The Math script provides Vec3
, Mat4
and Quat
classes to manage three dimensional vectors, four by four matrices and quaternions respectively.
One very interesting thing to point about the Math script is that all Vec3
, Mat4
and Quat
methods are generics. This means that all instance methods of Vec3
, Mat4
, and Quat
can also be accessed as static methods in which the first parameter of the static method is the receiver. The receiver does not have to be an instance of the class but can instead be a Vec3
-like, Mat4
-like or Quat
-like object. This means that a simple array (i.e []
) can be used as the receiver for these methods.
Although the syntax section for each method will include the generic and non-generic one, the arguments for each method will be described as with the instance method syntax.
All methods that do not return something in particular in the math package are chainable.
Say you want to add two Vec3
vectors, v1
and v2
. Then there are three ways of performing this operation:
v1.add(v2)
Returns a new class with the result of adding v1
and v2
. This operation does not modify v1
or v2
.v1.$add(v2)
Returns the result of adding v1
to v2
, but it alters v1
updating it with the result.vResult.add2(v1, v2)
Stores the result of adding v1
to v2
in vResult
, another Vec3
instance.These are the conventions we will be using for method naming. Methods altering the receiver will have a dollar sign (i.e. $
), as opposed to methods creating a new instance with the result. Methods requiring a receiver and the instances involved in the operation as formal parameters will be suffixed with the number 2
.
New from version 1.3:
All classes now extend from Array
or some DataView
class (i.e. some typed array). This means that Vec3
, Mat4
and Quat
-like objects are now plain arrays and not plain objects. I have added getters for all properties in Vec3
, Mat4
and Quat
classes so you can still access them via vec.x
, etc, but remember that the inner implementation is now an array, so vec3[0]
will also work. The examples have been updated to reflect this.
This implementation changes the signature for some methods and probably if you used object literals for Vec3
, Mat4
and Quat
classes these things will have to be changed into arrays. The good thing about this is a noticeable boost in performance everywhere in the library, and in particular in the math functions. More information about this can be found in my blog.
A class to handle three dimensional vectors.
Create a new Vec3
instance from the x
, y
, z
coordinates of a Quat.
PhiloGL.Vec3.fromQuat(q);
Quat
instance.Create a vector from a Quaternion.
var q = new PhiloGL.Quat(1, 2, 3, 4),
v = PhiloGL.Vec3.fromQuat(q); //Vec3(1, 2, 3)
Creates a new Vec3
instance.
var v = new PhiloGL.Vec3(x, y, z);
Create a (0, 0, 0) vector.
var v = new PhiloGL.Vec3();
Create a (1, 2, 3) vector.
var v = new PhiloGL.Vec3(1, 2, 3);
Set x
, y
, z
coordinates of one Vec3
into another Vec3
.
v1.setVec3(v2);
PhiloGL.Vec3.setVec3(v1, v2);
Vec3
instance.Create two vectors and assign one vectors components to the other one.
var v1 = new PhiloGL.Vec3(1, 2, 3),
v2 = new PhiloGL.Vec3(4, 5, 6);
v1.setVec3(v2); //v1 now contains (x=4, y=5, z=6)
Set an object’s x
, y
, z
components to another object.
var v1 = [],
v2 = [ 4, 5, 6 ];
PhiloGL.Vec3.setVec3(v1, v2); //v1 now has [4, 5, 6]
Set x
, y
, z
coordinates.
v1.set(x, y, z);
PhiloGL.Vec3.set(v1, x, y, z);
Create two vectors and assign one vectors components to the other one.
var v1 = new PhiloGL.Vec3(1, 2, 3),
v2 = new PhiloGL.Vec3(4, 5, 6);
v1.set(v2.x, v2.y, v2.z); //v1 now contains (x=4, y=5, z=6)
Set an object’s x
, y
, z
components to another object.
var v1 = [],
v2 = [ 4, 5, 6 ];
PhiloGL.Vec3.set(v1, v2.x, v2.y, v2.z); //v1 now has [4, 5, 6]
Adds the x
, y
, z
components of two Vec3
objects. Creates a new Vec3
instance and does not modify the original objects.
v1.add(v2);
PhiloGL.Vec3.add(v1, v2);
Vec3
instance.Create two vectors and add them.
var v1 = new PhiloGL.Vec3(1, 2, 3),
v2 = new PhiloGL.Vec3(4, 5, 6);
v1.add(v2); //v1 and v2 are still the same but a new Vec3(5, 7, 9) was created.
