Are you enjoying “Ballz series“? I really wanted to add a predictive trajectory, but it wasn’t that easy. Unlike Trick Shot which uses Box2D allowing you to play with time steps, Arcade physics does not feature any time step so you can’t fast forward the simulation.
But I found another solution, given the simplicity of the physics world we are dealing with given that:
1 – we only have squares, balls included, because a tiny ball can be approximated with a square.
2 – None of the bodies rotate. There isn’t rotation at all.
With these two points in mind, it’s quite easy to compute a predictive trajectory, following these steps:
1 – Break down each square into segments. If we have twenty squares in game, we will have 20 squares * 4 segments each + 4 segments representing world bounding box = 84 segments. A really tiny number, for a really dangerous situation. With 20 squares in game, you’re next to game over.
2 – Break down ball square into vertices, so you will have four vertices.
3 – Starting from each vertex, build a line according to player angle of fire.
4 – Check for intersection between each vertext line and each segment.
5 – The intersection – if any – with the shortest distance from its vertex is the collision point
6 – Knowing the vertex which collided, it’s easy to predict where the ball will hit a wall or a block, as well as to calculate the rebound.
End of the boring theory, now have a look:
Tap/click and drag to the bottom to aim the ball, release to launch it.
Green line represents the shortest line from a vertex to a segment, and red square is the collision point.
Have a look at the completely commented source code, this is quite big:
let game;
let gameOptions = {
// ball size, compared to game width
ballSize: 0.04,
// ball speed, in pixels per second
ballSpeed: 1000,
// blocks per line, or block columns :)
blocksPerLine: 7,
// block lines
blockLines: 8,
// max amount of blocks per line
maxBlocksPerLine: 4,
// probability 0 -> 100 of having an extra ball in each line
extraBallProbability: 60,
// predictive trajectory length, in pixels
trajectoryLength: 1200
}
window.onload = function() {
let gameConfig = {
type: Phaser.AUTO,
backgroundColor:0x444444,
scale: {
mode: Phaser.Scale.FIT,
autoCenter: Phaser.Scale.CENTER_BOTH,
parent: "thegame",
width: 640,
height: 960
},
physics: {
default: "arcade"
},
scene: playGame
}
game = new Phaser.Game(gameConfig);
window.focus();
}
// game states
const WAITING_FOR_PLAYER_INPUT = 0;
const PLAYER_IS_AIMING = 1;
const BALLS_ARE_RUNNING = 2;
const ARCADE_PHYSICS_IS_UPDATING = 3;
const PREPARING_FOR_NEXT_MOVE = 4;
class playGame extends Phaser.Scene {
constructor() {
super("PlayGame");
}
preload() {
this.load.image("ball", "ball.png");
this.load.image("panel", "panel.png");
this.load.image("block", "block.png");
}
create() {
// at the beginning of the game, we wait for player input
this.gameState = WAITING_FOR_PLAYER_INPUT;
// it's not game over... yet
this.gameOver = false;
// we start from level zero
this.level = 0;
// array used to recycle destroyed blocks
this.recycledBlocks = [];
// determine block size according to game width and the number of blocks for each line
this.blockSize = game.config.width / gameOptions.blocksPerLine;
// determine game field height according to block size and block lines
this.gameFieldHeight = this.blockSize * gameOptions.blockLines;
// empty space is the amount of the stage not covered by game field
this.emptySpace = game.config.height - this.gameFieldHeight;
// set bounds of the physics world
this.physics.world.setBounds(0, this.emptySpace / 2, game.config.width, this.gameFieldHeight);
// creation of physics groups where to place blocks, balls and extra balls
this.blockGroup = this.physics.add.group();
this.ballGroup = this.physics.add.group();
this.extraBallGroup = this.physics.add.group();
// the upper panel is called scorePanel because probably you'll want to display player score here
let scorePanel = this.add.sprite(game.config.width / 2, 0, "panel");
scorePanel.displayWidth = game.config.width;
scorePanel.displayHeight = this.emptySpace / 2;
