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Implement verlet integration
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Malte Schütze committed Apr 2, 2019
1 parent 7c4324a commit 1e13782
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Showing 2 changed files with 136 additions and 31 deletions.
36 changes: 29 additions & 7 deletions src/AttractorSim.kt
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Original file line number Diff line number Diff line change
Expand Up @@ -8,6 +8,7 @@ import kotlin.browser.window
import kotlin.math.PI
import kotlin.math.cos
import kotlin.math.sin
import kotlin.math.sqrt
import kotlin.random.Random

class AttractorSim {
Expand Down Expand Up @@ -41,12 +42,23 @@ class AttractorSim {

private val canvas: HTMLCanvasElement = initalizeCanvas()
private val context: CanvasRenderingContext2D = canvas.getContext("2d") as CanvasRenderingContext2D

private val particles: MutableList<Particle> = ArrayList()
private var time = 0.0
private var lastUpdate: Double? = null

private var pause = true

private var accumulated = 0.0

var size = 32.0
private set

var weight: Double = 0.0
get() = (size*size*size) * 1e-2
private set



fun play() {
if (pause) {
pause = false
Expand All @@ -65,9 +77,9 @@ class AttractorSim {
context.strokeStyle = "rgb(0, 0, 0)"
context.fillStyle = context.strokeStyle
context.shadowColor = "rgb(255, 255, 255)"
context.shadowBlur = 16.0
context.shadowBlur = size/2
context.beginPath()
context.ellipse(RADIUS, RADIUS, 32.0, 32.0, 0.0, 0.0, 2 * PI)
context.ellipse(RADIUS, RADIUS, size, size, 0.0, 0.0, 2 * PI)
context.fill()
context.stroke()

Expand Down Expand Up @@ -107,8 +119,14 @@ class AttractorSim {
}

fun update(deltaT: Double) {
particles.forEach { p -> p.update(deltaT) }
spawn()
particles.forEach { p -> p.update(deltaT, this) }
particles.removeAll { p -> p.dead }

accumulated += deltaT
if (accumulated >= 0.1) {
accumulated = 0.0
if (!pause) spawn()
}
}

fun clear() {
Expand Down Expand Up @@ -139,10 +157,14 @@ class AttractorSim {
val spawnY = cos(spawnAngle) * VIEWPORT_RADIUS

// Take a movement vector straight towards the center and angle it somewhat to the side (rotation around starting position)
val initialMoveAngle = Random.nextDouble(0.05 * PI, 0.25 * PI)
val initialMoveAngle = Random.nextDouble(0.25 * PI, 0.45 * PI)
val moveX = (-spawnX) * cos(initialMoveAngle) - (-spawnY) * sin(initialMoveAngle)
val moveY = (-spawnX) * sin(initialMoveAngle) + (-spawnY) * cos(initialMoveAngle)

particles.add(Particle(spawnX, spawnY, spawnX - moveX * 0.1, spawnY - moveY * 0.1))
val pxPerSecond = 300
val speedX = pxPerSecond * moveX / sqrt(moveX * moveX + moveY * moveY)
val speedY = pxPerSecond * moveY / sqrt(moveX * moveX + moveY * moveY)

particles.add(Particle(spawnX, spawnY, speedX, speedY))
}
}
131 changes: 107 additions & 24 deletions src/Particle.kt
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Original file line number Diff line number Diff line change
@@ -1,41 +1,116 @@

import AttractorSim.Companion.RADIUS
import org.w3c.dom.CanvasRenderingContext2D
import kotlin.math.abs
import kotlin.math.sqrt
import kotlin.math.*

const val GRAVITATION = 6.674e-11

class Particle(var x: Double, var y: Double, var lastX: Double, var lastY: Double) {
class PathSegment(val x: Double, val y: Double, val age: Double)

class Particle(x: Double, y: Double, speedX: Double, speedY: Double) {
companion object {
const val PATH_MAXAGE = 2.0
const val MAX_AGE = 50
const val PATH_MAX_AGE = 5.0
const val PHYSICS_STEP = 0.01
}

fun dirX() = (x - lastX) / sqrt((x - lastX) * (x - lastX) + (y - lastY) * (y - lastY))
fun dirY() = (y - lastY) / sqrt((x - lastX) * (x - lastX) + (y - lastY) * (y - lastY))
private var age = 0.0
private var lastAge = -1.0

private var accumulatedTime = 0.0


private var dist = sqrt(x * x + y * y)
private var angle = atan2(y, x)

private var lastDist = 0.0
private var lastAngle = 0.0

private val distROC
get() = (dist - lastDist) * (age - lastAge)
private val angleROC
get() = (angle - lastAngle) * (age - lastAge)