Create two x
, y
, z
objects and add them.
var v1 = [ 1, 2, 3 ],
v2 = [ 4, 5, 6 ];
PhiloGL.Vec3.add(v1, v2); //v1 and v2 are still the same but a new Vec3(5, 7, 9) was created.
Adds the x
, y
, z
components of two Vec3
objects. Modifies the original object.
v1.$add(v2);
PhiloGL.Vec3.$add(v1, v2);
Vec3
instance.Create two vectors and add them.
var v1 = new PhiloGL.Vec3(1, 2, 3),
v2 = new PhiloGL.Vec3(4, 5, 6);
v1.$add(v2); //v1 is now Vec3(5, 7, 9).
Create two x
, y
, z
objects and add them.
var v1 = [ 1, 2, 3 ],
v2 = [ 4, 5, 6 ];
PhiloGL.Vec3.$add(v1, v2); //v1 is now [ 5, 7, 9 ].
Adds the x
, y
, z
components of two Vec3
objects and stores the result in the receiver.
v1.add2(v2, v3);
PhiloGL.Vec3.add2(v1, v2, v3);
Vec3
instance.Vec3
instance.Create two vectors and add them.
var v1 = new PhiloGL.Vec3(),
v2 = new PhiloGL.Vec3(1, 2, 3),
v3 = new PhiloGL.Vec3(4, 5, 6);
v1.add2(v2, v3); //v1 is now Vec3(5, 7, 9), v2 and v3 are unchanged.
Create two x
, y
, z
objects and add them.
var v1 = [],
v2 = [ 1, 2, 3 ],
v3 = [ 4, 5, 6 ];
PhiloGL.Vec3.add2(v1, v2, v3); //v2 and v3 are still the same but v1 is [ 5, 7, 9 ].
Substracts the x
, y
, z
components of two Vec3
objects. Creates a new Vec3
instance and does not modify the original objects.
v1.sub(v2);
PhiloGL.Vec3.sub(v1, v2);
Vec3
instance.Create two vectors and substract them.
var v1 = new PhiloGL.Vec3(1, 2, 3),
v2 = new PhiloGL.Vec3(4, 5, 6);
v1.sub(v2); //v1 and v2 are still the same but a new Vec3(-3, -3, -3) was created.
Create two x
, y
, z
objects and substract them.
var v1 = [ 1, 2, 3 ],
v2 = [ 4, 5, 6 ];
PhiloGL.Vec3.sub(v1, v2); //v1 and v2 are still the same but a new Vec3(-3, -3, -3) was created.
Substracts the x
, y
, z
components of two Vec3
objects. Modifies the original object.
v1.$sub(v2);
PhiloGL.Vec3.$sub(v1, v2);
Vec3
instance.Create two vectors and substract them.
var v1 = new PhiloGL.Vec3(1, 2, 3),
v2 = new PhiloGL.Vec3(4, 5, 6);
v1.$sub(v2); //v1 is now Vec3(-3, -3, -3).
Create two x
, y
, z
objects and add them.
var v1 = [ 1, 2, 3 ],
v2 = [ 4, 5, 6 ];
PhiloGL.Vec3.$sub(v1, v2); //v1 is now [ -3, -3, -3 ].
Substracts the x
, y
, z
components of two Vec3
objects and stores the result in the receiver.
v1.sub2(v2, v3);
PhiloGL.Vec3.sub2(v1, v2, v3);
Vec3
instance.Vec3
instance.Create two vectors and substract them.
var v1 = new PhiloGL.Vec3(),
v2 = new PhiloGL.Vec3(1, 2, 3),
v3 = new PhiloGL.Vec3(4, 5, 6);
v1.sub2(v2, v3); //v1 is now Vec3(-3, -3, -3), v2 and v3 are unchanged.
Create two x
, y
, z
objects and substract them.
var v1 = [],
v2 = [ 1, 2, 3 ],
v3 = [ 4, 5, 6 ];
PhiloGL.Vec3.sub2(v1, v2, v3); //v2 and v3 are still the same but v1 is { x: -3, y: -3, z: -3 }.
Scales the Vec3 vector by a real number. Creates a new Vec3 with the scaled components.
v1.scale(s);
PhiloGL.Vec3.scale(v1, s);
Create a vector and scale it by 2.
var v1 = new PhiloGL.Vec3(1, 2, 3);
v1.scale(2); //v1 is unchanged but a new Vec3(2, 4, 6) is created.
