Draw distorted image on html5's canvas

Question

Is it possible, and if so how, to draw images with its four corners distorted to a non rectangular shape. For example if you were wanting to draw the image as if it had bee

Answer 1

A number of commenters above have asked about hiding the triangles - do this and they'll disappear (for info: @erbridge, @Constantin Groß):

All credit for the following still goes to @AndyPoes, since this was all his suggestion - I'm just adding the completed version he suggested.

Change this line:

render(true, image, triangle);

To this:

render(false, image, triangle);

...the black triangles will have gone, but you'll see gaps between the triangles, so now do this:

Change this:

var triangle1 = new Triangle(
            new Point(p1x, p1y),
            new Point(p3x, p3y),
            new Point(p4x, p4y),
            new TextCoord(u1, v1),
            new TextCoord(u2, v2),
            new TextCoord(u1, v2)
        );

        var triangle2 = new Triangle(
            new Point(p1x, p1y),
            new Point(p2x, p2y),
            new Point(p3x, p3y),
            new TextCoord(u1, v1),
            new TextCoord(u2, v1),
            new TextCoord(u2, v2)
        );

To this instead:

            var triangle1 = new Triangle(
            new Point(p1x-1, p1y),
            new Point(p3x+2, p3y+1),
            new Point(p4x-1, p4y+1),
            new TextCoord(u1, v1),
            new TextCoord(u2, v2),
            new TextCoord(u1, v2)
        );

        var triangle2 = new Triangle(
            new Point(p1x-2, p1y),
            new Point(p2x+1, p2y),
            new Point(p3x+1, p3y+1),
            new TextCoord(u1, v1),
            new TextCoord(u2, v1),
            new TextCoord(u2, v2)
        );

....and the gaps will be closed.

New fiddle = fiddler off the roof

Full code is here:

var controls = [];
var canvas;
var context;
var image;
var triangles = [];
var dirtyTriangles = false;

var rand = function(s,e) {
    return Math.random() * (e-s) + s;
}

// dom ready
$(document).ready(function() {
image = new Image();
$(image).load(function() {
    setInterval(draw, 1000 / 60);
});
$(image).attr('src', 'https://images.unsplash.com/photo-1500964757637-c85e8a162699?ixlib=rb-1.2.1&q=80&fm=jpg');

canvas = document.createElement('canvas');
$(canvas).attr('width', 500);
$(canvas).attr('height', 500);
$('body').append(canvas);

context = canvas.getContext('2d');

//
for (var i = 0; i < 4; ++i) {
    var control = document.createElement('div');
    $(control).addClass('node');
    $('body').append(control);
    controls.push(control);
}

$(controls[0]).css('left', rand(25, 225));
$(controls[0]).css('top', rand(25, 225));

$(controls[1]).css('left', rand(250, 475));
$(controls[1]).css('top', rand(25, 225));

$(controls[2]).css('left', rand(250, 475));
$(controls[2]).css('top', rand(250, 475));

$(controls[3]).css('left', rand(25, 225));
$(controls[3]).css('top', rand(250, 475));

$('body').mousedown(function(e) {
    if ($(e.target).hasClass('node')) {
        var node = e.target;

        $('body').mousemove(function(e) {
            var x = e.pageX;
            var y = e.pageY;
            $(node).css('left', x);
            $(node).css('top', y);
            dirtyTriangles = true;
        });

        $('body').mouseup(function(e) {
            $('body').off( "mousemove" );
            $('body').off( "mouseup" );
        });
    }
});
});

var draw = function() {
context.clearRect(0,0,500,500);

var render = function(wireframe, image, tri) {
    
    if (wireframe) {
        context.strokeStyle = "black";
        context.beginPath();
        context.moveTo(tri.p0.x, tri.p0.y);
        context.lineTo(tri.p1.x, tri.p1.y);
        context.lineTo(tri.p2.x, tri.p2.y);
        context.lineTo(tri.p0.x, tri.p0.y);
        context.stroke();
        context.closePath();
    }

    if (image) {
        drawTriangle(context, image,
                     tri.p0.x, tri.p0.y,
                     tri.p1.x, tri.p1.y,
                     tri.p2.x, tri.p2.y,
                     tri.t0.u, tri.t0.v,
                     tri.t1.u, tri.t1.v,
                     tri.t2.u, tri.t2.v);
    }
}

if (dirtyTriangles) {
    dirtyTriangles = false;
    calculateGeometry();
}

for (triangle of triangles) {
    render(true, image, triangle);
}
}

var calculateGeometry = function() {
// clear triangles out
triangles = [];

