Sampling an Arbitrary Curve

sampling_arbitrary_curve.kt

import kotlin.math.pow

// https://www.desmos.com/calculator/qjxcsxsl6t
// https://www.wolframalpha.com/input/?i=integral+-2(x-1)%5E2+%2B+2
fun main(args: Array<String>) {


    println(f(1.0))
    println(integratedF(0.0,2.0))

    println(inverseIntegratedF(4.0/3.0))
}

fun f(x: Double) = -2.0 * (x-1.0).pow(2) + 2.0

fun integratedF(x: Double) = -2.0 * ((1.0/3.0)*x.pow(3) - x.pow(2))

fun integratedF(lower: Double, upper: Double) = integratedF(upper) - integratedF(lower)


fun inverseIntegratedF(a: Double): Double {

    fun expr1(a: Double) = (3.0.sqrt() * (3.0*a.pow(2.0) - 8.0*a).sqrt() - 3.0*a + 4.0).cbrt()  // square rooting a negative here :/

    fun expr2(a: Double) = 2.0.pow(2.0/3.0)

    fun expr(a: Double) = (expr1(a) / expr2(a)) + (expr2(a) / expr1(a)) + 1

    return expr(a)
}

fun Double.sqrt() = pow(1.0/2.0)
fun Double.cbrt() = Math.cbrt(this)