- Author:
- David Nickerson <david.nickerson@gmail.com>
- Date:
- 2021-09-17 15:50:49+12:00
- Desc:
- tweak html formatting
- Permanent Source URI:
- https://models.fieldml.org/workspace/a1/rawfile/1b3862589abf79ae9119ee0b5e99a8b785d762e1/dojo-presentation/js/dojo/dojox/gfx/matrix.js
dojo.provide("dojox.gfx.matrix");
(function(){
var m = dojox.gfx.matrix;
// candidates for dojox.math:
m._degToRad = function(degree){ return Math.PI * degree / 180; };
m._radToDeg = function(radian){ return radian / Math.PI * 180; };
m.Matrix2D = function(arg){
// summary: a 2D matrix object
// description: Normalizes a 2D matrix-like object. If arrays is passed,
// all objects of the array are normalized and multiplied sequentially.
// arg: Object
// a 2D matrix-like object, a number, or an array of such objects
if(arg){
if(typeof arg == "number"){
this.xx = this.yy = arg;
}else if(arg instanceof Array){
if(arg.length > 0){
var matrix = m.normalize(arg[0]);
// combine matrices
for(var i = 1; i < arg.length; ++i){
var l = matrix, r = dojox.gfx.matrix.normalize(arg[i]);
matrix = new m.Matrix2D();
matrix.xx = l.xx * r.xx + l.xy * r.yx;
matrix.xy = l.xx * r.xy + l.xy * r.yy;
matrix.yx = l.yx * r.xx + l.yy * r.yx;
matrix.yy = l.yx * r.xy + l.yy * r.yy;
matrix.dx = l.xx * r.dx + l.xy * r.dy + l.dx;
matrix.dy = l.yx * r.dx + l.yy * r.dy + l.dy;
}
dojo.mixin(this, matrix);
}
}else{
dojo.mixin(this, arg);
}
}
};
// the default (identity) matrix, which is used to fill in missing values
dojo.extend(m.Matrix2D, {xx: 1, xy: 0, yx: 0, yy: 1, dx: 0, dy: 0});
dojo.mixin(m, {
// summary: class constants, and methods of dojox.gfx.matrix
// matrix constants
// identity: dojox.gfx.matrix.Matrix2D
// an identity matrix constant: identity * (x, y) == (x, y)
identity: new m.Matrix2D(),
// flipX: dojox.gfx.matrix.Matrix2D
// a matrix, which reflects points at x = 0 line: flipX * (x, y) == (-x, y)
flipX: new m.Matrix2D({xx: -1}),
// flipY: dojox.gfx.matrix.Matrix2D
// a matrix, which reflects points at y = 0 line: flipY * (x, y) == (x, -y)
flipY: new m.Matrix2D({yy: -1}),
// flipXY: dojox.gfx.matrix.Matrix2D
// a matrix, which reflects points at the origin of coordinates: flipXY * (x, y) == (-x, -y)
flipXY: new m.Matrix2D({xx: -1, yy: -1}),
// matrix creators
translate: function(a, b){
// summary: forms a translation matrix
// description: The resulting matrix is used to translate (move) points by specified offsets.
// a: Number: an x coordinate value
// b: Number: a y coordinate value
if(arguments.length > 1){
return new m.Matrix2D({dx: a, dy: b}); // dojox.gfx.matrix.Matrix2D
}
// branch
// a: dojox.gfx.Point: a point-like object, which specifies offsets for both dimensions
// b: null
return new m.Matrix2D({dx: a.x, dy: a.y}); // dojox.gfx.matrix.Matrix2D
},
scale: function(a, b){
// summary: forms a scaling matrix
// description: The resulting matrix is used to scale (magnify) points by specified offsets.
// a: Number: a scaling factor used for the x coordinate
// b: Number: a scaling factor used for the y coordinate
if(arguments.length > 1){
return new m.Matrix2D({xx: a, yy: b}); // dojox.gfx.matrix.Matrix2D
}
if(typeof a == "number"){
// branch
// a: Number: a uniform scaling factor used for the both coordinates
// b: null
return new m.Matrix2D({xx: a, yy: a}); // dojox.gfx.matrix.Matrix2D
}
// branch
// a: dojox.gfx.Point: a point-like object, which specifies scale factors for both dimensions
// b: null
return new m.Matrix2D({xx: a.x, yy: a.y}); // dojox.gfx.matrix.Matrix2D
},
rotate: function(angle){
// summary: forms a rotating matrix
// description: The resulting matrix is used to rotate points
// around the origin of coordinates (0, 0) by specified angle.
