- Author:
- David Nickerson <david.nickerson@gmail.com>
- Date:
- 2021-09-17 15:39:51+12:00
- Desc:
- tweak html formatting
- Permanent Source URI:
- https://models.fieldml.org/workspace/a1/rawfile/c47db6b2fedb368422c7f4d5191aeb9f319ad684/dojo-presentation/js/dojo/dojox/gfx3d/matrix.js
dojo.provide("dojox.gfx3d.matrix");
// candidates for dojox.math:
dojox.gfx3d.matrix._degToRad = function(degree){ return Math.PI * degree / 180; };
dojox.gfx3d.matrix._radToDeg = function(radian){ return radian / Math.PI * 180; };
dojox.gfx3d.matrix.Matrix3D = function(arg){
// summary: a 3D matrix object
// description: Normalizes a 3D matrix-like object. If arrays is passed,
// all objects of the array are normalized and multiplied sequentially.
// arg: Object
// a 3D matrix-like object, a number, or an array of such objects
if(arg){
if(typeof arg == "number"){
this.xx = this.yy = this.zz = arg;
}else if(arg instanceof Array){
if(arg.length > 0){
var m = dojox.gfx3d.matrix.normalize(arg[0]);
// combine matrices
for(var i = 1; i < arg.length; ++i){
var l = m;
var r = dojox.gfx3d.matrix.normalize(arg[i]);
m = new dojox.gfx3d.matrix.Matrix3D();
m.xx = l.xx * r.xx + l.xy * r.yx + l.xz * r.zx;
m.xy = l.xx * r.xy + l.xy * r.yy + l.xz * r.zy;
m.xz = l.xx * r.xz + l.xy * r.yz + l.xz * r.zz;
m.yx = l.yx * r.xx + l.yy * r.yx + l.yz * r.zx;
m.yy = l.yx * r.xy + l.yy * r.yy + l.yz * r.zy;
m.yz = l.yx * r.xz + l.yy * r.yz + l.yz * r.zz;
m.zx = l.zx * r.xx + l.zy * r.yx + l.zz * r.zx;
m.zy = l.zx * r.xy + l.zy * r.yy + l.zz * r.zy;
m.zz = l.zx * r.xz + l.zy * r.yz + l.zz * r.zz;
m.dx = l.xx * r.dx + l.xy * r.dy + l.xz * r.dz + l.dx;
m.dy = l.yx * r.dx + l.yy * r.dy + l.yz * r.dz + l.dy;
m.dz = l.zx * r.dx + l.zy * r.dy + l.zz * r.dz + l.dz;
}
dojo.mixin(this, m);
}
}else{
dojo.mixin(this, arg);
}
}
};
// the default (identity) matrix, which is used to fill in missing values
dojo.extend(dojox.gfx3d.matrix.Matrix3D, {xx: 1, xy: 0, xz: 0, yx: 0, yy: 1, yz: 0, zx: 0, zy: 0, zz: 1, dx: 0, dy: 0, dz: 0});
dojo.mixin(dojox.gfx3d.matrix, {
// summary: class constants, and methods of dojox.gfx3d.matrix
// matrix constants
// identity: dojox.gfx3d.matrix.Matrix3D
// an identity matrix constant: identity * (x, y, z) == (x, y, z)
identity: new dojox.gfx3d.matrix.Matrix3D(),
// matrix creators
translate: function(a, b, c){
// 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
// c: Number: a z coordinate value
if(arguments.length > 1){
return new dojox.gfx3d.matrix.Matrix3D({dx: a, dy: b, dz: c}); // dojox.gfx3d.matrix.Matrix3D
}
// branch
// a: Object: a point-like object, which specifies offsets for 3 dimensions
// b: null
return new dojox.gfx3d.matrix.Matrix3D({dx: a.x, dy: a.y, dz: a.z}); // dojox.gfx3d.matrix.Matrix3D
},
scale: function(a, b, c){
// 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
// c: Number: a scaling factor used for the z coordinate
if(arguments.length > 1){
return new dojox.gfx3d.matrix.Matrix3D({xx: a, yy: b, zz: c}); // dojox.gfx3d.matrix.Matrix3D
}
if(typeof a == "number"){
// branch
// a: Number: a uniform scaling factor used for the all coordinates
// b: null
return new dojox.gfx3d.matrix.Matrix3D({xx: a, yy: a, zz: a}); // dojox.gfx3d.matrix.Matrix3D
}
// branch
// a: Object: a point-like object, which specifies scale factors for 3 dimensions
// b: null
return new dojox.gfx3d.matrix.Matrix3D({xx: a.x, yy: a.y, zz: a.z}); // dojox.gfx3d.matrix.Matrix3D
},
rotateX: function(angle){
// summary: forms a rotating matrix (about the x axis)
// 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 dojox.gfx3d.matrix.Matrix3D({yy: c, yz: -s, zy: s, zz: c}); // dojox.gfx3d.matrix.Matrix3D
},
rotateXg: function(degree){
// summary: forms a rotating matrix (about the x axis)
// description: The resulting matrix is used to rotate points
// around the origin of coordinates (0, 0) by specified degree.