Create an x
, y
, z
object and scale it by 2.
var v1 = [ 1, 2, 3 ];
PhiloGL.Vec3.scale(v1, 2); //v1 is still the same but a new Vec3(2, 4, 6) was created.
Scales the Vec3 vector by a real number. Changes the original object.
v1.$scale(s);
PhiloGL.Vec3.$scale(v1, s);
Create a vector and scale it by 2.
var v1 = new PhiloGL.Vec3(1, 2, 3);
v1.$scale(2); //v1 is now Vec3(2, 4, 6).
Create an x
, y
, z
object and scale it by 2.
var v1 = [ 1, 2, 3 ];
PhiloGL.Vec3.$scale(v1, 2); //v1 is now [ 2, 4, 6 ].
Negates a Vec3
. Returns a new instance.
v1.neg();
PhiloGL.Vec3.neg(v1);
Create a vector and negate it.
var v1 = new PhiloGL.Vec3(1, 2, 3);
v1.neg(); //v1 is unchanged but a new Vec3(-1, -2, -3) is created.
Create an x
, y
, z
object and negate it.
var v1 = [ 1, 2, 3 ];
PhiloGL.Vec3.neg(v1); //v1 is still the same but a new Vec3(-1, -2, -3).
Negates a Vec3
. Changes the original object.
v1.$neg();
PhiloGL.Vec3.$neg(v1);
Create a vector and negate it.
var v1 = new PhiloGL.Vec3(1, 2, 3);
v1.$neg(); //v1 is now Vec3(-1, -2, -3).
Create an x
, y
, z
object and negate it.
var v1 = [ 1, 2, 3 ];
PhiloGL.Vec3.neg(v1); //v1 is now [ -1, -2, -3 ].
Creates a unit vector from the coordinates of Vec3
.
v1.unit();
PhiloGL.Vec3.unit(v1);
Create a vector and make a unit vector from it.
var v1 = new PhiloGL.Vec3(1, 2, 3);
v1.unit(); //v1 is unchanged but a new unit vector Vec3 is created.
Create an x
, y
, z
object and make a unit vector from it.
var v1 = [ 1, 2, 3 ];
PhiloGL.Vec3.unit(v1); //v1 is still the same but a new Vec3 that is a unit vector is created.
Creates a unit vector from the Vec3
coordinates. Changes the original object.
v1.$unit();
PhiloGL.Vec3.$unit(v1);
Create a vector and make a unit vector from it.
var v1 = new PhiloGL.Vec3(1, 2, 3);
v1.$unit(); //v1 is now a unit vector.
Create an x
, y
, z
object make a unit vector from it.
var v1 = [ 1, 2, 3 ];
PhiloGL.Vec3.$unit(v1); //v1 is now a unit vector object.
Makes a cross product of two Vec3
instances. Creates a new Vec3
and does not modify the original objects. You can find more information about the cross product here.
v1.cross(v2);
PhiloGL.Vec3.cross(v1, v2);
Vec3
instance.Create two vectors and make a cross product.
var v1 = new PhiloGL.Vec3(1, 2, 3),
v2 = new PhiloGL.Vec3(4, 5, 6);
v1.cross(v2); //v1 and v2 are still the same but a new Vec3 was created with the result.
Create two x
, y
, z
objects and make a cross product.
var v1 = [ 1, 2, 3 ],
v2 = [ 4, 5, 6 ];
//v1 and v2 are still the same but a new Vec3 with the result was created.
var ans = PhiloGL.Vec3.cross(v1, v2);
Makes a cross product of two Vec3
instances. Modifies the original object. You can find more information about the cross product here.
v1.$cross(v2);
PhiloGL.Vec3.$cross(v1, v2);
Vec3
instance.Create two vectors and make a cross product.
var v1 = new PhiloGL.Vec3(1, 2, 3),
v2 = new PhiloGL.Vec3(4, 5, 6);
v1.$cross(v2); //v1 contains now the result.
Create two x
, y
, z
objects and make a cross product.
var v1 = [ 1, 2, 3 ],
v2 = [ 4, 5, 6 ];
//v1 contains now the result.
var ans = PhiloGL.Vec3.$cross(v1, v2);
Calculates the distance between two Vec3
.
v1.distTo(v2);
PhiloGL.Vec3.distTo(v1, v2);
Vec3
instance.Create two vectors and calculate the distance.
var v1 = new PhiloGL.Vec3(1, 2, 3),
v2 = new PhiloGL.Vec3(4, 5, 6);
v1.distTo(v2); //a real value with the distance is returned.