// angle: Number: an angle of rotation in radians (>0 for CW)
var c = Math.cos(angle);
var s = Math.sin(angle);
return new m.Matrix2D({xx: c, xy: -s, yx: s, yy: c}); // dojox.gfx.matrix.Matrix2D
},
rotateg: function(degree){
// summary: forms a rotating matrix
// description: The resulting matrix is used to rotate points
// around the origin of coordinates (0, 0) by specified degree.
// See dojox.gfx.matrix.rotate() for comparison.
// degree: Number: an angle of rotation in degrees (>0 for CW)
return m.rotate(m._degToRad(degree)); // dojox.gfx.matrix.Matrix2D
},
skewX: function(angle) {
// summary: forms an x skewing matrix
// description: The resulting matrix is used to skew points in the x dimension
// around the origin of coordinates (0, 0) by specified angle.
// angle: Number: an skewing angle in radians
return new m.Matrix2D({xy: Math.tan(angle)}); // dojox.gfx.matrix.Matrix2D
},
skewXg: function(degree){
// summary: forms an x skewing matrix
// description: The resulting matrix is used to skew points in the x dimension
// around the origin of coordinates (0, 0) by specified degree.
// See dojox.gfx.matrix.skewX() for comparison.
// degree: Number: an skewing angle in degrees
return m.skewX(m._degToRad(degree)); // dojox.gfx.matrix.Matrix2D
},
skewY: function(angle){
// summary: forms a y skewing matrix
// description: The resulting matrix is used to skew points in the y dimension
// around the origin of coordinates (0, 0) by specified angle.
// angle: Number: an skewing angle in radians
return new m.Matrix2D({yx: Math.tan(angle)}); // dojox.gfx.matrix.Matrix2D
},
skewYg: function(degree){
// summary: forms a y skewing matrix
// description: The resulting matrix is used to skew points in the y dimension
// around the origin of coordinates (0, 0) by specified degree.
// See dojox.gfx.matrix.skewY() for comparison.
// degree: Number: an skewing angle in degrees
return m.skewY(m._degToRad(degree)); // dojox.gfx.matrix.Matrix2D
},
reflect: function(a, b){
// summary: forms a reflection matrix
// description: The resulting matrix is used to reflect points around a vector,
// which goes through the origin.
// a: dojox.gfx.Point: a point-like object, which specifies a vector of reflection
// b: null
if(arguments.length == 1){
b = a.y;
a = a.x;
}
// branch
// a: Number: an x coordinate value
// b: Number: a y coordinate value
// make a unit vector
var a2 = a * a, b2 = b * b, n2 = a2 + b2, xy = 2 * a * b / n2;
return new m.Matrix2D({xx: 2 * a2 / n2 - 1, xy: xy, yx: xy, yy: 2 * b2 / n2 - 1}); // dojox.gfx.matrix.Matrix2D
},
project: function(a, b){
// summary: forms an orthogonal projection matrix
// description: The resulting matrix is used to project points orthogonally on a vector,
// which goes through the origin.
// a: dojox.gfx.Point: a point-like object, which specifies a vector of projection
// b: null
if(arguments.length == 1){
b = a.y;
a = a.x;
}
// branch
// a: Number: an x coordinate value
// b: Number: a y coordinate value
// make a unit vector
var a2 = a * a, b2 = b * b, n2 = a2 + b2, xy = a * b / n2;
return new m.Matrix2D({xx: a2 / n2, xy: xy, yx: xy, yy: b2 / n2}); // dojox.gfx.matrix.Matrix2D
},
// ensure matrix 2D conformance
normalize: function(matrix){
// summary: converts an object to a matrix, if necessary
// description: Converts any 2D matrix-like object or an array of
// such objects to a valid dojox.gfx.matrix.Matrix2D object.
