Another long title for another update to the HTML5 circular endless runner prototype built with Phaser. I wanted to build a physics game without using physics and I am doing it quite well. I already developed gravity, jump, double jump and collision detection using only mathematics and trigonometry, and today I have a couple of new features: * You are not longer limited to jump and double jump, you can adjust the game to let the player make any number of consecutive jumps just by changing a variable. * There is a fog effect – which is actually a circular gradient fading to black to totally transparent black color – which makes the spikes appear and disappear giving the idea of an endless environment. But they are just 9 sprites placed here and there according to player position. Have a look at the prototype: Click or tap to jump and double jump, or even to make a triple jump and see how spikes smoothly appear and disappear. What about the source code? I commented it line by line. There is still some – or better a lot of – room for improvement but having a source code with all comments will allow you to better understand how I built this prototype and above all to port the game in other languages, since I did not use any physics engine, just mathematics.

// the game itself
var game;

// global object with all customizable options
var gameOptions = {

    // radius of the big circle - the "planet" - in pixels
    bigCircleRadius: 250,

    // radius of the small circle, in pixels
    playerRadius: 25,

    // player speed, in degrees per frame
    playerSpeed: 1,

    // world gravity
    worldGravity: 0.8,

    // jump force. First element is the first jump, second element - if any -  the double jump, third element - if any - the triple jump and so on
    jumpForce: [12, 9, 6],

    // spike size - width, height - in pixels
    spikeSize: [25, 50],

    // distance needed to consider the player close to a spike, in degrees
    closeToSpike: 10,

    // distance needed to consider the player far from a spike, in degrees
    farFromSpike: 35
}

window.onload = function() {

    // game configuration object
    var gameConfig = {
        thpe: Phaser.CANVAS,
        width: 800,
        height: 800,
        scene: [playGame]
    }
    game = new Phaser.Game(gameConfig);
    window.focus()
    resize();
    window.addEventListener("resize", resize, false);
}
class playGame extends Phaser.Scene{
    constructor(){
        super("PlayGame");
    }
    preload(){
        this.load.image("bigcircle", "bigcircle.png");
        this.load.image("player", "player.png");
        this.load.image("spike", "spike.png");
        this.load.image("mask", "mask.png");
    }
    create(){

        // adding a group which will contain all spikes
        this.spikeGroup = this.add.group();

        // adding the big circle, the "planet", placed in the middle of the canvas
        this.bigCircle = this.add.sprite(game.config.width / 2, game.config.height / 2, "bigcircle");
        this.bigCircle.displayWidth = gameOptions.bigCircleRadius * 2;
        this.bigCircle.displayHeight = gameOptions.bigCircleRadius * 2;

        // placing the player, just above the top of the "planet"
        this.player = this.add.sprite(game.config.width / 2, game.config.height / 2 - gameOptions.bigCircleRadius - gameOptions.playerRadius, "player");
        this.player.displayWidth = gameOptions.playerRadius * 2;
        this.player.displayHeight = gameOptions.playerRadius * 2;

        // a few custom properties: currentAngle is the angle of the player
        this.player.currentAngle = -90;

        // jumpOffset is the amount of pixels to be added to player position when it jumps
        this.player.jumpOffset = 0;

        // how many jumps is the player doing?
        this.player.jumps = 0;

        // current jump force
        this.player.jumpForce = 0;

        // when the player clicks/taps on the canvas...
        this.input.on("pointerdown", function(e){

            // can the player jump?
            if(this.player.jumps < gameOptions.jumpForce.length){

                // player is jumping once more
                this.player.jumps ++;

                // adding the proper jump force to player's jumpForce property
                this.player.jumpForce = gameOptions.jumpForce[this.player.jumps - 1];
            }
        }, this);

        // we are going to place nine spikes
        for(var i = 0; i < 9; i ++){

            // adding the spike on the canvas
            var spike = this.add.sprite(0, 0, "spike");

            // set spike origin point to left and horizontal middle
            spike.setOrigin(0, 0.5);

            // adding the spike to spike group
            this.spikeGroup.add(spike);

            // place the spike. Arguments are the spike itself and the quadrant of the big circle
            this.placeSpike(spike, Math.floor(i / 3));
        }

        // adding the mask image which will act like a "fog" to hide and show spikes
        this.maskImage = this.add.sprite(game.config.width / 2, game.config.height / 2, "mask");
    }

    // method to randomly place a spike into a quadrant
    placeSpike(spike, quadrant){

        // choosing a random angle
        var randomAngle = Phaser.Math.Angle.WrapDegrees(Phaser.Math.Between(quadrant * 90, (quadrant + 1) * 90));

        // this is the same random angle converted in radians
        var randomAngleRadians = Phaser.Math.DegToRad(randomAngle);

        // determining spike position according to its angle
        var spikeX = this.bigCircle.x + (gameOptions.bigCircleRadius - Phaser.Math.Between(4, 25)) * Math.cos(randomAngleRadians);
        var spikeY = this.bigCircle.y + (gameOptions.bigCircleRadius - Phaser.Math.Between(4, 25)) * Math.sin(randomAngleRadians);
        spike.x = spikeX;
        spike.y = spikeY;

        // saving spike's quadrant in a custom property
        spike.quadrant = quadrant;

        // setting spike angke
        spike.angle = randomAngle;