Create two x
, y
, z
objects and calculate their distance.
var v1 = [ 1, 2, 3 ],
v2 = [ 4, 5, 6 ];
//a real number with the distance is returned.
var ans = PhiloGL.Vec3.distTo(v1, v2);
Calculates the squared distance between two Vec3
.
v1.distToSq(v2);
PhiloGL.Vec3.distToSq(v1, v2);
Vec3
instance.Create two vectors and calculate the squared distance.
var v1 = new PhiloGL.Vec3(1, 2, 3),
v2 = new PhiloGL.Vec3(4, 5, 6);
v1.distToSq(v2); //a real value with the squared distance is returned.
Create two x
, y
, z
objects and calculate their squared distance.
var v1 = [ 1, 2, 3 ],
v2 = [ 4, 5, 6 ];
//a real number with the squared distance is returned.
var ans = PhiloGL.Vec3.distToSq(v1, v2);
Calculates the norm of Vec3
.
v1.norm();
PhiloGL.Vec3.norm(v1);
Create a vector and calculate its norm.
var v1 = new PhiloGL.Vec3(1, 2, 3);
vi.norm(); //returns the real valued norm.
Create an x
, y
, z
object and calculate its norm.
var v1 = [ 1, 2, 3 ];
//A real number with the norm is returned.
var ans = PhiloGL.Vec3.norm(v1);
Calculates the squared norm of Vec3
.
v1.normSq();
PhiloGL.Vec3.normSq(v1);
Create a vector and calculate its squared norm.
var v1 = new PhiloGL.Vec3(1, 2, 3);
vi.normSq(); //returns the real valued norm.
Create an x
, y
, z
object and calculate its squared norm.
var v1 = [ 1, 2, 3 ];
//A real number with the squared norm is returned.
var ans = PhiloGL.Vec3.normSq(v1);
Calculates the dot product between two Vec3
. You can find more information about the dot product here.
v1.dot(v2);
PhiloGL.Vec3.dot(v1, v2);
Vec3
instance.Create two vectors and calculate the dot product.
var v1 = new PhiloGL.Vec3(1, 2, 3),
v2 = new PhiloGL.Vec3(4, 5, 6);
v1.dot(v2); //a real value with the dot product is returned.
Create two x
, y
, z
objects and calculate the dot product.
var v1 = [ 1, 2, 3 ],
v2 = [ 4, 5, 6 ];
//a real number with the dot product is returned.
var ans = PhiloGL.Vec3.dot(v1, v2);
Clones a vector.
v1.clone();
PhiloGL.Vec3.clone(v1);
A class to handle four by four matrices.
Create a new Mat4
instance from a Quat instance. The Quaternion must be a unit quaternion.
PhiloGL.Mat4.fromQuat(q);
Quat
instance.Create a matrix from a Quaternion.
var q = new PhiloGL.Quat(1, 2, 3, 4).$unit(),
m = PhiloGL.Mat4.fromQuat(q); //a new Mat4 instance
Creates a new Mat4
instance. If no arguments are set then an Identity matrix is created.
var m = new PhiloGL.Mat4();
var m = new PhiloGL.Mat4(n11, n12, n13, n14,
n21, n22, n23, n24,
n31, n32, n33, n34,
n41, n42, n43, n44);
Create an identity matrix.
var m = new PhiloGL.Mat4();
Create a null matrix.
var m = new PhiloGL.Mat4( 0, 0, 0, 0,
0, 0, 0, 0,
0, 0, 0, 0,
0, 0, 0, 0 );
Modifies the matrix to be an Identity matrix.
m.id();
PhiloGL.Mat4.id(m);
Create an identity matrix from some random matrix.
var m = new PhiloGL.Mat4( 1, 2, 3, 4,
1, 2, 3, 4,
1, 2, 3, 4,
1, 2, 3, 4);
m.id(); //m is now the Identity matrix.
Create an identity matrix object.
var m = [];
PhiloGL.Mat4.id(m); //m object components are the Identity matrix ones.
