| Safe Haskell | None |
|---|---|
| Language | Haskell2010 |
Math.SphericalHarmonics
Description
Provides spherical harmonic models of scalar-valued functions.
Synopsis
- data SphericalHarmonicModel a
- sphericalHarmonicModel :: Fractional a => [[(a, a)]] -> SphericalHarmonicModel a
- scaledSphericalHarmonicModel :: Fractional a => a -> [[(a, a)]] -> SphericalHarmonicModel a
- evaluateModel :: (RealFloat a, Ord a) => SphericalHarmonicModel a -> a -> a -> a -> a
- evaluateModelCartesian :: (RealFloat a, Ord a) => SphericalHarmonicModel a -> a -> a -> a -> a
- evaluateModelGradient :: (RealFloat a, Ord a) => SphericalHarmonicModel a -> a -> a -> a -> (a, a, a)
- evaluateModelGradientCartesian :: (RealFloat a, Ord a) => SphericalHarmonicModel a -> a -> a -> a -> (a, a, a)
- evaluateModelGradientInLocalTangentPlane :: (RealFloat a, Ord a) => SphericalHarmonicModel a -> a -> a -> a -> (a, a, a)
Documentation
data SphericalHarmonicModel a Source #
Represents a spherical harmonic model of a scalar-valued function.
Instances
| Functor SphericalHarmonicModel Source # | |
Defined in Math.SphericalHarmonics Methods fmap :: (a -> b) -> SphericalHarmonicModel a -> SphericalHarmonicModel b # (<$) :: a -> SphericalHarmonicModel b -> SphericalHarmonicModel a # | |
| (Fractional a, Eq a) => VectorSpace (SphericalHarmonicModel a) Source # | |
Defined in Math.SphericalHarmonics Associated Types type Scalar (SphericalHarmonicModel a) :: Type # Methods (*^) :: Scalar (SphericalHarmonicModel a) -> SphericalHarmonicModel a -> SphericalHarmonicModel a # | |
| (Fractional a, Eq a) => AdditiveGroup (SphericalHarmonicModel a) Source # | |
Defined in Math.SphericalHarmonics Methods zeroV :: SphericalHarmonicModel a # (^+^) :: SphericalHarmonicModel a -> SphericalHarmonicModel a -> SphericalHarmonicModel a # negateV :: SphericalHarmonicModel a -> SphericalHarmonicModel a # (^-^) :: SphericalHarmonicModel a -> SphericalHarmonicModel a -> SphericalHarmonicModel a # | |
| type Scalar (SphericalHarmonicModel a) Source # | |
Defined in Math.SphericalHarmonics | |
sphericalHarmonicModel Source #
Arguments
| :: Fractional a | |
| => [[(a, a)]] | A list of g and h coefficients for the model |
| -> SphericalHarmonicModel a | The spherical harmonic model |
Creates a spherical harmonic model. Result in an error if the length of the list is not a triangular number.
scaledSphericalHarmonicModel Source #
Arguments
| :: Fractional a | |
| => a | The reference radius |
| -> [[(a, a)]] | A list of g and h coefficients for the model |
| -> SphericalHarmonicModel a | The spherical harmonic model |
Creates a spherical harmonic model, scaling coefficients for the supplied reference radius. Result in an error if the length of the list is not a triangular number.
Arguments
| :: (RealFloat a, Ord a) | |
| => SphericalHarmonicModel a | Spherical harmonic model |
| -> a | Spherical radius |
| -> a | Spherical colatitude (radian) |
| -> a | Spherical longitude (radian) |
| -> a | Model value |
Computes the scalar value of the spherical harmonic model at a specified spherical position.
evaluateModelCartesian Source #
Arguments
| :: (RealFloat a, Ord a) | |
| => SphericalHarmonicModel a | Spherical harmonic model |
| -> a | X position |
| -> a | Y position |
| -> a | Z position |
| -> a | Model value |
Computes the scalar value of the spherical harmonic model at a specified Cartesian position.
evaluateModelGradient Source #
Arguments
| :: (RealFloat a, Ord a) | |
| => SphericalHarmonicModel a | Spherical harmonic model |
| -> a | Spherical radius |
| -> a | Spherical colatitude (radian) |
| -> a | Spherical longitude (radian) |
| -> (a, a, a) | Radial, colatitudinal, and longitudinal components of gradient |
Computes the gradient of the scalar value of the spherical harmonic model, in spherical coordinates, at a specified location.
evaluateModelGradientCartesian Source #
Arguments
| :: (RealFloat a, Ord a) | |
| => SphericalHarmonicModel a | Spherical harmonic model |
| -> a | X position |
| -> a | Y position |
| -> a | Z position |
| -> (a, a, a) |
Computes the gradient of the scalar value of the spherical harmonic model at a specified location, in Cartesian coordinates. The result is expressed in right-handed coordinates centered at the origin of the sphere, with the positive Z-axis piercing the north pole and the positive x-axis piercing the reference meridian.
evaluateModelGradientInLocalTangentPlane Source #
Arguments
| :: (RealFloat a, Ord a) | |
| => SphericalHarmonicModel a | Spherical harmonic model |
| -> a | Spherical radius |
| -> a | Spherical colatitude (radian) |
| -> a | Spherical longitude (radian) |
| -> (a, a, a) | East, North, and up components of gradient |
Computes the gradient of the scalar value of the spherical harmonic model at a specified location, in Cartesian coordinates. The result is expressed in a reference frame locally tangent to the sphere at the specified location.