DSMC.Util.Vector

Simple 3-vectors and matrices built atop tuples.

Documentation

type Vec3 = (Double, Double, Double)

Vector in R^3.

type Matrix = (Vec3, Vec3, Vec3)

Matrix given by its rows.

type Point = Vec3

Point in R^3.

origin :: Point

Origin point (0, 0, 0).

Vector operations

(<+>) :: Vec3 -> Vec3 -> Vec3

Add two vectors.

(<->) :: Vec3 -> Vec3 -> Vec3

Subtract two vectors.

(><) :: Vec3 -> Vec3 -> Vec3

Vec3 cross product.

(.^) :: Vec3 -> Double -> Vec3

Scale vector.

(.*) :: Vec3 -> Vec3 -> Double

Vec3 dot product.

norm :: Vec3 -> Double

Euclidean norm of vector.

normalize :: Vec3 -> Vec3

Produce unit vector with same direction as the original one.

invert :: Vec3 -> Vec3

Scale vector by -1.

distance :: Point -> Point -> Double

Euclidean distance between two points.

moveBy

Arguments

:: Point

Current position.

-> Vec3

Velocity.

-> Double

Time step.

-> Point

Move point by velocity vector for given time and return new position.

Matrix operations

mxv :: Matrix -> Vec3 -> Vec3

Multiply matrix (given by row vectors) and vector

vxv :: Vec3 -> Vec3 -> Matrix

Transpose vector and multiply it by another vector, producing a matrix.

dotM :: Vec3 -> Vec3 -> Matrix -> Double

Generic vector dot product.

Multiply transpose of first vector by given matrix, then multiply the result by second vector.

diag :: Double -> Matrix

Produce matrix with diagonal elements equal to given value.

addM :: Matrix -> Matrix -> Matrix

Add two matrices.

We could add Applicative instance for Matrix and lift (+) to it.

Cartesian system

buildCartesian :: Double -> Double -> (Vec3, Vec3, Vec3)

Build cartesian axes from yaw and pitch with 0 roll. Angles are in radians.