var age = 0.0
var speed = 50 // px/second
private val x
get() = dist * cos(angle)
private val y
get() = dist * sin(angle)

class PathSegment(val x: Double, val y: Double, val age: Double)
private var previousPhysicsStepX = lastDist * cos(lastAngle)
private var previousPhysicsStepY = lastDist * sin(lastAngle)

val paths: MutableList<PathSegment> = ArrayList()

var dead = false
private set

private var decaying = false


private val paths: MutableList<PathSegment> = ArrayList()

init {
paths.add(PathSegment(x, y, 0.0))
val lastX = x - speedX * PHYSICS_STEP
val lastY = y - speedY * PHYSICS_STEP
lastDist = sqrt(lastX * lastX + lastY * lastY)
lastAngle = atan2(lastY, lastX)
}

fun update(fullDeltaT: Double, state: AttractorSim) {
accumulatedTime += fullDeltaT

while (accumulatedTime >= 0) {
// Simulate one step into the future. We will interpolate during rendering
// println("Physics step - ${accumulatedTime / PHYSICS_STEP + 1} steps remaining")
previousPhysicsStepX = x
previousPhysicsStepY = y

fixedUpdate(PHYSICS_STEP, state)
accumulatedTime -= PHYSICS_STEP
}
}

fun fixedUpdate(deltaT: Double, state: AttractorSim) {
paths.removeAll { segment -> segment.age < age - PATH_MAX_AGE }

if (age != lastAge && !decaying) {
paths.add(PathSegment(x, y, age))

// println("r(n-1)=$lastDist, t(n-1)=$lastAngle")
// println("r( n )=$dist, t( n )=$angle")
// println("v_r(n)=$distROC, v_t(n)=$angleROC")

val distAccel = dist * angleROC * angleROC - (GRAVITATION * state.weight) / (dist * dist)
val angleAccel = -2.0 * distROC * angleROC / dist
// println("a_r(n)=$distAccel, a_t(n)=$angleAccel")

fun update(deltaT: Double) {
paths.add(PathSegment(x, y, age))
while (paths[0].age < age - PATH_MAXAGE) paths.removeAt(0)
val nextDist = 2 * dist - lastDist + distAccel * deltaT * deltaT
val nextAngle = 2 * angle - lastAngle + angleAccel * deltaT * deltaT
// println("r(n+1)=$nextDist, t(n+1)=$nextAngle")

lastDist = dist
lastAngle = angle

dist = nextDist
angle = nextAngle
}

lastAge = age
age += deltaT

val newX = x + dirX() * speed * deltaT
val newY = y + dirY() * speed * deltaT
lastX = x
lastY = y
x = newX
y = newY
if (sqrt(x * x + y * y) > 2 * RADIUS) {
decaying = true
}

if (sqrt(x * x + y * y) < state.size) {
decaying = true
}

if (age > MAX_AGE) {
decaying = true
}

if (decaying && paths.isEmpty()) {
dead = true
}
}

fun render(ctx: CanvasRenderingContext2D) {
Expand All @@ -44,6 +119,10 @@ class Particle(var x: Double, var y: Double, var lastX: Double, var lastY: Doubl
ctx.lineWidth = 1.0
//ctx.beginPath()

if (paths.isEmpty()) {
return
}

val first = paths[0]
var fromX = first.x
var fromY = first.y
Expand All @@ -58,7 +137,11 @@ class Particle(var x: Double, var y: Double, var lastX: Double, var lastY: Doubl
i++
}

drawSecantLine(ctx, fromX, fromY, x, y)
// Interpolate final position between last physics step and the step simulated into the future
val alpha = (accumulatedTime + PHYSICS_STEP) / PHYSICS_STEP
val actualX = x * alpha + previousPhysicsStepX * (1 - alpha)
val actualY = y * alpha + previousPhysicsStepY * (1 - alpha)
drawSecantLine(ctx, fromX, fromY, actualX, actualY)
ctx.beginPath()
// ctx.ellipse(x + AttractorSim.RADIUS, y + AttractorSim.RADIUS, 2.0, 2.0, 0.0, 0.0, 2 * PI)
ctx.fill()
Expand Down Expand Up @@ -93,8 +176,8 @@ fun drawSecantLine(ctx: CanvasRenderingContext2D, fromX: Double, fromY: Double,
var y2 = (-determinant * dx - abs(dy) * discriminantRoot) / distSq


var posOnLineP1 = (x1 - fromX)/dx
var posOnLineP2 = (x2 - fromX)/dx
var posOnLineP1 = (x1 - fromX) / dx
var posOnLineP2 = (x2 - fromX) / dx

if (posOnLineP1 > posOnLineP2) {
// Make sure that p1 is closer to from than p2
Expand Down

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