        // saving the three spike vertices in custom properties
        spike.top = new Phaser.Math.Vector2(spikeX + gameOptions.spikeSize[1] * Math.cos(randomAngleRadians), spikeY + gameOptions.spikeSize[1] * Math.sin(randomAngleRadians));
        spike.base1 = new Phaser.Math.Vector2(spikeX + gameOptions.spikeSize[0] / 2 * Math.cos(randomAngleRadians + Math.PI / 2), spikeY + gameOptions.spikeSize[0] / 2 * Math.sin(randomAngleRadians + Math.PI / 2));
        spike.base2 = new Phaser.Math.Vector2(spikeX + gameOptions.spikeSize[0] / 2 * Math.cos(randomAngleRadians - Math.PI / 2), spikeY + gameOptions.spikeSize[0] / 2 * Math.sin(randomAngleRadians - Math.PI / 2));

        // is the player approaching to the spike?
        spike.approaching = false;
    }

    // method to be executed at each frame
    update(){

        // is the player jumping?
        if(this.player.jumps &gt; 0){

            // adjusting player jump offset
            this.player.jumpOffset += this.player.jumpForce;

            // decreasing jump force due to gravity
            this.player.jumpForce -= gameOptions.worldGravity;

            // if jumpOffset is less than zero, it means the player touched the ground
            if(this.player.jumpOffset < 0){

                // setting jump offset to zero
                this.player.jumpOffset = 0;

                // player is not jumping anymore
                this.player.jumps = 0;

                // there is no jump force
                this.player.jumpForce = 0;
            }
        }

        // setting new player current angle according to current position and speed
        this.player.currentAngle = Phaser.Math.Angle.WrapDegrees(this.player.currentAngle + gameOptions.playerSpeed);

        // moving the mask image accordingly
        this.maskImage.angle = this.player.currentAngle + 90;

        // getting the same angle in radians
        var radians = Phaser.Math.DegToRad(this.player.currentAngle);

        // determining the distance from the center according to planet radius, player radius and jump offset
        var distanceFromCenter = (gameOptions.bigCircleRadius * 2 + gameOptions.playerRadius * 2) / 2 + this.player.jumpOffset;

        // position the player using trigonometry
        this.player.x = this.bigCircle.x + distanceFromCenter * Math.cos(radians);
        this.player.y = this.bigCircle.y + distanceFromCenter * Math.sin(radians);

        // determining the number of revolutions the player has to do move according to planet and player size
        var revolutions = (gameOptions.bigCircleRadius * 2) / (gameOptions.playerRadius * 2) + 1;

        // set player rotation according to current angle and the number of revolutions needed
        this.player.angle = this.player.currentAngle * revolutions;

        // looping through each spike, as child of spikeGroup
        this.spikeGroup.children.iterate(function(spike){

            // getting angle difference between the spike and the player
            var angleDiff = this.getAngleDifference(spike.angle, this.player.currentAngle);

            // if the player is not approaching the spike and it's close enough...
            if(!spike.approaching &amp;&amp; angleDiff < gameOptions.closeToSpike){

                // player is approaching the spike
                spike.approaching = true;
            }

            // if the player is approaching the spike...
            if(spike.approaching){

                // checking for collision between the player and the two triangle sizes
                if(this.distToSegmentSquared(new Phaser.Math.Vector2(this.player.x, this.player.y), gameOptions.playerRadius, spike.top, spike.base1) || this.distToSegmentSquared(new Phaser.Math.Vector2(this.player.x, this.player.y), gameOptions.playerRadius, spike.top, spike.base2)){

                    // restart the game if the collision occurs
                    this.scene.start("PlayGame");
                }

                // if we are getting too far from the spike...
                if(angleDiff &gt; gameOptions.farFromSpike){

                    // recycle the spike and move it in a random position three quadrants further
                    this.placeSpike(spike, (spike.quadrant + 3) % 4);
                }
            }
        }, this)
    }

    // function to get the minimum difference between two angles a1 and a2
    getAngleDifference(a1, a2){
        var angleDifference = a1 - a2
        angleDifference += (angleDifference &gt; 180) ? -360 : (angleDifference < -180) ? 360 : 0
        return Math.abs(angleDifference);
    }

    // function to get the distance between two points p1 and p2
    getDistance(p1, p2){
        return (p1.x - p2.x) * (p1.x - p2.x) + (p1.y - p2.y) * (p1.y - p2.y);
    }

    // function to determine if a circle is touching a line segment given the circle center, the radius and the points defining the segment
    distToSegmentSquared(circleCenter, circleRadius, segmentStart, segmentEnd){
        var l2 = this.getDistance(segmentStart, segmentEnd);
        var t = ((circleCenter.x - segmentStart.x) * (segmentEnd.x - segmentStart.x) + (circleCenter.y - segmentStart.y) * (segmentEnd.y - segmentStart.y)) / l2;
        t = Math.max(0, Math.min(1, t));
        var tX = segmentStart.x + t * (segmentEnd.x - segmentStart.x);
        var tY = segmentStart.y + t * (segmentEnd.y - segmentStart.y);
        var tPoint = {
            x: tX,
            y: tY
        }
        return this.getDistance(circleCenter, tPoint) < circleRadius * circleRadius;
    }
}

// pure javascript to scale the game
function resize() {
    var canvas = document.querySelector("canvas");
    var windowWidth = window.innerWidth;
    var windowHeight = window.innerHeight;
    var windowRatio = windowWidth / windowHeight;
    var gameRatio = game.config.width / game.config.height;
    if(windowRatio < gameRatio){
        canvas.style.width = windowWidth + "px";
        canvas.style.height = (windowWidth / gameRatio) + "px";
    }
    else{
        canvas.style.width = (windowHeight * gameRatio) + "px";
        canvas.style.height = windowHeight + "px";
    }
}

Now it’s time to add some kind of score and increase somehow the difficulty as you progress in the game, will do it next week, meanwhile download the source code.