JavaScript
function adj(m) { // Compute the adjugate of m
return [
m[4]*m[8]-m[5]*m[7], m[2]*m[7]-m[1]*m[8], m[1]*m[5]-m[2]*m[4],
m[5]*m[6]-m[3]*m[8], m[0]*m[8]-m[2]*m[6], m[2]*m[3]-m[0]*m[5],
m[3]*m[7]-m[4]*m[6], m[1]*m[6]-m[0]*m[7], m[0]*m[4]-m[1]*m[3]
];
}
function multmm(a, b) { // multiply two matrices
var c = Array(9);
for (var i = 0; i != 3; ++i) {
for (var j = 0; j != 3; ++j) {
var cij = 0;
for (var k = 0; k != 3; ++k) {
cij += a[3*i + k]*b[3*k + j];
}
c[3*i + j] = cij;
}
}
return c;
}
function multmv(m, v) { // multiply matrix and vector
return [
m[0]*v[0] + m[1]*v[1] + m[2]*v[2],
m[3]*v[0] + m[4]*v[1] + m[5]*v[2],
m[6]*v[0] + m[7]*v[1] + m[8]*v[2]
];
}
function pdbg(m, v) {
var r = multmv(m, v);
return r + " (" + r[0]/r[2] + ", " + r[1]/r[2] + ")";
}
function basisToPoints(x1, y1, x2, y2, x3, y3, x4, y4) {
var m = [
x1, x2, x3,
y1, y2, y3,
1, 1, 1
];
var v = multmv(adj(m), [x4, y4, 1]);
return multmm(m, [
v[0], 0, 0,
0, v[1], 0,
0, 0, v[2]
]);
}
function general2DProjection(
x1s, y1s, x1d, y1d,
x2s, y2s, x2d, y2d,
x3s, y3s, x3d, y3d,
x4s, y4s, x4d, y4d
) {
var s = basisToPoints(x1s, y1s, x2s, y2s, x3s, y3s, x4s, y4s);
var d = basisToPoints(x1d, y1d, x2d, y2d, x3d, y3d, x4d, y4d);
return multmm(d, adj(s));
}
function project(m, x, y) {
var v = multmv(m, [x, y, 1]);
return [v[0]/v[2], v[1]/v[2]];
}
function transform2d(elt, x1, y1, x2, y2, x3, y3, x4, y4) {
var w = elt.offsetWidth, h = elt.offsetHeight;
var t = general2DProjection
(0, 0, x1, y1, w, 0, x2, y2, 0, h, x3, y3, w, h, x4, y4);
for(i = 0; i != 9; ++i) t[i] = t[i]/t[8];
t = [t[0], t[3], 0, t[6],
t[1], t[4], 0, t[7],
0 , 0 , 1, 0 ,
t[2], t[5], 0, t[8]];
t = "matrix3d(" + t.join(", ") + ")";
elt.style["-webkit-transform"] = t;
elt.style["-moz-transform"] = t;
elt.style["-o-transform"] = t;
elt.style.transform = t;
}
corners...