Set all matrix coordinates.
m.set(n11, n12, n13, n14,
n21, n22, n23, n24,
n31, n32, n33, n34,
n41, n42, n43, n44);
PhiloGL.Mat4.set(m, n11, n12, n13, n14,
n21, n22, n23, n24,
n31, n32, n33, n34,
n41, n42, n43, n44);
Create a matrix and set some values to it.
var m = new PhiloGL.Mat4();
m.set(1, 2, 3, 4,
1, 2, 3, 4,
1, 2, 3, 4,
1, 2, 3, 4);
Set an empty object matrix coordinates onto some values.
var m = [];
PhiloGL.Mat4.set(m, 1, 2, 3, 4,
1, 2, 3, 4,
1, 2, 3, 4,
1, 2, 3, 4);
Multiplies a Mat4
by a Vec3
. Returns a new Vec3
without modifying the passed in object.
m.mulVec3(v);
PhiloGL.Mat4.mulVec3(m, v);
Vec3
instance.Create a matrix and a vector and multiply them.
var m = new PhiloGL.Mat4(),
v = new PhiloGL.Vec3(1, 1, 1);
m.mulVec3(v);
Create a matrix object and a vector object and multiply them.
var m = [],
v = [];
PhiloGL.Mat4.id(m);
PhiloGL.Vec3.set(v, 1, 1, 1);
PhiloGL.Mat4.mulVec3(m, v);
Multiplies a Mat4
by a Vec3
. Modifies the receiver.
m.$mulVec3(v);
PhiloGL.Mat4.$mulVec3(m, v);
Vec3
instance.Create a matrix and a vector and multiply them.
var m = new PhiloGL.Mat4(),
v = new PhiloGL.Vec3(1, 1, 1);
m.$mulVec3(v);
Create a matrix object and a vector object and multiply them.
var m = [],
v = [];
PhiloGL.Mat4.id(m);
PhiloGL.Vec3.set(v, 1, 1, 1);
PhiloGL.Mat4.$mulVec3(m, v);
Multiplies two Mat4
. Creates a new Mat4
with the result and does not modify the original instances.
m.mulMat4(m1);
PhiloGL.Mat4.mulMat4(m, m1);
Mat4
instance.Create two matrices and multiply them.
var m = new PhiloGL.Mat4(),
m1 = new PhiloGL.Mat4();
m.mulMat4(m1); //the result is a new Identity matrix
Create a two matrices objects and multiply them.
var m = [],
m1 = [];
PhiloGL.Mat4.id(m);
PhiloGL.Mat4.id(m1);
PhiloGL.Mat4.mulMat4(m, m1);
Multiplies two Mat4
, storing the result in the receiver.
m.$mulMat4(m1);
PhiloGL.Mat4.$mulMat4(m, m1);
Mat4
instance.Create two matrices and multiply them.
var m = new PhiloGL.Mat4(),
m1 = new PhiloGL.Mat4();
m.$mulMat4(m1); //the result is stored in m.
Create a two matrices objects and multiply them.
var m = [],
m1 = [];
PhiloGL.Mat4.id(m);
PhiloGL.Mat4.id(m1);
PhiloGL.Mat4.$mulMat4(m, m1);
Multiplies two Mat4
, storing the result in the receiver.
m.mulMat42(m1, m2);
PhiloGL.Mat4.mulMat42(m, m1, m2);
Mat4
instance.Mat4
instance.Create two matrices and multiply them.
var m = new PhiloGL.Mat4(),
m1 = new PhiloGL.Mat4(),
m2 = new PhiloGL.Mat4();
m.mulMat42(m1, m2); //the result is stored in m.
Create a two matrices objects and multiply them.
var m = [],
m1 = [],
m2 = [];
PhiloGL.Mat4.id(m1);
PhiloGL.Mat4.id(m2);
PhiloGL.Mat4.mulMat42(m, m1, m2);
Adds two Mat4
. Creates a new Mat4
with the result and does not modify the original instances.
m.add(m1);
PhiloGL.Mat4.add(m, m1);
Mat4
instance.Create two matrices and add them.
var m = new PhiloGL.Mat4(),
m1 = new PhiloGL.Mat4();
m.add(m1); //the result is a new matrix
Create a two matrices objects and add them.
var m = [],
m1 = [];
PhiloGL.Mat4.id(m);
PhiloGL.Mat4.id(m1);
PhiloGL.Mat4.add(m, m1);
Adds two Mat4
, storing the result in the receiver.
m.$add(m1);
PhiloGL.Mat4.$add(m, m1);
Mat4
instance.Create two matrices and add them.
var m = new PhiloGL.Mat4(),
m1 = new PhiloGL.Mat4();
m.$add(m1); //the result is stored in m.