// See dojox.gfx3d.matrix.rotateX() for comparison.
// degree: Number: an angle of rotation in degrees (>0 for CW)
return dojox.gfx3d.matrix.rotateX(dojox.gfx3d.matrix._degToRad(degree)); // dojox.gfx3d.matrix.Matrix3D
},
rotateY: function(angle){
// summary: forms a rotating matrix (about the y axis)
// 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 dojox.gfx3d.matrix.Matrix3D({xx: c, xz: s, zx: -s, zz: c}); // dojox.gfx3d.matrix.Matrix3D
},
rotateYg: function(degree){
// summary: forms a rotating matrix (about the y axis)
// description: The resulting matrix is used to rotate points
// around the origin of coordinates (0, 0) by specified degree.
// See dojox.gfx3d.matrix.rotateY() for comparison.
// degree: Number: an angle of rotation in degrees (>0 for CW)
return dojox.gfx3d.matrix.rotateY(dojox.gfx3d.matrix._degToRad(degree)); // dojox.gfx3d.matrix.Matrix3D
},
rotateZ: function(angle){
// summary: forms a rotating matrix (about the z axis)
// 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 dojox.gfx3d.matrix.Matrix3D({xx: c, xy: -s, yx: s, yy: c}); // dojox.gfx3d.matrix.Matrix3D
},
rotateZg: function(degree){
// summary: forms a rotating matrix (about the z axis)
// description: The resulting matrix is used to rotate points
// around the origin of coordinates (0, 0) by specified degree.
// See dojox.gfx3d.matrix.rotateZ() for comparison.
// degree: Number: an angle of rotation in degrees (>0 for CW)
return dojox.gfx3d.matrix.rotateZ(dojox.gfx3d.matrix._degToRad(degree)); // dojox.gfx3d.matrix.Matrix3D
},
// camera transformation
cameraTranslate: function(a, b, c){
// 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
// c: Number: a z coordinate value
if(arguments.length > 1){
return new dojox.gfx3d.matrix.Matrix3D({dx: -a, dy: -b, dz: -c}); // dojox.gfx3d.matrix.Matrix3D
}
// branch
// a: Object: a point-like object, which specifies offsets for 3 dimensions
// b: null
return new dojox.gfx3d.matrix.Matrix3D({dx: -a.x, dy: -a.y, dz: -a.z}); // dojox.gfx3d.matrix.Matrix3D
},
cameraRotateX: function(angle){
// summary: forms a rotating matrix (about the x axis) in cameraTransform manner
// 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 dojox.gfx3d.matrix.Matrix3D({yy: c, yz: -s, zy: s, zz: c}); // dojox.gfx3d.matrix.Matrix3D
},
cameraRotateXg: function(degree){
// summary: forms a rotating matrix (about the x axis)in cameraTransform manner
// description: The resulting matrix is used to rotate points
// around the origin of coordinates (0, 0) by specified degree.
// See dojox.gfx3d.matrix.rotateX() for comparison.
// degree: Number: an angle of rotation in degrees (>0 for CW)
return dojox.gfx3d.matrix.rotateX(dojox.gfx3d.matrix._degToRad(degree)); // dojox.gfx3d.matrix.Matrix3D
},
cameraRotateY: function(angle){
// summary: forms a rotating matrix (about the y axis) in cameraTransform manner
// 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 dojox.gfx3d.matrix.Matrix3D({xx: c, xz: s, zx: -s, zz: c}); // dojox.gfx3d.matrix.Matrix3D
},
cameraRotateYg: function(degree){
// summary: forms a rotating matrix (about the y axis) in cameraTransform manner
// description: The resulting matrix is used to rotate points
// around the origin of coordinates (0, 0) by specified degree.
