Copyright	(c) Scott N. Walck 2012-2018
License	BSD3 (see LICENSE)
Maintainer	Scott N. Walck <walck@lvc.edu>
Stability	experimental
Safe Haskell	Safe
Language	Haskell2010

Physics.Learn.Curve

Contents

Curves
Line Integrals

Description

This module contains functions for working with Curves and line integrals along Curves.

Synopsis

data Curve = Curve {
- curveFunc :: Double -> Position
- startingCurveParam :: Double
- endingCurveParam :: Double
}
normalizeCurve :: Curve -> Curve
concatCurves :: Curve -> Curve -> Curve
concatenateCurves :: [Curve] -> Curve
reverseCurve :: Curve -> Curve
evalCurve :: Curve -> Double -> Position
shiftCurve :: Displacement -> Curve -> Curve
straightLine :: Position -> Position -> Curve
simpleLineIntegral :: (InnerSpace v, Scalar v ~ Double) => Int -> Field v -> Curve -> v
dottedLineIntegral :: Int -> VectorField -> Curve -> Double
crossedLineIntegral :: Int -> VectorField -> Curve -> Vec
compositeTrapezoidDottedLineIntegral :: Int -> VectorField -> Curve -> Double
compositeTrapezoidCrossedLineIntegral :: Int -> VectorField -> Curve -> Vec
compositeSimpsonDottedLineIntegral :: Int -> VectorField -> Curve -> Double
compositeSimpsonCrossedLineIntegral :: Int -> VectorField -> Curve -> Vec

Curves

data Curve Source #

Curve is a parametrized function into three-space, an initial limit, and a final limit.

Constructors

Curve
Fields curveFunc :: Double -> Position function from one parameter into space startingCurveParam :: Double starting value of the parameter endingCurveParam :: Double ending value of the parameter

normalizeCurve :: Curve -> Curve Source #

Reparametrize a curve from 0 to 1.

concatCurves Source #

Arguments

:: Curve	go first along this curve
-> Curve	then along this curve
-> Curve	to produce this new curve

Concatenate two curves.

concatenateCurves :: [Curve] -> Curve Source #

Concatenate a list of curves. Parametrizes curves equally.

reverseCurve :: Curve -> Curve Source #

Reverse a curve.

evalCurve Source #

Arguments

:: Curve	the curve
-> Double	the parameter
-> Position	position of the point on the curve at that parameter

Evaluate the position of a curve at a parameter.

shiftCurve Source #

Arguments

:: Displacement	amount to shift
-> Curve	original curve
-> Curve	shifted curve

Shift a curve by a displacement.

straightLine Source #

Arguments

:: Position	starting position
-> Position	ending position
-> Curve	straight-line curve

The straight-line curve from one position to another.

Line Integrals

simpleLineIntegral Source #

Arguments

:: (InnerSpace v, Scalar v ~ Double)
=> Int	number of intervals
-> Field v	scalar or vector field
-> Curve	curve to integrate over
-> v	scalar or vector result

Calculates integral f dl over curve, where dl is a scalar line element.

dottedLineIntegral Source #

Arguments

:: Int	number of half-intervals (one less than the number of function evaluations)
-> VectorField	vector field
-> Curve	curve to integrate over
-> Double	scalar result

A dotted line integral. Convenience function for compositeSimpsonDottedLineIntegral.

crossedLineIntegral Source #

Arguments

:: Int	number of half-intervals (one less than the number of function evaluations)
-> VectorField	vector field
-> Curve	curve to integrate over
-> Vec	vector result

Calculates integral vf x dl over curve. Convenience function for compositeSimpsonCrossedLineIntegral.

compositeTrapezoidDottedLineIntegral Source #

Arguments

:: Int	number of intervals
-> VectorField	vector field
-> Curve	curve to integrate over
-> Double	scalar result

A dotted line integral, performed in an unsophisticated way.

compositeTrapezoidCrossedLineIntegral Source #

Arguments

:: Int	number of intervals
-> VectorField	vector field
-> Curve	curve to integrate over
-> Vec	vector result

Calculates integral vf x dl over curve in an unsophisticated way.

compositeSimpsonDottedLineIntegral Source #

Arguments

:: Int	number of half-intervals (one less than the number of function evaluations)
-> VectorField	vector field
-> Curve	curve to integrate over
-> Double	scalar result

Quadratic approximation to vector field. Quadratic approximation to curve. Composite strategy. Dotted line integral.

compositeSimpsonCrossedLineIntegral Source #

Arguments

:: Int	number of half-intervals (one less than the number of function evaluations)
-> VectorField	vector field
-> Curve	curve to integrate over
-> Vec	vector result

Quadratic approximation to vector field. Quadratic approximation to curve. Composite strategy. Crossed line integral.