Pinch/pucker an image in canvas

How can I pinch/pucker some area of an image in canvas?

I've made a solar system animation some time ago, and I started rewriting it. Now, I want to add gravity effect to masses. To make the effect visible, I turned the background into a grid and I'll be modifying it.

Desired effect is something like this (made in PS)

context.background("rgb(120,130,145)");
context.grid(25, "rgba(255,255,255,.1)");

var sun = {
    fill        : "rgb(220,210,120)",
    radius      : 30,
    boundingBox : 30*2 + 3*2,
    position    : {
        x       : 200,
        y       : 200,
    },
};
sun.img = saveToImage(sun);

context.drawImage(sun.img, sun.position.x - sun.boundingBox/2, sun.position.y - sun.boundingBox/2);

jsFiddle

Update: I've done some googling and found some resources, but since I've never done pixel manipulation before, I can't put these together.

Pixel Distortions with Bilinear Filtration in HTML5 Canvas | Splashnology.com (functions only)

glfx.js (WebGL library with demos)

JSFiddle (spherize, zoom, twirl examples)

The spherize effect in inverted form would be good for the job, I guess.

Solution

I've had time to revisit this problem and came up with a solution. Instead of solving the problem directly, first, I needed to understand how the math behind the calculation and pixel manipulation works.

So, instead of using an image/pixels, I decided to use particles. A JavaScript object is something I'm much more familiar with, so it was easy to manipulate.

I'll not try to explain the method because I think it's self-explanatory, and I tried to keep it as simple as it can get.

var canvas = document.getElementById("canvas");
var context = canvas.getContext("2d");

canvas.width  = 400;
canvas.height = 400;

var particles = [];

function Particle() {
    this.position = {
        actual : {
            x : 0,
            y : 0
        },
        affected : {
            x : 0,
            y : 0
        },
    };
}

// space between particles
var gridSize = 25;

var columns  = canvas.width / gridSize;
var rows     = canvas.height / gridSize;

// create grid using particles
for (var i = 0; i < rows+1; i++) {
    for (var j = 0; j < canvas.width; j += 2) {
        var p = new Particle();
        p.position.actual.x = j;
        p.position.actual.y = i * gridSize;
        p.position.affected = Object.create(p.position.actual);
        particles.push(p);
    }
}
for (var i = 0; i < columns+1; i++) {
    for (var j = 0; j < canvas.height; j += 2) {
        var p = new Particle();
        p.position.actual.x = i * gridSize;
        p.position.actual.y = j;
        p.position.affected = Object.create(p.position.actual);
        particles.push(p);
    }
}

// track mouse coordinates as it is the source of mass/gravity
var mouse = {
    x : -100,
    y : -100,
};

var effectRadius = 75;
var effectStrength = 50;

function draw() {
    context.clearRect(0, 0, canvas.width, canvas.height);
    
    particles.forEach(function (particle) {
        // move the particle to its original position
        particle.position.affected = Object.create(particle.position.actual);
        
        // calculate the effect area
        var a = mouse.y - particle.position.actual.y;
        var b = mouse.x - particle.position.actual.x;
        var dist = Math.sqrt(a*a + b*b);
        
        // check if the particle is in the affected area
        if (dist < effectRadius) {
            
            // angle of the mouse relative to the particle
            var a = angle(particle.position.actual.x, particle.position.actual.y, mouse.x, mouse.y);
            
            // pull is stronger on the closest particle
            var strength = dist.map(0, effectRadius, effectStrength, 0);
            
            if (strength > dist) {
                strength = dist;
            }
            
            // new position for the particle that's affected by gravity
            var p = pos(particle.position.actual.x, particle.position.actual.y, a, strength);
            
            particle.position.affected.x = p.x;
            particle.position.affected.y = p.y;
        }
        
        context.beginPath();
        context.rect(particle.position.affected.x -1, particle.position.affected.y -1, 2, 2);
        context.fill();
    });
}

draw();

window.addEventListener("mousemove", function (e) {
    mouse.x = e.x - canvas.offsetLeft;
    mouse.y = e.y - canvas.offsetTop;
    requestAnimationFrame(draw);
});

function angle(originX, originY, targetX, targetY) {
    var dx = targetX - originX;
    var dy = targetY - originY;
    var theta = Math.atan2(dy, dx) * (180 / Math.PI);
    if (theta < 0) theta = 360 + theta;
    return theta;
}

Number.prototype.map = function (in_min, in_max, out_min, out_max) {
    return (this - in_min) * (out_max - out_min) / (in_max - in_min) + out_min;
};

function pos(x, y, angle, length) {
    angle *= Math.PI / 180;
    return {
        x : Math.round(x + length * Math.cos(angle)),
        y : Math.round(y + length * Math.sin(angle)),
    };
}