scorePanel.setOrigin(0.5, 0);
// bottom panel
this.bottomPanel = this.add.sprite(game.config.width / 2, game.config.height, "panel");
this.bottomPanel.displayWidth = game.config.width;
this.bottomPanel.displayHeight = this.emptySpace / 2;
this.bottomPanel.setOrigin(0.5, 1);
// determine actual ball size in pixels
this.ballSize = game.config.width * gameOptions.ballSize;
// add the first ball
this.addBall(game.config.width / 2, game.config.height - this.bottomPanel.displayHeight - this.ballSize / 2, false);
// add the trajectory graphics
this.trajectoryGraphics = this.add.graphics();
// add a block line
this.addBlockLine();
// input listeners
this.input.on("pointerdown", this.startAiming, this);
this.input.on("pointerup", this.shootBall, this);
this.input.on("pointermove", this.adjustAim, this);
// lister for collision with world bounds
this.physics.world.on("worldbounds", this.checkBoundCollision, this);
}
// method to add the ball at a given position x, y. The third argument tells us if it's an extra ball
addBall(x, y, isExtraBall) {
// ball creation as a child of ballGroup or extraBallGroup
let ball = isExtraBall ? this.extraBallGroup.create(x, y, "ball") : this.ballGroup.create(x, y, "ball");
// resize the ball
ball.displayWidth = this.ballSize;
ball.displayHeight = this.ballSize;
// maximum bounce
ball.body.setBounce(1, 1);
// if it's an extra ball...
if(isExtraBall) {
// set a custom "row" property to 1
ball.row = 1;
// set a custom "collected" property to false
ball.collected = false;
}
// if it's not an extra ball...
else {
// ball collides with world bounds
ball.body.collideWorldBounds = true;
// ball fires a listener when colliding on world bounds
ball.body.onWorldBounds = true;
}
}
// method to add a block line
addBlockLine() {
// increase level number
this.level ++;
// array where to store placed blocks positions
let placedBlocks = [];
// will we place an extra ball too?
let placeExtraBall = Phaser.Math.Between(0, 100) < gameOptions.extraBallProbability;
// execute the block "gameOptions.maxBlocksPerLine" times
for(let i = 0; i < gameOptions.maxBlocksPerLine; i ++) {
// random block position
let blockPosition = Phaser.Math.Between(0, gameOptions.blocksPerLine - 1);
// is this block position empty?
if(placedBlocks.indexOf(blockPosition) == -1) {
// save this block position
placedBlocks.push(blockPosition);
// should we place an extra ball?
if(placeExtraBall) {
// no more extra balls
placeExtraBall = false;
// add the extra ball
this.addBall(blockPosition * this.blockSize + this.blockSize / 2, this.blockSize / 2 + this.emptySpace / 2, true);
}
// this time we don't place an extra ball, but a block
else {
// if we don't have any block to recycle...
if(this.recycledBlocks.length == 0) {
// add a block
this.addBlock(blockPosition * this.blockSize + this.blockSize / 2, this.blockSize / 2 + this.emptySpace / 2, false);
}
else{
// recycle a block
this.addBlock(blockPosition * this.blockSize + this.blockSize / 2, this.blockSize / 2 + this.emptySpace / 2, true)
}
}
}
}
// here we store all segments where to check for collisions
this.fieldSegments = [];
// get physics world bounds
let boundRectangle = new Phaser.Geom.Rectangle(0, this.emptySpace / 2, game.config.width, this.gameFieldHeight);
// turn world bounds into segments
this.addTofieldSegments(boundRectangle);
// iterate through all blocks
Phaser.Actions.Call(this.blockGroup.getChildren(), function(block) {
// get block bounding box
let rectangle = block.getBounds();
// turn bounding box into segments
this.addTofieldSegments(rectangle);
}, this);
}
// method to add a block at a given x,y position. The third argument tells us if the block is recycled
addBlock(x, y, isRecycled) {
// block creation as a child of blockGroup
let block = isRecycled ? this.recycledBlocks.shift() : this.blockGroup.create(x, y, "block");
// resize the block
block.displayWidth = this.blockSize;
block.displayHeight = this.blockSize;
// custom property to save block value
block.value = this.level;
// custom property to save block row
block.row = 1;
// if the block is recycled...
