Physics.Learn.Volume

This module contains functions for working with Volumes and volume integrals over Volumes.

Volumes

data Volume

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

Constructors

Volume

Fields

• volumeFunc :: (Double, Double, Double) -> Position

  function from 3 parameters to space

• loLimit :: Double

  s_a

• upLimit :: Double

  s_b

• loCurve :: Double -> Double

  t_a(s)

• upCurve :: Double -> Double

  t_b(s)

• loSurf :: Double -> Double -> Double

  u_a(s,t)

• upSurf :: Double -> Double -> Double

  u_b(s,t)

unitBall :: Volume

A unit ball, centered at the origin.

unitBallCartesian :: Volume

A unit ball, centered at the origin. Specified in Cartesian coordinates.

centeredBall :: Double -> Volume

A ball with given radius, centered at the origin.

ball

Arguments

:: Double

radius

-> Position

center

-> Volume

ball with given radius and center

Ball with given radius and center.

northernHalfBall :: Volume

Upper half ball, unit radius, centered at origin.

centeredCylinder :: Double -> Double -> Volume

Cylinder with given radius and height. Circular base of the cylinder is centered at the origin. Circular top of the cylinder lies in plane z = h.

shiftVolume :: Displacement -> Volume -> Volume

Shift a volume by a displacement.

Volume Integral

volumeIntegral

Arguments

:: (VectorSpace v, Scalar v ~ Double)

=> Int

number of intervals for first parameter (s)

-> Int

number of intervals for second parameter (t)

-> Int

number of intervals for third parameter (u)

-> Field v

scalar or vector field

-> Volume

the volume

-> v

scalar or vector result

A volume integral