// See dojox.gfx3d.matrix.rotateY() for comparison.
// degree: Number: an angle of rotation in degrees (>0 for CW)
return dojox.gfx3d.matrix.rotateY(dojox.gfx3d.matrix._degToRad(degree)); // dojox.gfx3d.matrix.Matrix3D
},
cameraRotateZ: function(angle){
// summary: forms a rotating matrix (about the z axis) in cameraTransform manner
// 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 dojox.gfx3d.matrix.Matrix3D({xx: c, xy: -s, yx: s, yy: c}); // dojox.gfx3d.matrix.Matrix3D
},
cameraRotateZg: function(degree){
// summary: forms a rotating matrix (about the z axis) in cameraTransform manner
// description: The resulting matrix is used to rotate points
// around the origin of coordinates (0, 0) by specified degree.
// See dojox.gfx3d.matrix.rotateZ() for comparison.
// degree: Number: an angle of rotation in degrees (>0 for CW)
return dojox.gfx3d.matrix.rotateZ(dojox.gfx3d.matrix._degToRad(degree)); // dojox.gfx3d.matrix.Matrix3D
},
// ensure matrix 3D conformance
normalize: function(matrix){
// summary: converts an object to a matrix, if necessary
// description: Converts any 3D matrix-like object or an array of
// such objects to a valid dojox.gfx3d.matrix.Matrix3D object.
// matrix: Object: an object, which is converted to a matrix, if necessary
return (matrix instanceof dojox.gfx3d.matrix.Matrix3D) ? matrix : new dojox.gfx3d.matrix.Matrix3D(matrix); // dojox.gfx3d.matrix.Matrix3D
},
// common operations
clone: function(matrix){
// summary: creates a copy of a 3D matrix
// matrix: dojox.gfx3d.matrix.Matrix3D: a 3D matrix-like object to be cloned
var obj = new dojox.gfx3d.matrix.Matrix3D();
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.gfx3d.matrix.Matrix3D
},
invert: function(matrix){
// summary: inverts a 2D matrix
// matrix: dojox.gfx.matrix.Matrix3D: a 2D matrix-like object to be inverted
var m = dojox.gfx3d.matrix.normalize(matrix);
var D = m.xx * m.yy * m.zz + m.xy * m.yz * m.zx + m.xz * m.yx * m.zy - m.xx * m.yz * m.zy - m.xy * m.yx * m.zz - m.xz * m.yy * m.zx;
var M = new dojox.gfx3d.matrix.Matrix3D({
xx: (m.yy * m.zz - m.yz * m.zy) / D,
xy: (m.xz * m.zy - m.xy * m.zz) / D,
xz: (m.xy * m.yz - m.xz * m.yy) / D,
yx: (m.yz * m.zx - m.yx * m.zz) / D,
yy: (m.xx * m.zz - m.xz * m.zx) / D,
yz: (m.xz * m.yx - m.xx * m.yz) / D,
zx: (m.yx * m.zy - m.yy * m.zx) / D,
zy: (m.xy * m.zx - m.xx * m.zy) / D,
zz: (m.xx * m.yy - m.xy * m.yx) / D,
dx: -1 * (m.xy * m.yz * m.dz + m.xz * m.dy * m.zy + m.dx * m.yy * m.zz - m.xy * m.dy * m.zz - m.xz * m.yy * m.dz - m.dx * m.yz * m.zy) / D,
dy: (m.xx * m.yz * m.dz + m.xz * m.dy * m.zx + m.dx * m.yx * m.zz - m.xx * m.dy * m.zz - m.xz * m.yx * m.dz - m.dx * m.yz * m.zx) / D,
dz: -1 * (m.xx * m.yy * m.dz + m.xy * m.dy * m.zx + m.dx * m.yx * m.zy - m.xx * m.dy * m.zy - m.xy * m.yx * m.dz - m.dx * m.yy * m.zx) / D
});
return M; // dojox.gfx3d.matrix.Matrix3D
},
_multiplyPoint: function(m, x, y, z){
// summary: applies a matrix to a point
// matrix: dojox.gfx3d.matrix.Matrix3D: a 3D matrix object to be applied
// x: Number: an x coordinate of a point
// y: Number: a y coordinate of a point
// z: Number: a z coordinate of a point