* {
  margin: 0;
  padding: 0;
  box-sizing: inherit;
  line-height: inherit;
  font-size: inherit;
  font-family: inherit;
}

body {
  font-family: sans-serif;
  box-sizing: border-box;
  background-color: hsl(0, 0%, 90%);
}

canvas {
  display: block;
  background: white;
  box-shadow: 0 0 2px rgba(0, 0, 0, .2), 0 1px 1px rgba(0, 0, 0, .1);
  margin: 20px auto;
}

canvas:hover {
  cursor: none;
}

<canvas id="canvas"></canvas>

I might try to create twirl effect some other time, and move these into WebGL for better performance.

Update:

Now, I'm working on the twirl effect, and I've made it work to some degree.

var canvas = document.getElementById("canvas");
var context = canvas.getContext("2d");

canvas.width  = 400;
canvas.height = 400;

var particles = [];

function Particle() {
    this.position = {
        actual : {
            x : 0,
            y : 0
        },
        affected : {
            x : 0,
            y : 0
        },
    };
}

// space between particles
var gridSize = 25;

var columns  = canvas.width / gridSize;
var rows     = canvas.height / gridSize;

// create grid using particles
for (var i = 0; i < rows+1; i++) {
    for (var j = 0; j < canvas.width; j += 2) {
        var p = new Particle();
        p.position.actual.x = j;
        p.position.actual.y = i * gridSize;
        p.position.affected = Object.create(p.position.actual);
        particles.push(p);
    }
}
for (var i = 0; i < columns+1; i++) {
    for (var j = 0; j < canvas.height; j += 2) {
        var p = new Particle();
        p.position.actual.x = i * gridSize;
        p.position.actual.y = j;
        p.position.affected = Object.create(p.position.actual);
        particles.push(p);
    }
}

// track mouse coordinates as it is the source of mass/gravity
var mouse = {
    x : -100,
    y : -100,
};

var effectRadius = 75;
var twirlAngle   = 90;

function draw(e) {
    context.clearRect(0, 0, canvas.width, canvas.height);
    
    particles.forEach(function (particle) {
        // move the particle to its original position
        particle.position.affected = Object.create(particle.position.actual);
        
        // calculate the effect area
        var a = mouse.y - particle.position.actual.y;
        var b = mouse.x - particle.position.actual.x;
        var dist = Math.sqrt(a*a + b*b);
        
        // check if the particle is in the affected area
        if (dist < effectRadius) {
            
            // angle of the particle relative to the mouse
            var a = angle(mouse.x, mouse.y, particle.position.actual.x, particle.position.actual.y);
            
            var strength = dist.map(0, effectRadius, twirlAngle, 0);
            
            // twirl
            a += strength;
            
            // new position for the particle that's affected by gravity
            var p = rotate(a, dist, mouse.x, mouse.y);
            
            particle.position.affected.x = p.x;
            particle.position.affected.y = p.y;
        }
        
        context.beginPath();
        context.rect(particle.position.affected.x -1, particle.position.affected.y -1, 2, 2);
        context.fillStyle = "black";
        context.fill();
    });
}

draw();

window.addEventListener("mousemove", function (e) {
    mouse.x = e.x - canvas.offsetLeft;
    mouse.y = e.y - canvas.offsetTop;
    requestAnimationFrame(draw);
});

function angle(originX, originY, targetX, targetY) {
    var dx = targetX - originX;
    var dy = targetY - originY;
    var theta = Math.atan2(dy, dx) * (180 / Math.PI);
    if (theta < 0) theta = 360 + theta;
    return theta;
}

Number.prototype.map = function (in_min, in_max, out_min, out_max) {
    return (this - in_min) * (out_max - out_min) / (in_max - in_min) + out_min;
};

function pos(x, y, angle, length) {
    angle *= Math.PI / 180;
    return {
        x : Math.round(x + length * Math.cos(angle)),
        y : Math.round(y + length * Math.sin(angle)),
    };
}

function rotate(angle, distance, originX, originY) {
    return {
        x : originX + Math.cos(angle * Math.PI/180) * distance,
        y : originY + Math.sin(angle * Math.PI/180) * distance,
    }
}

* {
  margin: 0;
  padding: 0;
  box-sizing: inherit;
  line-height: inherit;
  font-size: inherit;
  font-family: inherit;
}

body {
  font-family: sans-serif;
  box-sizing: border-box;
  background-color: hsl(0, 0%, 90%);
}

canvas {
  display: block;
  background: white;
  box-shadow: 0 0 2px rgba(0, 0, 0, .2), 0 1px 1px rgba(0, 0, 0, .1);
  margin: 20px auto;
}

<canvas id="canvas"></canvas>

There is a slight issue with the mapping of strength of the twirl. I've used the same function map that I've used with pinch effect, but I think twirl doesn't use linear mapping, but eased mapping. Compare the JS version with the PS filter. PS filter is smoother. I need to rewrite the map function.

