I am making a game like this :

Yellow smiley has to escape from red smileys, when yellow smiley hits the boundary game is over, when red smileys hit the boundary they should bounce back with the same angle they came, like shown below:

Every 10 seconds a new red smiley comes in the big circle, when red smiley hits yellow, game is over, speed and starting angle of red smileys should be random. I control the yellow smiley with arrow keys. The biggest problem I have reflecting the red smileys from the boundary with the angle they came. I don't know how I can give a starting angle to a red smiley and bouncing it with the angle it came. After some tips I did the reflection, looks reasonable but I am not sure if it is working because sometimes it just bounces to the way they came from.
Now the problem is after each bounce the speed of the red smiley increases and after 4-5 bounces they the speed goes to infinity and balls disappear.
How can I overcome this?
My js source code :
//Smiley.js var canvas = document.getElementById("mycanvas"); var ctx = canvas.getContext("2d"); var vx; var vy; var twiceProjFactor; // Object containing some global Smiley properties. var SmileyApp = { radius: 15, xspeed: 0, yspeed: 0, xpos:200, // x-position of smiley ypos: 200 // y-position of smiley }; var SmileyRed = { radius: 15, xspeed: 0, yspeed: 0, xpos:350, // x-position of smiley ypos: 67 // y-position of smiley }; var SmileyReds = new Array(); for (var i=0; i<5; i++){ SmileyReds[i] = { radius: 15, xspeed: 0, yspeed: 0, xpos:350, // x-position of smiley ypos: 67 // y-position of smiley }; SmileyReds[i].xspeed = Math.floor((Math.random()*50)+1); SmileyReds[i].yspeed = Math.floor((Math.random()*50)+1); } function drawBigCircle() { var centerX = canvas.width / 2; var centerY = canvas.height / 2; var radiusBig = 300; ctx.beginPath(); ctx.arc(centerX, centerY, radiusBig, 0, 2 * Math.PI, false); // context.fillStyle = 'green'; // context.fill(); ctx.lineWidth = 5; // context.strokeStyle = '#003300'; // green ctx.stroke(); } function lineDistance( positionx, positiony ) { var xs = 0; var ys = 0; xs = positionx - 350; xs = xs * xs; ys = positiony - 350; ys = ys * ys; return Math.sqrt( xs + ys ); } function drawSmiley(x,y,r) { // outer border ctx.lineWidth = 3; ctx.beginPath(); ctx.arc(x,y,r, 0, 2*Math.PI); //red ctx.fillStyle="rgba(255,0,0, 0.5)"; ctx.fillStyle="rgba(255,255,0, 0.5)"; ctx.fill(); ctx.stroke(); // mouth ctx.beginPath(); ctx.moveTo(x+0.7*r, y); ctx.arc(x,y,0.7*r, 0, Math.PI, false); // eyes var reye = r/10; var f = 0.4; ctx.moveTo(x+f*r, y-f*r); ctx.arc(x+f*r-reye, y-f*r, reye, 0, 2*Math.PI); ctx.moveTo(x-f*r, y-f*r); ctx.arc(x-f*r+reye, y-f*r, reye, -Math.PI, Math.PI); // nose ctx.moveTo(x,y); ctx.lineTo(x, y-r/2); ctx.lineWidth = 1; ctx.stroke(); } function drawSmileyRed(x,y,r) { // outer border ctx.lineWidth = 3; ctx.beginPath(); ctx.arc(x,y,r, 0, 2*Math.PI); //red ctx.fillStyle="rgba(255,0,0, 0.5)"; //yellow ctx.fillStyle="rgba(255,255,0, 0.5)"; ctx.fill(); ctx.stroke(); // mouth ctx.beginPath(); ctx.moveTo(x+0.4*r, y+10); ctx.arc(x,y+10,0.4*r, 0, Math.PI, true); // eyes var reye = r/10; var f = 0.4; ctx.moveTo(x+f*r, y-f*r); ctx.arc(x+f*r-reye, y-f*r, reye, 0, 2*Math.PI); ctx.moveTo(x-f*r, y-f*r); ctx.arc(x-f*r+reye, y-f*r, reye, -Math.PI, Math.PI); // nose ctx.moveTo(x,y); ctx.lineTo(x, y-r/2); ctx.lineWidth = 1; ctx.stroke(); } // --- Animation of