// generate subdivision
var subs = 7; // vertical subdivisions
var divs = 7; // horizontal subdivisions

var p1 = new Point(parseInt($(controls[0]).css('left')) + 6, parseInt($(controls[0]).css('top')) + 6);
var p2 = new Point(parseInt($(controls[1]).css('left')) + 6, parseInt($(controls[1]).css('top')) + 6);
var p3 = new Point(parseInt($(controls[2]).css('left')) + 6, parseInt($(controls[2]).css('top')) + 6);
var p4 = new Point(parseInt($(controls[3]).css('left')) + 6, parseInt($(controls[3]).css('top')) + 6);

var dx1 = p4.x - p1.x;
var dy1 = p4.y - p1.y;
var dx2 = p3.x - p2.x;
var dy2 = p3.y - p2.y;

var imgW = image.naturalWidth;
var imgH = image.naturalHeight;

for (var sub = 0; sub < subs; ++sub) {
    var curRow = sub / subs;
    var nextRow = (sub + 1) / subs;

    var curRowX1 = p1.x + dx1 * curRow;
    var curRowY1 = p1.y + dy1 * curRow;
    
    var curRowX2 = p2.x + dx2 * curRow;
    var curRowY2 = p2.y + dy2 * curRow;

    var nextRowX1 = p1.x + dx1 * nextRow;
    var nextRowY1 = p1.y + dy1 * nextRow;
    
    var nextRowX2 = p2.x + dx2 * nextRow;
    var nextRowY2 = p2.y + dy2 * nextRow;

    for (var div = 0; div < divs; ++div) {
        var curCol = div / divs;
        var nextCol = (div + 1) / divs;

        var dCurX = curRowX2 - curRowX1;
        var dCurY = curRowY2 - curRowY1;
        var dNextX = nextRowX2 - nextRowX1;
        var dNextY = nextRowY2 - nextRowY1;

        var p1x = curRowX1 + dCurX * curCol;
        var p1y = curRowY1 + dCurY * curCol;

        var p2x = curRowX1 + (curRowX2 - curRowX1) * nextCol;
        var p2y = curRowY1 + (curRowY2 - curRowY1) * nextCol;

        var p3x = nextRowX1 + dNextX * nextCol;
        var p3y = nextRowY1 + dNextY * nextCol;

        var p4x = nextRowX1 + dNextX * curCol;
        var p4y = nextRowY1 + dNextY * curCol;

        var u1 = curCol * imgW;
        var u2 = nextCol * imgW;
        var v1 = curRow * imgH;
        var v2 = nextRow * imgH;

        var triangle1 = new Triangle(
            new Point(p1x-1, p1y),
            new Point(p3x+2, p3y+1),
            new Point(p4x-1, p4y+1),
            new TextCoord(u1, v1),
            new TextCoord(u2, v2),
            new TextCoord(u1, v2)
        );

        var triangle2 = new Triangle(
            new Point(p1x-2, p1y),
            new Point(p2x+1, p2y),
            new Point(p3x+1, p3y+1),
            new TextCoord(u1, v1),
            new TextCoord(u2, v1),
            new TextCoord(u2, v2)
        );

        triangles.push(triangle1);
        triangles.push(triangle2);
    }
}
}

// from http://tulrich.com/geekstuff/canvas/jsgl.js
var drawTriangle = function(ctx, im, x0, y0, x1, y1, x2, y2,
sx0, sy0, sx1, sy1, sx2, sy2) {
ctx.save();

// Clip the output to the on-screen triangle boundaries.
ctx.beginPath();
ctx.moveTo(x0, y0);
ctx.lineTo(x1, y1);
ctx.lineTo(x2, y2);
ctx.closePath();
//ctx.stroke();//xxxxxxx for wireframe
ctx.clip();

/*
ctx.transform(m11, m12, m21, m22, dx, dy) sets the context transform matrix.