if(isRecycled) {
block.x = x;
block.y = y;
block.text.setText(block.value);
block.text.x = block.x;
block.text.y = block.y;
block.setVisible(true);
block.text.setVisible(true);
this.blockGroup.add(block);
}
// if the block is not recycled...
else {
// text object to show block value
let text = this.add.text(block.x, block.y, block.value, {
font: "bold 32px Arial",
align: "center",
color: "#000000"
});
text.setOrigin(0.5);
// text object is stored as a block custom property
block.text = text;
}
// block is immovable, does not react to collisions
block.body.immovable = true;
}
// given the center point, return ball vertices
getBallVertices(p) {
let halfBallSize = this.ballSize / 2;
return [
new Phaser.Geom.Point(p.x - halfBallSize, p.y - halfBallSize),
new Phaser.Geom.Point(p.x + halfBallSize, p.y - halfBallSize),
new Phaser.Geom.Point(p.x + halfBallSize, p.y + halfBallSize),
new Phaser.Geom.Point(p.x - halfBallSize, p.y + halfBallSize)
]
}
// method to get the ball position
getBallPosition() {
// select gallGroup children
let children = this.ballGroup.getChildren();
// return x and y properties of first child
return new Phaser.Geom.Point(children[0].x, children[0].y);
}
// method to start aiming
startAiming() {
// are we waiting for player input?
if(this.gameState == WAITING_FOR_PLAYER_INPUT) {
// the angle of fire is not legal at the moment
this.legalAngleOfFire = false;
// change game state because now the player is aiming
this.gameState = PLAYER_IS_AIMING;
}
}
// method to adjust the aim
adjustAim(e) {
// is the player aiming?
if(this.gameState == PLAYER_IS_AIMING) {
// determine x and y distance between current and initial input
let distX = e.x - e.downX;
let distY = e.y - e.downY;
// is y distance greater than 10, that is: is the player dragging down?
if(distY > 10) {
// this is a legal agne of fire
this.legalAngleOfFire = true;
// determine dragging direction
this.direction = Phaser.Math.Angle.Between(e.x, e.y, e.downX, e.downY);
// trajectory direction at the moment is the same as future ball direction
let trajectoryDirection = this.direction;
// set trajectory length
let trajectoryLength = gameOptions.trajectoryLength;
// clear trajectory graphics
this.trajectoryGraphics.clear();
// set trajectory graphics line style
this.trajectoryGraphics.lineStyle(1, 0x00ff00);
// get ball bounding box vertices
this.ballVertices = this.getBallVertices(this.getBallPosition());
// predictive trajectory loop
do {
// here we will store all collision information, starting from the distance, initally set as a very high number
let collisionObject = {
collisionDistance: 10000
}
// loop through all ball vertices
this.ballVertices.forEach(function(vertex, index) {
// determine trajectory line
let trajectoryLine = new Phaser.Geom.Line(vertex.x, vertex.y, vertex.x + trajectoryLength * Math.cos(trajectoryDirection), vertex.y + trajectoryLength * Math.sin(trajectoryDirection));
// iterate through all field segments
Phaser.Actions.Call(this.fieldSegments, function(line) {
// create a new temp point outside game field
let intersectionPoint = new Phaser.Geom.Point(-1, -1);
// assign temp point the valie of the intersection point between trajectory and polygon line, if any
Phaser.Geom.Intersects.LineToLine(trajectoryLine, line, intersectionPoint);
// if the intersection point is inside the field...