return {x: m.xx * x + m.xy * y + m.xz * z + m.dx, y: m.yx * x + m.yy * y + m.yz * z + m.dy, z: m.zx * x + m.zy * y + m.zz * z + m.dz}; // Object
},
multiplyPoint: function(matrix, /* Number||Point */ a, /* Number, optional */ b, /* Number, optional */ c){
// summary: applies a matrix to a point
// matrix: dojox.gfx3d.matrix.Matrix3D: a 3D matrix object to be applied
// a: Number: an x coordinate of a point
// b: Number: a y coordinate of a point
// c: Number: a z coordinate of a point
var m = dojox.gfx3d.matrix.normalize(matrix);
if(typeof a == "number" && typeof b == "number" && typeof c == "number"){
return dojox.gfx3d.matrix._multiplyPoint(m, a, b, c); // Object
}
// branch
// matrix: dojox.gfx3d.matrix.Matrix3D: a 3D matrix object to be applied
// a: Object: a point
// b: null
// c: null
return dojox.gfx3d.matrix._multiplyPoint(m, a.x, a.y, a.z); // Object
},
multiply: function(matrix){
// summary: combines matrices by multiplying them sequentially in the given order
// matrix: dojox.gfx3d.matrix.Matrix3D...: a 3D matrix-like object,
// all subsequent arguments are matrix-like objects too
var m = dojox.gfx3d.matrix.normalize(matrix);
// combine matrices
for(var i = 1; i < arguments.length; ++i){
var l = m;
var r = dojox.gfx3d.matrix.normalize(arguments[i]);
m = new dojox.gfx3d.matrix.Matrix3D();
m.xx = l.xx * r.xx + l.xy * r.yx + l.xz * r.zx;
m.xy = l.xx * r.xy + l.xy * r.yy + l.xz * r.zy;
m.xz = l.xx * r.xz + l.xy * r.yz + l.xz * r.zz;
m.yx = l.yx * r.xx + l.yy * r.yx + l.yz * r.zx;
m.yy = l.yx * r.xy + l.yy * r.yy + l.yz * r.zy;
m.yz = l.yx * r.xz + l.yy * r.yz + l.yz * r.zz;
m.zx = l.zx * r.xx + l.zy * r.yx + l.zz * r.zx;
m.zy = l.zx * r.xy + l.zy * r.yy + l.zz * r.zy;
m.zz = l.zx * r.xz + l.zy * r.yz + l.zz * r.zz;
m.dx = l.xx * r.dx + l.xy * r.dy + l.xz * r.dz + l.dx;
m.dy = l.yx * r.dx + l.yy * r.dy + l.yz * r.dz + l.dy;
m.dz = l.zx * r.dx + l.zy * r.dy + l.zz * r.dz + l.dz;
}
return m; // dojox.gfx3d.matrix.Matrix3D
},
_project: function(m, x, y, z){
// summary: applies a matrix to a point
// matrix: dojox.gfx3d.matrix.Matrix3D: a 3D matrix object to be applied
// x: Number: an x coordinate of a point
// y: Number: a y coordinate of a point
// z: Number: a z coordinate of a point
return { // Object
x: m.xx * x + m.xy * y + m.xz * z + m.dx,
y: m.yx * x + m.yy * y + m.yz * z + m.dy,
z: m.zx * x + m.zy * y + m.zz * z + m.dz};
},
project: function(matrix, /* Number||Point */ a, /* Number, optional */ b, /* Number, optional */ c){
// summary: applies a matrix to a point
// matrix: dojox.gfx3d.matrix.Matrix3D: a 3D matrix object to be applied
// a: Number: an x coordinate of a point
// b: Number: a y coordinate of a point
// c: Number: a z coordinate of a point
var m = dojox.gfx3d.matrix.normalize(matrix);
if(typeof a == "number" && typeof b == "number" && typeof c == "number"){
return dojox.gfx3d.matrix._project(m, a, b, c); // Object
}
// branch
// matrix: dojox.gfx3d.matrix.Matrix3D: a 3D matrix object to be applied
// a: Object: a point
// b: null
// c: null
return dojox.gfx3d.matrix._project(m, a.x, a.y, a.z); // Object
}
});
// propagate matrix up
dojox.gfx3d.Matrix3D = dojox.gfx3d.matrix.Matrix3D;