The context matrix is:

[ m11 m21 dx ]
[ m12 m22 dy ]
[  0   0   1 ]

Coords are column vectors with a 1 in the z coord, so the transform is:
x_out = m11 * x + m21 * y + dx;
y_out = m12 * x + m22 * y + dy;

From Maxima, these are the transform values that map the source
coords to the dest coords:

sy0 (x2 - x1) - sy1 x2 + sy2 x1 + (sy1 - sy2) x0
[m11 = - -----------------------------------------------------,
sx0 (sy2 - sy1) - sx1 sy2 + sx2 sy1 + (sx1 - sx2) sy0

sy1 y2 + sy0 (y1 - y2) - sy2 y1 + (sy2 - sy1) y0
m12 = -----------------------------------------------------,
sx0 (sy2 - sy1) - sx1 sy2 + sx2 sy1 + (sx1 - sx2) sy0

sx0 (x2 - x1) - sx1 x2 + sx2 x1 + (sx1 - sx2) x0
m21 = -----------------------------------------------------,
sx0 (sy2 - sy1) - sx1 sy2 + sx2 sy1 + (sx1 - sx2) sy0

sx1 y2 + sx0 (y1 - y2) - sx2 y1 + (sx2 - sx1) y0
m22 = - -----------------------------------------------------,
sx0 (sy2 - sy1) - sx1 sy2 + sx2 sy1 + (sx1 - sx2) sy0

sx0 (sy2 x1 - sy1 x2) + sy0 (sx1 x2 - sx2 x1) + (sx2 sy1 - sx1 sy2) x0
dx = ----------------------------------------------------------------------,
sx0 (sy2 - sy1) - sx1 sy2 + sx2 sy1 + (sx1 - sx2) sy0

sx0 (sy2 y1 - sy1 y2) + sy0 (sx1 y2 - sx2 y1) + (sx2 sy1 - sx1 sy2) y0
dy = ----------------------------------------------------------------------]
sx0 (sy2 - sy1) - sx1 sy2 + sx2 sy1 + (sx1 - sx2) sy0
  */

// TODO: eliminate common subexpressions.
var denom = sx0 * (sy2 - sy1) - sx1 * sy2 + sx2 * sy1 + (sx1 - sx2) * sy0;
if (denom == 0) {
    return;
}
var m11 = -(sy0 * (x2 - x1) - sy1 * x2 + sy2 * x1 + (sy1 - sy2) * x0) / denom;
var m12 = (sy1 * y2 + sy0 * (y1 - y2) - sy2 * y1 + (sy2 - sy1) * y0) / denom;
var m21 = (sx0 * (x2 - x1) - sx1 * x2 + sx2 * x1 + (sx1 - sx2) * x0) / denom;
var m22 = -(sx1 * y2 + sx0 * (y1 - y2) - sx2 * y1 + (sx2 - sx1) * y0) / denom;
var dx = (sx0 * (sy2 * x1 - sy1 * x2) + sy0 * (sx1 * x2 - sx2 * x1) + (sx2 * sy1 - sx1 * sy2) * x0) / denom;
var dy = (sx0 * (sy2 * y1 - sy1 * y2) + sy0 * (sx1 * y2 - sx2 * y1) + (sx2 * sy1 - sx1 * sy2) * y0) / denom;

ctx.transform(m11, m12, m21, m22, dx, dy);

// Draw the whole image.  Transform and clip will map it onto the
// correct output triangle.
//
// TODO: figure out if drawImage goes faster if we specify the rectangle that
// bounds the source coords.
ctx.drawImage(im, 0, 0);
ctx.restore();
};

// point class

var Point = function(x,y) {
this.x = x?x:0;
this.y = y?y:0;
}

var p = Point.prototype;

p.length = function(point) {
    point = point?point:new Point();
    var xs =0, ys =0;
    xs = point.x - this.x;
    xs = xs * xs;

    ys = point.y - this.y;
    ys = ys * ys;
    return Math.sqrt( xs + ys );
}

var TextCoord = function(u,v) {
this.u = u?u:0;
this.v = v?v:0;
}

var Triangle = function(p0, p1, p2, t0, t1, t2) {
this.p0 = p0;
this.p1 = p1;
this.p2 = p2;

this.t0 = t0;
this.t1 = t1;
this.t2 = t2;
}