Create a two matrices objects and add them.
var m = [],
m1 = [];
PhiloGL.Mat4.id(m);
PhiloGL.Mat4.id(m1);
PhiloGL.Mat4.$add(m, m1);
Transposes a Mat4
matrix. More info about this operation can be found here. Creates a new Mat4
with the result.
m.transpose();
PhiloGL.Mat4.transpose(m);
Create a Mat4
matrix and transpose it.
var m = new PhiloGL.Mat4();
m.transpose(); //the result is a new Identity matrix
Transposes a Mat4
matrix. More info about this operation can be found here. Modifies the current matrix.
m.$transpose();
PhiloGL.Mat4.$transpose(m);
Create a Mat4
matrix and transpose it.
var m = new PhiloGL.Mat4();
m.$transpose(); //the result is stored in m
Applies a rotation of theta
by vec
to a Mat4
matrix returning the result in a new matrix.
m.rotateAxis(theta, vec);
PhiloGL.Mat4.rotateAxis(m, theta, vec);
Vec3
(or array).Create a rotation by theta
and v
.
var m = new PhiloGL.Mat4(),
v = new PhiloGL.Vec3(1, 1, 1);
m.rotateAxis(Math.PI, v); //the result is a new matrix
Another way of doing the same thing without creating a Vec3
.
var m = new PhiloGL.Mat4(),
v = [ 1, 1, 1 ];
m.rotateAxis(Math.PI, v); //the result is a new matrix
Applies a rotation of angle theta
by vector vec
to a Mat4
altering the current matrix.
m.$rotateAxis(theta, vec);
PhiloGL.Mat4.$rotateAxis(m, theta, vec);
Vec3
(or array).Create a rotation by theta
and v
.
var m = new PhiloGL.Mat4(),
v = new PhiloGL.Vec3(1, 1, 1);
m.$rotateAxis(Math.PI, v); //the result is in m
Another way of doing the same thing without creating a Vec3
.
var m = new PhiloGL.Mat4(),
v = [ 1, 1, 1 ];
m.$rotateAxis(Math.PI, v); //the result is in m
Applies a rotation of angle rx
in the x-axis, ry
in the y-axis and rz
in the z-axis. Creates a new Mat4
with the result.
m.rotateXYZ(rx, ry, rz);
PhiloGL.Mat4.rotateXYZ(m, rx, ry, rz);
Create a rotation on the x-axis.
var m = new PhiloGL.Mat4();
m.rotateXYZ(Math.PI, 0, 0); //the result is a new matrix
Another way of doing it with generics:
var m = [];
PhiloGL.Mat4.id(m);
PhiloGL.Mat4.rotateXYZ(m, Math.PI, 0, 0); //creates a new Mat4 with the result.
Applies a rotation of angle rx
in the x-axis, ry
in the y-axis and rz
in the z-axis. Alters the matrix.
m.$rotateXYZ(rx, ry, rz);
PhiloGL.Mat4.$rotateXYZ(m, rx, ry, rz);
Create a rotation on the x-axis.
var m = new PhiloGL.Mat4();
m.$rotateXYZ(Math.PI, 0, 0); //alters m
Another way of doing it with generics:
var m = [];
PhiloGL.Mat4.id(m);
PhiloGL.Mat4.$rotateXYZ(m, Math.PI, 0, 0); //alters m
Applies a translation to Mat4
in the directions x
, y
and z
. Stores the result in a new Mat4
instance.
m.translate(x, y, z);
PhiloGL.Mat4.translate(m, x, y, z);
Create a translation on the x-axis.
var m = new PhiloGL.Mat4();
m.translate(10, 0, 0); //the result is a new matrix
Another way of doing it with generics:
var m = [];
PhiloGL.Mat4.id(m);
PhiloGL.Mat4.translate(m, 10, 0, 0); //creates a new Mat4 with the result.
