Geom.Vector

Definitions

solveQuadratic : Double -> Double -> Double -> Maybe (Double, Double)

  Tries to find solutions to the quadratic equation
  `ax^2 + bx + c = 0`.

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record LinearTransformation : Type

  A linear transformation in a two-dimensional vector space
  is a sequence of scalings and rotations.
  
  By not using a matrix here we make sure that a transformation
  is invertible, without the risk of a division by zero.
  This might be a performance issue, but only if we create large
  trees of wild mixtures of linear transformations. However,
  in a UI we often work with sequences of the same type of
  transformations such as a sequence of scalings or a sequence of
  rotations. These are merged automatically in the `Semigroup`
  implementation.

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Constructor: 

LT : Scale -> Angle -> LinearTransformation

Projections:

.rotate : LinearTransformation -> Angle

.scale : LinearTransformation -> Scale

Hints:

Eq (Vector t)

Interpolation (Vector t)

Monoid LinearTransformation

Ord (Vector t)

Semigroup LinearTransformation

Show (Vector t)

.scale : LinearTransformation -> Scale

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scale : LinearTransformation -> Scale

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.rotate : LinearTransformation -> Angle

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rotate : LinearTransformation -> Angle

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Id : LinearTransformation

  The identity transformation

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rotation : Angle -> LinearTransformation

  A clockwise rotation by the given angle.

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scaling : Scale -> LinearTransformation

  A scaling by the given factor.

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inverse : LinearTransformation -> LinearTransformation

  Computes the inverse of a linear transformation, so
  `x <+> inverse x` corresponse to the identity (modulo rounding
  errors).

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record Vector : LinearTransformation -> Type

  A two-dimensional vector.

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Constructor: 

V : Double -> Double -> Vector t

Projections:

.x : Vector t -> Double

.y : Vector t -> Double

Hints:

Eq (Vector t)

Interpolation (Vector t)

Ord (Vector t)

Show (Vector t)

.x : Vector t -> Double

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x : Vector t -> Double

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.y : Vector t -> Double

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y : Vector t -> Double

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vzero : Vector t

  The zero vector.

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vone : Vector t

  Unity vector along the x axis

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vid : Double -> Double -> Vector Id

  Utility to help with type inference when using vectors in `Id`

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length : Vector t -> Double

  Computes the length of a vector.

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(+) : Vector t -> Vector t -> Vector t

  Vector addition.

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Fixity Declaration: infixl operator, level 8

negate : Neg ty => ty -> ty

  The underlying of unary minus. `-5` desugars to `negate (fromInteger 5)`.

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Fixity Declaration: prefix operator, level 10

(-) : Vector t -> Vector t -> Vector t

  Vector subtraction.

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Fixity Declarations:
infixl operator, level 8
prefix operator, level 10

negate : Vector t -> Vector t

  Inverts the given vector by negating its coordinates.

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Fixity Declaration: prefix operator, level 10

scale : Double -> Vector t -> Vector t

  Multiply a vector with a scalar.

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scaleTo : Double -> Vector t -> Vector t

  Scales the vector to the given length.

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normalize : Vector t -> Vector t

  Normalize a vector to length 1.

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transform : LinearTransformation -> Vector t -> Vector t

  Apply a linear transformation to a vector

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polar : Scale -> Angle -> Vector t

  Define a vector by giving its length and its angle

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rotate : Angle -> Vector t -> Vector t

  Rotate a vector by the specified number of degrees

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angle : Vector t -> Maybe Angle

  Tries to calculate the angle of the given vector.
  Fails in case this is the zero vector.

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angleOrZero : Vector t -> Angle

  Like `angle` but returns `zero` in case the vector is the empty vector.

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perpendicular : Vector t -> Vector t

  From a given vector `v` computes a vector perpendicular
  to `v` so that `dot v (perpendicular v) === 0.0` (up to rounding
  errors).

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dot : Vector t -> Vector t -> Double

  Computes the dot product of two vectors.

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