// matrix: Object: an object, which is converted to a matrix, if necessary
return (matrix instanceof m.Matrix2D) ? matrix : new m.Matrix2D(matrix); // dojox.gfx.matrix.Matrix2D
},
// common operations
clone: function(matrix){
// summary: creates a copy of a 2D matrix
// matrix: dojox.gfx.matrix.Matrix2D: a 2D matrix-like object to be cloned
var obj = new m.Matrix2D();
for(var i in matrix){
if(typeof(matrix[i]) == "number" && typeof(obj[i]) == "number" && obj[i] != matrix[i]) obj[i] = matrix[i];
}
return obj; // dojox.gfx.matrix.Matrix2D
},
invert: function(matrix){
// summary: inverts a 2D matrix
// matrix: dojox.gfx.matrix.Matrix2D: a 2D matrix-like object to be inverted
var M = m.normalize(matrix),
D = M.xx * M.yy - M.xy * M.yx,
M = new m.Matrix2D({
xx: M.yy/D, xy: -M.xy/D,
yx: -M.yx/D, yy: M.xx/D,
dx: (M.xy * M.dy - M.yy * M.dx) / D,
dy: (M.yx * M.dx - M.xx * M.dy) / D
});
return M; // dojox.gfx.matrix.Matrix2D
},
_multiplyPoint: function(matrix, x, y){
// summary: applies a matrix to a point
// matrix: dojox.gfx.matrix.Matrix2D: a 2D matrix object to be applied
// x: Number: an x coordinate of a point
// y: Number: a y coordinate of a point
return {x: matrix.xx * x + matrix.xy * y + matrix.dx, y: matrix.yx * x + matrix.yy * y + matrix.dy}; // dojox.gfx.Point
},
multiplyPoint: function(matrix, /* Number||Point */ a, /* Number, optional */ b){
// summary: applies a matrix to a point
// matrix: dojox.gfx.matrix.Matrix2D: a 2D matrix object to be applied
// a: Number: an x coordinate of a point
// b: Number: a y coordinate of a point
var M = m.normalize(matrix);
if(typeof a == "number" && typeof b == "number"){
return m._multiplyPoint(M, a, b); // dojox.gfx.Point
}
// branch
// matrix: dojox.gfx.matrix.Matrix2D: a 2D matrix object to be applied
// a: dojox.gfx.Point: a point
// b: null
return m._multiplyPoint(M, a.x, a.y); // dojox.gfx.Point
},
multiply: function(matrix){
// summary: combines matrices by multiplying them sequentially in the given order
// matrix: dojox.gfx.matrix.Matrix2D...: a 2D matrix-like object,
// all subsequent arguments are matrix-like objects too
var M = m.normalize(matrix);
// combine matrices
for(var i = 1; i < arguments.length; ++i){
var l = M, r = m.normalize(arguments[i]);
M = new m.Matrix2D();
M.xx = l.xx * r.xx + l.xy * r.yx;
M.xy = l.xx * r.xy + l.xy * r.yy;
M.yx = l.yx * r.xx + l.yy * r.yx;
M.yy = l.yx * r.xy + l.yy * r.yy;
M.dx = l.xx * r.dx + l.xy * r.dy + l.dx;
M.dy = l.yx * r.dx + l.yy * r.dy + l.dy;
}
return M; // dojox.gfx.matrix.Matrix2D
},
// high level operations
_sandwich: function(matrix, x, y){
// summary: applies a matrix at a centrtal point
// matrix: dojox.gfx.matrix.Matrix2D: a 2D matrix-like object, which is applied at a central point
// x: Number: an x component of the central point
// y: Number: a y component of the central point
return m.multiply(m.translate(x, y), matrix, m.translate(-x, -y)); // dojox.gfx.matrix.Matrix2D
},
scaleAt: function(a, b, c, d){
// summary: scales a picture using a specified point as a center of scaling
// description: Compare with dojox.gfx.matrix.scale().
// a: Number: a scaling factor used for the x coordinate
// b: Number: a scaling factor used for the y coordinate
// c: Number: an x component of a central point
// d: Number: a y component of a central point
// accepts several signatures:
// 1) uniform scale factor, Point
// 2) uniform scale factor, x, y
// 3) x scale, y scale, Point
// 4) x scale, y scale, x, y
switch(arguments.length){
case 4:
// a and b are scale factor components, c and d are components of a point
return m._sandwich(m.scale(a, b), c, d); // dojox.gfx.matrix.Matrix2D
case 3:
if(typeof c == "number"){
// branch
// a: Number: a uniform scaling factor used for both coordinates
// b: Number: an x component of a central point
// c: Number: a y component of a central point
// d: null
return m._sandwich(m.scale(a), b, c); // dojox.gfx.matrix.Matrix2D
}
// branch
// a: Number: a scaling factor used for the x coordinate
// b: Number: a scaling factor used for the y coordinate
// c: dojox.gfx.Point: a central point
// d: null
return m._sandwich(m.scale(a, b), c.x, c.y); // dojox.gfx.matrix.Matrix2D
}
// branch
// a: Number: a uniform scaling factor used for both coordinates
// b: dojox.gfx.Point: a central point
// c: null
// d: null
return m._sandwich(m.scale(a), b.x, b.y); // dojox.gfx.matrix.Matrix2D
},
rotateAt: function(angle, a, b){
// summary: rotates a picture using a specified point as a center of rotation
// description: Compare with dojox.gfx.matrix.rotate().