Applies a translation to Mat4
in the directions x
, y
and z
. Alters the original matrix.
m.$translate(x, y, z);
PhiloGL.Mat4.$translate(m, x, y, z);
Create a translation on the x-axis.
var m = new PhiloGL.Mat4();
m.$translate(10, 0, 0); //the result is in m
Another way of doing it with generics:
var m = [];
PhiloGL.Mat4.id(m);
PhiloGL.Mat4.$translate(m, 10, 0, 0); //the result is in m
Applies scaling to Mat4
in the directions x
, y
and z
. Stores the result in a new Mat4
instance.
m.scale(x, y, z);
PhiloGL.Mat4.scale(m, x, y, z);
Create a scaling on the x-axis.
var m = new PhiloGL.Mat4();
m.scale(10, 0, 0); //the result is a new matrix
Another way of doing it with generics:
var m = [];
PhiloGL.Mat4.id(m);
PhiloGL.Mat4.scale(m, 10, 0, 0); //creates a new Mat4 with the result.
Applies scaling to Mat4
in the directions x
, y
and z
. Alters the original matrix.
m.$scale(x, y, z);
PhiloGL.Mat4.$scale(m, x, y, z);
Create a scaling on the x-axis.
var m = new PhiloGL.Mat4();
m.$scale(10, 0, 0); //the result is in m
Another way of doing it with generics:
var m = [];
PhiloGL.Mat4.id(m);
PhiloGL.Mat4.$scale(m, 10, 0, 0); //the result is in m
Inverts a Mat4
matrix. The matrix has to be invertible. Creates a new Mat4
with the result.
m.invert();
PhiloGL.Mat4.invert(m);
Create a Mat4
matrix and invert it.
var m = new PhiloGL.Mat4();
m.invert(); //the result is a new matrix
Inverts a Mat4
matrix. The matrix has to be invertible. Modifies the current matrix.
m.$invert();
PhiloGL.Mat4.$invert(m);
Create a Mat4
matrix and invert it.
var m = new PhiloGL.Mat4();
m.$invert(); //the result is stored in m
Performs a lookAt
operation on a matrix. Modifies the current matrix. Ths method is useful when setting a camera matrix class. For more information about the lookAt
operation look here.
m.lookAt(eye, center, up);
PhiloGL.Mat4.lookAt(m, eye, center, up);
Vec3
(or x,y,z object).Vec3
(or x,y,z object).Vec3
(or x,y,z object).Create a lookAt matrix. The eye is looking at the origin.
var m = new PhiloGL.Mat4(),
eye = [ 1, 0, 1 ],
center = [ 0, 0, 0 ],
up = [ 0, 1, 0 ];
m.lookAt(eye, center, up); //the original matrix is modified.
Another way of doing it with generics:
var m = [],
eye = [ 1, 0, 1 ],
center = [ 0, 0, 0 ],
up = [ 0, 1, 0 ];
PhiloGL.Mat4.lookAt(m, eye, center, up); //the original object is modified.
Performs a frustum
operation on a matrix. Modifies the current matrix. This method is useful when setting a camera projection matrix class. For more information about the frustum
geometry look here.
m.frustum(left, right, bottom, top, near, far);
PhiloGL.Mat4.frustum(m, left, right, bottom, top, near, far);
Creates an orthographic projection. Modifies the current matrix. For more information about the orthographic projection
geometry look here.
m.ortho(left, right, bottom, top, near, far);
PhiloGL.Mat4.ortho(m, left, right, bottom, top, near, far);
Creates a perspective matrix. This operation is based on creating a frustum matrix. Modifies the current matrix. This method is useful when setting a camera projection matrix class.
m.perspective(fov, aspect, near, far);
PhiloGL.Mat4.perspective(m, fov, aspect, near, far);
canvas.width / canvas.height
.Converts the matrix in a Float32Array. Useful when setting matrix uniforms.
m.toFloat32Array();
Clones a matrix.
m.clone();
PhiloGL.Mat4.clone(m);
A class to handle Quaternions. More information on quternions can be found here. The quaternion will be represented by an instance with x
, y
, z
, w
components that make a quaternion like: xi + yj + zk + w
.
Create a new Quat
instance from the x
, y
, z
coordinates of a Vec3 and a real component.
PhiloGL.Quat.fromVec3(v[, r]);
Vec3
instance.0
.Create a Quaternion from a Vec3.
var v = new PhiloGL.Vec3(1, 2, 3),
q = PhiloGL.Quat.fromVec3(v, 7); //Quat(1, 2, 3, 7)
Create a new Quat
instance from a Mat4. The Mat4
instance must be an orthogonal matrix.
PhiloGL.Quat.fromMat4(m);
Mat4
instance.Create a Quaternion from a Mat4
.
var m = new PhiloGL.Mat4(),
q = PhiloGL.Quat.fromMat4(m); //Quat
Create a new Quat
instance from a rotation around the x-axis in radians.
