LPFPCore.Integrals

Code needed in chapter 24 of the book Learn Physics with Functional Programming

Documentation

type CurveApprox = Curve -> [(Position, Vec)]

type SurfaceApprox = Surface -> [(Position, Vec)]

type VolumeApprox = Volume -> [(Position, R)]

scalarLineIntegral :: CurveApprox -> ScalarField -> Curve -> R

scalarSurfaceIntegral :: SurfaceApprox -> ScalarField -> Surface -> R

scalarVolumeIntegral :: VolumeApprox -> ScalarField -> Volume -> R

vectorLineIntegral :: CurveApprox -> VectorField -> Curve -> Vec

vectorSurfaceIntegral :: SurfaceApprox -> VectorField -> Surface -> Vec

vectorVolumeIntegral :: VolumeApprox -> VectorField -> Volume -> Vec

curveSample :: Int -> Curve -> [(Position, Vec)]

type Segment = (Position, Position)

segments :: Int -> Curve -> [Segment]

linSpaced :: Int -> R -> R -> [R]

surfaceSample :: Int -> Surface -> [(Position, Vec)]

data Triangle

Constructors

Tri Position Position Position

triCenter :: Triangle -> Position

triArea :: Triangle -> Vec

triangles :: Int -> Surface -> [Triangle]

volumeSample :: Int -> Volume -> [(Position, R)]

data Tet

Constructors

Tet Position Position Position Position

tetCenter :: Tet -> Position

tetVolume :: Tet -> R

data ParamCube

Constructors

PC

Fields

• v000 :: (R, R, R)
• v001 :: (R, R, R)
• v010 :: (R, R, R)
• v011 :: (R, R, R)
• v100 :: (R, R, R)
• v101 :: (R, R, R)
• v110 :: (R, R, R)
• v111 :: (R, R, R)

tetrahedrons :: Int -> Volume -> [Tet]