Update 2:

I've managed to make it work the same way PS filter does. Using an ease function, i.e., easeOutQuad solved the problem. Enjoy :)

var canvas = document.getElementById("canvas");
var context = canvas.getContext("2d");

canvas.width  = 400;
canvas.height = 400;

var particles = [];

function Particle() {
    this.position = {
        actual : {
            x : 0,
            y : 0
        },
        affected : {
            x : 0,
            y : 0
        },
    };
}

// space between particles
var gridSize = 25;

var columns  = canvas.width / gridSize;
var rows     = canvas.height / gridSize;

// create grid using particles
for (var i = 0; i < rows+1; i++) {
    for (var j = 0; j < canvas.width; j+=2) {
        var p = new Particle();
        p.position.actual.x = j;
        p.position.actual.y = i * gridSize;
        p.position.affected = Object.create(p.position.actual);
        particles.push(p);
    }
}
for (var i = 0; i < columns+1; i++) {
    for (var j = 0; j < canvas.height; j+=2) {
        var p = new Particle();
        p.position.actual.x = i * gridSize;
        p.position.actual.y = j;
        p.position.affected = Object.create(p.position.actual);
        particles.push(p);
    }
}

// track mouse coordinates as it is the source of mass/gravity
var mouse = {
    x : -100,
    y : -100,
};

var effectRadius = 75;
var twirlAngle   = 90;

function draw(e) {
    context.clearRect(0, 0, canvas.width, canvas.height);
    
    particles.forEach(function (particle) {
        // move the particle to its original position
        particle.position.affected = Object.create(particle.position.actual);
        
        // calculate the effect area
        var a = mouse.y - particle.position.actual.y;
        var b = mouse.x - particle.position.actual.x;
        var dist = Math.sqrt(a*a + b*b);
        
        // check if the particle is in the affected area
        if (dist < effectRadius) {
            
            // angle of the particle relative to the mouse
            var a = angle(mouse.x, mouse.y, particle.position.actual.x, particle.position.actual.y);
            
            var strength = twirlAngle - easeOutQuad(dist, 0, twirlAngle, effectRadius);
            
            // twirl
            a += strength;
            
            // new position for the particle that's affected by gravity
            var p = rotate(a, dist, mouse.x, mouse.y);
            
            particle.position.affected.x = p.x;
            particle.position.affected.y = p.y;
        }
        
        context.beginPath();
        context.rect(particle.position.affected.x-1, particle.position.affected.y-1, 2, 2);
        context.fillStyle = "black";
        context.fill();
    });
}

draw();

window.addEventListener("mousemove", function (e) {
    mouse.x = e.x - canvas.offsetLeft;
    mouse.y = e.y - canvas.offsetTop;
    requestAnimationFrame(draw);
});

function easeOutQuad(t, b, c, d) {
    t /= d;
    return -c * t*(t-2) + b;
};

function angle(originX, originY, targetX, targetY) {
    var dx = targetX - originX;
    var dy = targetY - originY;
    var theta = Math.atan2(dy, dx) * (180 / Math.PI);
    if (theta < 0) theta = 360 + theta;
    return theta;
}

Number.prototype.map = function (in_min, in_max, out_min, out_max) {
    return (this - in_min) / (in_max - in_min) * (out_max - out_min) + out_min;
};

function pos(x, y, angle, length) {
    angle *= Math.PI / 180;
    return {
        x : Math.round(x + length * Math.cos(angle)),
        y : Math.round(y + length * Math.sin(angle)),
    };
}

function rotate(angle, distance, originX, originY) {
    return {
        x : originX + Math.cos(angle * Math.PI/180) * distance,
        y : originY + Math.sin(angle * Math.PI/180) * distance,
    }
}

* {
  margin: 0;
  padding: 0;
  box-sizing: inherit;
  line-height: inherit;
  font-size: inherit;
  font-family: inherit;
}

body {
  font-family: sans-serif;
  box-sizing: border-box;
  background-color: hsl(0, 0%, 90%);
}

canvas {
  display: block;
  background: white;
  box-shadow: 0 0 2px rgba(0, 0, 0, .2), 0 1px 1px rgba(0, 0, 0, .1);
  margin: 20px auto;
}

<canvas id="canvas"></canvas>