonVerticalHyperPlane d r) d r = ()

asNonVerticalHyperPlane :: (HyperPlane_ hyperPlane d r, Fractional r, Eq r, 1 <= d) => hyperPlane -> Maybe (NonVerticalHyperPlane d r) Source #

Try to construct a Non-vertical hyperplane out of some generic hyperplane.

>>> asNonVerticalHyperPlane $ (HyperPlane2 10 1 2 :: HyperPlane 2 Double)
Just (NonVerticalHyperPlane [-0.5,-5.0])
>>> asNonVerticalHyperPlane $ (HyperPlane2 10 1 0 :: HyperPlane 2 Double)
Nothing
>>> asNonVerticalHyperPlane myOtherLine
Just (NonVerticalHyperPlane [-1.5,-2.0])
>>> asNonVerticalHyperPlane myPlane
Just (NonVerticalHyperPlane [2.0,3.0,10.0])

type Plane = NonVerticalHyperPlane 3 Source #

Shorthand for non-vertical hyperplanes in R^3

type Plane_ plane = NonVerticalHyperPlane_ plane 3 Source #

Shorthand for Non-vertical hyperplanes in R^3

pattern Plane_ :: Plane_ plane r => r -> r -> r -> plane Source #

Destructs a Plane in R^3 into the equation z = ax + by + c