// angle: Number: an angle of rotation in radians (>0 for CW)
// a: Number: an x component of a central point
// b: Number: a y component of a central point
// accepts several signatures:
// 1) rotation angle in radians, Point
// 2) rotation angle in radians, x, y
if(arguments.length > 2){
return m._sandwich(m.rotate(angle), a, b); // dojox.gfx.matrix.Matrix2D
}
// branch
// angle: Number: an angle of rotation in radians (>0 for CCW)
// a: dojox.gfx.Point: a central point
// b: null
return m._sandwich(m.rotate(angle), a.x, a.y); // dojox.gfx.matrix.Matrix2D
},
rotategAt: function(degree, a, b){
// summary: rotates a picture using a specified point as a center of rotation
// description: Compare with dojox.gfx.matrix.rotateg().
// degree: Number: an angle of rotation in degrees (>0 for CW)
// a: Number: an x component of a central point
// b: Number: a y component of a central point
// accepts several signatures:
// 1) rotation angle in degrees, Point
// 2) rotation angle in degrees, x, y
if(arguments.length > 2){
return m._sandwich(m.rotateg(degree), a, b); // dojox.gfx.matrix.Matrix2D
}
// branch
// degree: Number: an angle of rotation in degrees (>0 for CCW)
// a: dojox.gfx.Point: a central point
// b: null
return m._sandwich(m.rotateg(degree), a.x, a.y); // dojox.gfx.matrix.Matrix2D
},
skewXAt: function(angle, a, b){
// summary: skews a picture along the x axis using a specified point as a center of skewing
// description: Compare with dojox.gfx.matrix.skewX().
// angle: Number: an skewing angle in radians
// a: Number: an x component of a central point
// b: Number: a y component of a central point
// accepts several signatures:
// 1) skew angle in radians, Point
// 2) skew angle in radians, x, y
if(arguments.length > 2){
return m._sandwich(m.skewX(angle), a, b); // dojox.gfx.matrix.Matrix2D
}
// branch
// angle: Number: an skewing angle in radians
// a: dojox.gfx.Point: a central point
// b: null
return m._sandwich(m.skewX(angle), a.x, a.y); // dojox.gfx.matrix.Matrix2D
},
skewXgAt: function(degree, a, b){
// summary: skews a picture along the x axis using a specified point as a center of skewing
// description: Compare with dojox.gfx.matrix.skewXg().
// degree: Number: an skewing angle in degrees
// a: Number: an x component of a central point
// b: Number: a y component of a central point
// accepts several signatures:
// 1) skew angle in degrees, Point
// 2) skew angle in degrees, x, y
if(arguments.length > 2){
return m._sandwich(m.skewXg(degree), a, b); // dojox.gfx.matrix.Matrix2D
}
// branch
// degree: Number: an skewing angle in degrees
// a: dojox.gfx.Point: a central point
// b: null
return m._sandwich(m.skewXg(degree), a.x, a.y); // dojox.gfx.matrix.Matrix2D
},
skewYAt: function(angle, a, b){
// summary: skews a picture along the y axis using a specified point as a center of skewing
// description: Compare with dojox.gfx.matrix.skewY().
// angle: Number: an skewing angle in radians
// a: Number: an x component of a central point
// b: Number: a y component of a central point
// accepts several signatures:
// 1) skew angle in radians, Point
// 2) skew angle in radians, x, y
if(arguments.length > 2){
return m._sandwich(m.skewY(angle), a, b); // dojox.gfx.matrix.Matrix2D
}
// branch
// angle: Number: an skewing angle in radians
// a: dojox.gfx.Point: a central point
// b: null
return m._sandwich(m.skewY(angle), a.x, a.y); // dojox.gfx.matrix.Matrix2D
},
skewYgAt: function(/* Number */ degree, /* Number||Point */ a, /* Number, optional */ b){
// summary: skews a picture along the y axis using a specified point as a center of skewing
// description: Compare with dojox.gfx.matrix.skewYg().
// degree: Number: an skewing angle in degrees
// a: Number: an x component of a central point
// b: Number: a y component of a central point
// accepts several signatures:
// 1) skew angle in degrees, Point
// 2) skew angle in degrees, x, y
if(arguments.length > 2){
return m._sandwich(m.skewYg(degree), a, b); // dojox.gfx.matrix.Matrix2D
}
// branch
// degree: Number: an skewing angle in degrees
// a: dojox.gfx.Point: a central point
// b: null
return m._sandwich(m.skewYg(degree), a.x, a.y); // dojox.gfx.matrix.Matrix2D
}
//TODO: rect-to-rect mapping, scale-to-fit (isotropic and anisotropic versions)
});
})();
// propagate Matrix2D up
dojox.gfx.Matrix2D = dojox.gfx.matrix.Matrix2D;
