Copyright	(c) Scott N. Walck 2012-2014
License	BSD3 (see LICENSE)
Maintainer	Scott N. Walck <walck@lvc.edu>
Stability	experimental
Safe Haskell	Trustworthy
Language	Haskell98

Physics.Learn.Surface

Contents

Surfaces
Surface Integrals

Description

This module contains functions for working with Surfaces and surface integrals over Surfaces.

Synopsis

data Surface = Surface {
- surfaceFunc :: (Double, Double) -> Position
- lowerLimit :: Double
- upperLimit :: Double
- lowerCurve :: Double -> Double
- upperCurve :: Double -> Double
}
unitSphere :: Surface
centeredSphere :: Double -> Surface
sphere :: Double -> Position -> Surface
northernHemisphere :: Surface
disk :: Double -> Surface
shiftSurface :: Displacement -> Surface -> Surface
surfaceIntegral :: (VectorSpace v, Scalar v ~ Double) => Int -> Int -> Field v -> Surface -> v
dottedSurfaceIntegral :: Int -> Int -> VectorField -> Surface -> Double

Surfaces

data Surface #

Surface is a parametrized function from two parameters to space, lower and upper limits on the first parameter, and lower and upper limits for the second parameter (expressed as functions of the first parameter).

Constructors

Surface
Fields surfaceFunc :: (Double, Double) -> Position function from two parameters (s,t) into space lowerLimit :: Double s_l upperLimit :: Double s_u lowerCurve :: Double -> Double t_l(s) upperCurve :: Double -> Double t_u(s)

unitSphere :: Surface #

A unit sphere, centered at the origin.

centeredSphere :: Double -> Surface #

A sphere with given radius centered at the origin.

sphere :: Double -> Position -> Surface #

Sphere with given radius and center.

northernHemisphere :: Surface #

The upper half of a unit sphere, centered at the origin.

disk :: Double -> Surface #

A disk with given radius, centered at the origin.

shiftSurface :: Displacement -> Surface -> Surface #

Shift a surface by a displacement.

Surface Integrals

surfaceIntegral #

Arguments

:: (VectorSpace v, Scalar v ~ Double)
=> Int	number of intervals for first parameter, s
-> Int	number of intervals for second parameter, t
-> Field v	the scalar or vector field to integrate
-> Surface	the surface over which to integrate
-> v	the resulting scalar or vector

A plane surface integral, in which area element is a scalar.

dottedSurfaceIntegral #

Arguments

:: Int	number of intervals for first parameter, s
-> Int	number of intervals for second parameter, t
-> VectorField	the vector field to integrate
-> Surface	the surface over which to integrate
-> Double	the resulting scalar

A dotted surface integral, in which area element is a vector.