if(intersectionPoint.x != -1) {
// determine distance between intersection point and vertex
let distance = Phaser.Math.Distance.BetweenPoints(intersectionPoint, vertex);
// if the distance is less than current collision object distance, but greater than 1, to avoid collision with the line we just checked...
if(distance < collisionObject.collisionDistance && distance > 1) {
// update collision object distance
collisionObject.collisionDistance = distance;
// save collision point
collisionObject.collisionPoint = new Phaser.Geom.Point(intersectionPoint.x, intersectionPoint.y);
// save collision angle
collisionObject.collisionAngle = Phaser.Geom.Line.Angle(line);
// save collision line
collisionObject.collisionLine = Phaser.Geom.Line.Clone(line);
// save vertex index
collisionObject.vertexIndex = index;
}
}
}, this);
}.bind(this));
// if there was a collision point...
if(collisionObject.collisionPoint) {
// draw a line between the vertex and the collision point
this.trajectoryGraphics.lineBetween(this.ballVertices[collisionObject.vertexIndex].x, this.ballVertices[collisionObject.vertexIndex].y, collisionObject.collisionPoint.x, collisionObject.collisionPoint.y);
// set trajectoryGraphics fill style
this.trajectoryGraphics.fillStyle(0xff0000, 0.5);
// squareOrigin will contain the center of the ball, given the collision point
let squareOrigin = new Phaser.Geom.Point();
// different actions to do according to vertex index
switch(collisionObject.vertexIndex) {
// top left
case 0 :
this.trajectoryGraphics.fillRect(collisionObject.collisionPoint.x, collisionObject.collisionPoint.y, this.ballSize, this.ballSize);
squareOrigin.x = collisionObject.collisionPoint.x + this.ballSize / 2;
squareOrigin.y = collisionObject.collisionPoint.y + this.ballSize / 2;
break;
// top right
case 1 :
this.trajectoryGraphics.fillRect(collisionObject.collisionPoint.x - this.ballSize, collisionObject.collisionPoint.y, this.ballSize, this.ballSize);
squareOrigin.x = collisionObject.collisionPoint.x - this.ballSize / 2;
squareOrigin.y = collisionObject.collisionPoint.y + this.ballSize / 2;
break;
// bottom right
case 2 :
this.trajectoryGraphics.fillRect(collisionObject.collisionPoint.x - this.ballSize, collisionObject.collisionPoint.y - this.ballSize, this.ballSize, this.ballSize);
squareOrigin.x = collisionObject.collisionPoint.x - this.ballSize / 2;
squareOrigin.y = collisionObject.collisionPoint.y - this.ballSize / 2;
break;
// bottom left
case 3 :
this.trajectoryGraphics.fillRect(collisionObject.collisionPoint.x, collisionObject.collisionPoint.y - this.ballSize, this.ballSize, this.ballSize);
squareOrigin.x = collisionObject.collisionPoint.x + this.ballSize / 2;
squareOrigin.y = collisionObject.collisionPoint.y - this.ballSize / 2;
break;
}
// determine new trajectory direction according to surface angle
if(Phaser.Math.RadToDeg(collisionObject.collisionAngle) % 180 == 0) {
trajectoryDirection = 2 * Math.PI - trajectoryDirection;
}
else {
trajectoryDirection = Math.PI - trajectoryDirection;
}
trajectoryDirection = Phaser.Math.Angle.Wrap(trajectoryDirection);
// determine new ball vertices
this.ballVertices = this.getBallVertices(squareOrigin);
}
// calculate the lenght of the remaining trajectory
trajectoryLength -= collisionObject.collisionDistance;
// keep looping while trajectory length is greater than zero
} while (trajectoryLength > 0);
}
// y distance is smaller than 10, that is: player is not dragging down
else{
// not a legal angle of fire
this.legalAngleOfFire = false;
// hide trajectory graphics
this.trajectoryGraphics.clear();
}
}
}
// method to turn a rectangle into 4 segments
addTofieldSegments(rectangle) {
this.fieldSegments.push(rectangle.getLineA());
this.fieldSegments.push(rectangle.getLineB());
this.fieldSegments.push(rectangle.getLineC());
this.fieldSegments.push(rectangle.getLineD());
}
// method to shoot the ball
shootBall() {
// is the player aiming?
