Physics.Learn.Surface

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

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.