- Author:
- David Nickerson <david.nickerson@gmail.com>
- Date:
- 2021-09-16 00:41:19+12:00
- Desc:
- Updating Noble 1962 model:
* Exposing the membrane potential to the top-level model;
* adding SED-ML for the paced and pacemaker variants of the model.
Using OpenCOR Snapshot release 2021-09-14.
- Permanent Source URI:
- https://models.fieldml.org/workspace/a1/rawfile/f954e59183314cd37f86c8832dc81317d01c8ec5/dojo-presentation/js/dojo/dojox/gfx/decompose.js
dojo.provide("dojox.gfx.decompose");
dojo.require("dojox.gfx.matrix");
(function(){
var m = dojox.gfx.matrix;
var eq = function(/* Number */ a, /* Number */ b){
// summary: compare two FP numbers for equality
return Math.abs(a - b) <= 1e-6 * (Math.abs(a) + Math.abs(b)); // Boolean
};
var calcFromValues = function(/* Number */ r1, /* Number */ m1, /* Number */ r2, /* Number */ m2){
// summary: uses two close FP ration and their original magnitudes to approximate the result
if(!isFinite(r1)){
return r2; // Number
}else if(!isFinite(r2)){
return r1; // Number
}
m1 = Math.abs(m1), m2 = Math.abs(m2);
return (m1 * r1 + m2 * r2) / (m1 + m2); // Number
};
var transpose = function(/* dojox.gfx.matrix.Matrix2D */ matrix){
// matrix: dojox.gfx.matrix.Matrix2D: a 2D matrix-like object
var M = new m.Matrix2D(matrix);
return dojo.mixin(M, {dx: 0, dy: 0, xy: M.yx, yx: M.xy}); // dojox.gfx.matrix.Matrix2D
};
var scaleSign = function(/* dojox.gfx.matrix.Matrix2D */ matrix){
return (matrix.xx * matrix.yy < 0 || matrix.xy * matrix.yx > 0) ? -1 : 1; // Number
};
var eigenvalueDecomposition = function(/* dojox.gfx.matrix.Matrix2D */ matrix){
// matrix: dojox.gfx.matrix.Matrix2D: a 2D matrix-like object
var M = m.normalize(matrix),
b = -M.xx - M.yy,
c = M.xx * M.yy - M.xy * M.yx,
d = Math.sqrt(b * b - 4 * c),
l1 = -(b + (b < 0 ? -d : d)) / 2,
l2 = c / l1,
vx1 = M.xy / (l1 - M.xx), vy1 = 1,
vx2 = M.xy / (l2 - M.xx), vy2 = 1;
if(eq(l1, l2)){
vx1 = 1, vy1 = 0, vx2 = 0, vy2 = 1;
}
if(!isFinite(vx1)){
vx1 = 1, vy1 = (l1 - M.xx) / M.xy;
if(!isFinite(vy1)){
vx1 = (l1 - M.yy) / M.yx, vy1 = 1;
if(!isFinite(vx1)){
vx1 = 1, vy1 = M.yx / (l1 - M.yy);
}
}
}
if(!isFinite(vx2)){
vx2 = 1, vy2 = (l2 - M.xx) / M.xy;
if(!isFinite(vy2)){
vx2 = (l2 - M.yy) / M.yx, vy2 = 1;
if(!isFinite(vx2)){
vx2 = 1, vy2 = M.yx / (l2 - M.yy);
}
}
}
var d1 = Math.sqrt(vx1 * vx1 + vy1 * vy1),
d2 = Math.sqrt(vx2 * vx2 + vy2 * vy2);
if(!isFinite(vx1 /= d1)){ vx1 = 0; }
if(!isFinite(vy1 /= d1)){ vy1 = 0; }
if(!isFinite(vx2 /= d2)){ vx2 = 0; }
if(!isFinite(vy2 /= d2)){ vy2 = 0; }
return { // Object
value1: l1,
value2: l2,
vector1: {x: vx1, y: vy1},
vector2: {x: vx2, y: vy2}
};
};
var decomposeSR = function(/* dojox.gfx.matrix.Matrix2D */ M, /* Object */ result){
// summary: decomposes a matrix into [scale, rotate]; no checks are done.
var sign = scaleSign(M),
a = result.angle1 = (Math.atan2(M.yx, M.yy) + Math.atan2(-sign * M.xy, sign * M.xx)) / 2,
cos = Math.cos(a), sin = Math.sin(a);
result.sx = calcFromValues(M.xx / cos, cos, -M.xy / sin, sin);
result.sy = calcFromValues(M.yy / cos, cos, M.yx / sin, sin);
return result; // Object
};
var decomposeRS = function(/* dojox.gfx.matrix.Matrix2D */ M, /* Object */ result){
// summary: decomposes a matrix into [rotate, scale]; no checks are done
var sign = scaleSign(M),
a = result.angle2 = (Math.atan2(sign * M.yx, sign * M.xx) + Math.atan2(-M.xy, M.yy)) / 2,
cos = Math.cos(a), sin = Math.sin(a);
result.sx = calcFromValues(M.xx / cos, cos, M.yx / sin, sin);
result.sy = calcFromValues(M.yy / cos, cos, -M.xy / sin, sin);
return result; // Object
};
dojox.gfx.decompose = function(matrix){
// summary: decompose a 2D matrix into translation, scaling, and rotation components
// description: this function decompose a matrix into four logical components:
// translation, rotation, scaling, and one more rotation using SVD.
// The components should be applied in following order:
// | [translate, rotate(angle2), scale, rotate(angle1)]
// matrix: dojox.gfx.matrix.Matrix2D: a 2D matrix-like object
var M = m.normalize(matrix),
result = {dx: M.dx, dy: M.dy, sx: 1, sy: 1, angle1: 0, angle2: 0};
// detect case: [scale]
if(eq(M.xy, 0) && eq(M.yx, 0)){
return dojo.mixin(result, {sx: M.xx, sy: M.yy}); // Object
}
// detect case: [scale, rotate]
if(eq(M.xx * M.yx, -M.xy * M.yy)){
return decomposeSR(M, result); // Object
}
// detect case: [rotate, scale]
if(eq(M.xx * M.xy, -M.yx * M.yy)){
return decomposeRS(M, result); // Object
}
// do SVD
var MT = transpose(M),
u = eigenvalueDecomposition([M, MT]),
v = eigenvalueDecomposition([MT, M]),
U = new m.Matrix2D({xx: u.vector1.x, xy: u.vector2.x, yx: u.vector1.y, yy: u.vector2.y}),
VT = new m.Matrix2D({xx: v.vector1.x, xy: v.vector1.y, yx: v.vector2.x, yy: v.vector2.y}),
S = new m.Matrix2D([m.invert(U), M, m.invert(VT)]);
decomposeSR(VT, result);
S.xx *= result.sx;
S.yy *= result.sy;
decomposeRS(U, result);
S.xx *= result.sx;
S.yy *= result.sy;
return dojo.mixin(result, {sx: S.xx, sy: S.yy}); // Object
};
})();