if(this.gameState == PLAYER_IS_AIMING) {
// hide trajectory graphics
this.trajectoryGraphics.clear();
// do we have a legal angle of fire?
if(this.legalAngleOfFire) {
// change game state
this.gameState = BALLS_ARE_RUNNING;
// no balls have landed already
this.landedBalls = 0;
// iterate through all balls
this.ballGroup.getChildren().forEach(function(ball, index) {
// add a timer event which fires a ball every 0.1 seconds
this.time.addEvent({
delay: 100 * index,
callbackScope: this,
callback: function() {
// set ball velocity
ball.body.setVelocity(gameOptions.ballSpeed * Math.cos(this.direction), gameOptions.ballSpeed * Math.sin(this.direction));
}
});
}.bind(this))
}
// we don't have a legal angle of fire
else {
// let's wait for player input again
this.gameState = WAITING_FOR_PLAYER_INPUT;
}
}
}
// method to check collision between a ball and the bounds
checkBoundCollision(ball, up, down, left, right) {
// we only want to check lower bound and only if balls are running
if(down && this.gameState == BALLS_ARE_RUNNING) {
// stop the ball
ball.setVelocity(0);
// increase the amount of landed balls
this.landedBalls ++;
// if this is the first landed ball...
if(this.landedBalls == 1) {
// save the ball in firstBallToLand variable
this.firstBallToLand = ball;
}
}
}
// method to be executed at each frame
update() {
// if Arcade physics is updating or balls are running and all balls have landed...
if((this.gameState == ARCADE_PHYSICS_IS_UPDATING) || this.gameState == BALLS_ARE_RUNNING && this.landedBalls == this.ballGroup.getChildren().length) {
// if the game state is still set to BALLS_ARE_RUNNING...
if(this.gameState == BALLS_ARE_RUNNING) {
// ... basically wait a frame to let Arcade physics update body positions
this.gameState = ARCADE_PHYSICS_IS_UPDATING;
}
// if Arcade already updated body positions...
else{
// time to prepare for next move
this.gameState = PREPARING_FOR_NEXT_MOVE;
// move the blocks
this.moveBlocks();
// move the balls
this.moveBalls();
// move the extra balls
this.moveExtraBalls();
}
}
// if balls are running...
if(this.gameState == BALLS_ARE_RUNNING) {
// handle collisions between balls and blocks
this.handleBallVsBlock();
// handle collisions between ball and extra balls
this.handleBallVsExtra();
}
}
// method to move all blocks down a row
moveBlocks() {
// we will move blocks with a tween
this.tweens.add({
// we set all blocks as tween target
targets: this.blockGroup.getChildren(),
// which properties are we going to tween?
props: {
// y property
y: {
// each block is moved down from its position by its display height
getEnd: function(target) {
return target.y + target.displayHeight;
}
},
},
// scope of callback function
callbackScope: this,
// each time the tween updates...
onUpdate: function(tween, target) {
// tween down the value text too
target.text.y = target.y;
},
// once the tween completes...
onComplete: function() {
// wait for player input again
this.gameState = WAITING_FOR_PLAYER_INPUT;
// execute an action on all blocks
Phaser.Actions.Call(this.blockGroup.getChildren(), function(block) {
// update row custom property
block.row ++;
// if a block reached the bottom of the game area...
if(block.row == gameOptions.blockLines) {
// ... it's game over
this.gameOver = true;
}
}, this);
// if it's not game over...
if(!this.gameOver) {
// add another block line
this.addBlockLine();
}
// if it's game over...