smiley moving with constant speed and bounce back at edges of canvas --- var tprev = 0; // this is used to calculate the time step between two successive calls of run function run(t) { requestAnimationFrame(run); if (t === undefined) { t=0; } var h = t - tprev; // time step tprev = t; SmileyApp.xpos += SmileyApp.xspeed * h/1000; // update position according to constant speed SmileyApp.ypos += SmileyApp.yspeed * h/1000; // update position according to constant speed for (var i=0; i<SmileyReds.length; i++){ SmileyReds[i].xpos += SmileyReds[i].xspeed * h/1000; // update position according to constant speed SmileyReds[i].ypos += SmileyReds[i].yspeed * h/1000; // update position according to constant speed } // change speed direction if smiley hits canvas edges if (lineDistance(SmileyApp.xpos, SmileyApp.ypos) + SmileyApp.radius > 300) { alert("Game Over"); } for (var i=0; i<SmileyReds.length; i++){ if (lineDistance(SmileyReds[i].xpos, SmileyReds[i].ypos) + SmileyReds[i].radius > 300) { // Red Smiley collusion //SmileyReds[i].xpos //SmileyReds[i].xspeed //SmileyReds[i].ypos //SmileyReds[i].yspeed // r = v − [2 (n · v) n] formula //n calculation nx = 350 - SmileyReds[i].xpos ; ny = 350 - SmileyReds[i].ypos ; nx = nx / (Math.sqrt(nx * nx + ny * ny)); ny = ny / (Math.sqrt(nx * nx + ny * ny)); //new calc v_newx = SmileyReds[i].xspeed - (2 *( nx * SmileyReds[i].xspeed + ny * SmileyReds[i].yspeed ) ) * nx; v_newy = SmileyReds[i].yspeed - (2 *( nx * SmileyReds[i].xspeed + ny * SmileyReds[i].yspeed ) ) * ny; SmileyReds[i].xspeed = v_newx; SmileyReds[i].yspeed = v_newy; //to calculate "n," you do (626/L, 282/L) where L=sqrt(xpos^2+ypos^2) } } /* Square canvas if ((SmileyApp.xpos + SmileyApp.radius > canvas.width) || (SmileyApp.xpos - SmileyApp.radius) < 0) { SmileyApp.xspeed = -SmileyApp.xspeed; } if ((SmileyApp.ypos + SmileyApp.radius > canvas.height) || (SmileyApp.ypos - SmileyApp.radius) < 0) { SmileyApp.yspeed = -SmileyApp.yspeed; } */ // redraw smiley at new position ctx.clearRect(0,0,canvas.height, canvas.width); drawBigCircle(); drawSmiley(SmileyApp.xpos, SmileyApp.ypos, SmileyApp.radius); for (var i=0; i<SmileyReds.length; i++){ drawSmileyRed(SmileyReds[i].xpos, SmileyReds[i].ypos, SmileyReds[i].radius); } } // uncomment these two lines to get every going // SmileyApp.speed = 100; run(); // --- Mouse wheel event handler to grow and shrink smiley function mousewheelCB(event){ // alert("Hallo"); event.preventDefault(); event.stopPropagation(); SmileyApp.radius += event.wheelDelta/40; } canvas.addEventListener('mousewheel', mousewheelCB, false); // --- Control smiley motion with left/right arrow keys function arrowkeyCB(event) { event.preventDefault(); if (event.keyCode === 37) { // left arrow SmileyApp.xspeed = -100; SmileyApp.yspeed = 0; } else if (event.keyCode === 39) { // right arrow SmileyApp.xspeed = 100; SmileyApp.yspeed = 0; } else if (event.keyCode === 38) { // up arrow SmileyApp.yspeed = -100; SmileyApp.xspeed = 0; } else if (event.keyCode === 40) { // right arrow SmileyApp.yspeed = 100; SmileyApp.xspeed = 0; } } document.addEventListener('keydown', arrowkeyCB, true); /* function run(){ console.log("Here is run"); console.log(Date.now()); ctx.clearRect(0,0,canvas.width, canvas.height); xpos = 200; drawSmiley2(100,100,20); xpos = xpos-50; // decent animation 30 pictures per second } setInterval(run, 50); */ JSFiddle : http://jsfiddle.net/gj4Q7/2/