else {
// ...restart the game
this.scene.start("PlayGame");
}
},
// tween duration, 1/2 second
duration: 500,
// tween easing
ease: "Cubic.easeInOut"
});
}
// method to move all balls to first landed ball position
moveBalls() {
// we will move balls with a tween
this.tweens.add({
// we set all balls as tween target
targets: this.ballGroup.getChildren(),
// set x to match the horizontal position of the first landed ball
x: this.firstBallToLand.gameObject.x,
// tween duration, 1/2 second
duration: 500,
// tween easing
ease: "Cubic.easeInOut"
});
}
// method to move all extra balls
moveExtraBalls() {
// execute an action on all extra balls
Phaser.Actions.Call(this.extraBallGroup.getChildren(), function(ball) {
// if a ball reached the bottom of the game field...
if(ball.row == gameOptions.blockLines) {
// set it as "collected"
ball.collected = true;
}
})
// we will move balls with a tween
this.tweens.add({
// we set all extra balls as tween target
targets: this.extraBallGroup.getChildren(),
// which properties are we going to tween?
props: {
// x property
x: {
getEnd: function(target) {
// is the ball marked as collected?
if(target.collected) {
// set x to match the horizontal position of the first landed ball
return target.scene.firstBallToLand.gameObject.x;
}
// ... or leave it in its place
return target.x;
}
},
// same thing with y position
y: {
getEnd: function(target) {
if(target.collected) {
return target.scene.firstBallToLand.gameObject.y;
}
return target.y + target.scene.blockSize;
}
},
},
// scope of callback function
callbackScope: this,
// once the tween completes...
onComplete: function() {
// execute an action on all extra balls
Phaser.Actions.Call(this.extraBallGroup.getChildren(), function(ball) {
// if the ball is not collected...
if(!ball.collected) {
// ... increase its row property
ball.row ++;
}
// if the ball has been collected...
else {
// remove the ball from extra ball group
this.extraBallGroup.remove(ball);
// add the ball to ball group
this.ballGroup.add(ball);
// set extra ball properties
ball.body.collideWorldBounds = true;
ball.body.onWorldBounds = true;
ball.body.setBounce(1, 1);
}
}, this);
},
// tween duration, 1/2 second
duration: 500,
// tween easing
ease: "Cubic.easeInOut"
});
}
// method to handle collision between a ball and a block
handleBallVsBlock() {
// check collision between ballGroup and blockGroup members
this.physics.world.collide(this.ballGroup, this.blockGroup, function(ball, block) {
// decrease block value
block.value --;
// if block value reaches zero...
if(block.value == 0) {
// push block into recycledBlocks array
this.recycledBlocks.push(block);
// remove the block from blockGroup
this.blockGroup.remove(block);
// hide the block
block.visible = false;
// hide block text
block.text.visible = false;
}
// if block value does not reach zero...
else{
// update block text
block.text.setText(block.value);
}
}, null, this);
}
// method to handle collision between a ball and an extra ball
handleBallVsExtra() {
// check overlap between ballGroup and extraBallGroup members
this.physics.world.overlap(this.ballGroup, this.extraBallGroup, function(ball, extraBall) {
// set extra ball as collected
extraBall.collected = true;
// add a tween to move the ball down
this.tweens.add({
// the target is the extra ball
targets: extraBall,
// y destination position is the very bottom of game area
y: game.config.height - this.bottomPanel.displayHeight - extraBall.displayHeight / 2,
// tween duration, 0.2 seconds
duration: 200,
// tween easing
ease: "Cubic.easeOut"
});
}, null, this);
}
}
In some rare cases, it won’t be that accurate. Why? Probably because the way I determine the collision point, ready for continuous collision detection, is not the same way Arcade physics handle collisions, in a discrete environment.
With an easy and simple physics world like this one, we could even write the game without any physics engine, but this is an experiment I may consider later on, meanwhile download the source code.