PhiloGL.Quat.fromXRotation(angle);
Create a Quaternion from an x-axis rotation.
var q = PhiloGL.Quat.fromXRotation(Math.PI); //Quat(1, 0, 0, 0)
Create a new Quat
instance from a rotation around the y-axis in radians.
PhiloGL.Quat.fromYRotation(angle);
Create a Quaternion from an y-axis rotation.
var q = PhiloGL.Quat.fromYRotation(Math.PI); //Quat(0, 1, 0, 0)
Create a new Quat
instance from a rotation around the z-axis in radians.
PhiloGL.Quat.fromZRotation(angle);
Create a Quaternion from an z-axis rotation.
var q = PhiloGL.Quat.fromZRotation(Math.PI); //Quat(0, 0, 1, 0)
Create a new Quat
instance from a rotation around an axis.
PhiloGL.Quat.fromAxisRotation(v, angle);
Vec3
-like object (i.e an array of three components).Create a Quaternion from an z-axis rotation.
var v = new PhiloGL.Vec3(0, 0, 1),
q = PhiloGL.Quat.fromAxisRotation(v, Math.PI); //Quat(0, 0, 1, 0)
Creates a new Quat
instance.
var q = new PhiloGL.Quat(x, y, z, w);
Create a (0, 0, 0, 0) quaternion.
var q = new PhiloGL.Quat();
Create a (1, 2, 3, 4) quaternion.
var q = new PhiloGL.Quat(1, 2, 3, 4);
Set x
, y
, z
, w
coordinates of one Quat
into another Quat
.
q1.setQuat(q2);
PhiloGL.Quat.setQuat(q1, q2);
Quat
instance.Create two quaternions and assign one quaternions components to the other one.
var q1 = new PhiloGL.Quat(1, 2, 3, 4),
q2 = new PhiloGL.Quat(4, 5, 6, 7);
q1.setQuat(q2); //v1 now contains [ 4, 5, 6, 7 ]
Set an object’s x
, y
, z
, w
components to another object.
var q1 = [],
q2 = [ 4, 5, 6, 7 ];
PhiloGL.Quat.setQuat(q1, q2); //q1 now has [ 4, 5, 6, 7 ]
Set x
, y
, z
, w
coordinates.
q1.set(x, y, z, w);
PhiloGL.Quat.set(q1, x, y, z, w);
Create two quaternions and assign one quaternions components to the other one.
var q1 = new PhiloGL.Quat(1, 2, 3, 4),
q2 = new PhiloGL.Quat(4, 5, 6, 7);
q1.set(q2.x, q2.y, q2.z, q2.w); //q1 now contains [ 4, 5, 6, 7 ]
Set an object’s x
, y
, z
, w
components to another object.
var q1 = [],
q2 = [ 4, 5, 6, 7 ];
PhiloGL.Quat.set(q1, q2.x, q2.y, q2.z, q2.w); //q1 now has [ 4, 5, 6, 7 ]
Adds the x
, y
, z
components of two Quat
objects. Creates a new Quat
instance and does not modify the original objects.
q1.add(q2);
PhiloGL.Quat.add(q1, q2);
Quat
instance.Create two quaternions and add them.
var q1 = new PhiloGL.Quat(1, 2, 3, 4),
q2 = new PhiloGL.Quat(4, 5, 6, 7);
q1.add(q2); //q1 and q2 are still the same but a new Quat(5, 7, 9, 11) was created.
Create two x
, y
, z
, w
objects and add them.
var q1 = [ 1, 2, 3, 4 ],
q2 = [ 4, 5, 6, 7 ];
PhiloGL.Quat.add(q1, q2); //q1 and q2 are still the same but a new Quat(5, 7, 9, 11) was created.
Adds the x
, y
, z
, w
components of two Quat
objects. Modifies the original object.
q1.$add(q2);
PhiloGL.Quat.$add(q1, q2);
Quat
instance.Create two quaternions and add them.
var q1 = new PhiloGL.Quat(1, 2, 3, 4),
q2 = new PhiloGL.Quat(4, 5, 6, 7);
q1.$add(q2); //q1 is now Quat(5, 7, 9, 11).
Create two x
, y
, z
, w
objects and add them.
var q1 = [ 1, 2, 3, 4 ],
q2 = [ 4, 5, 6, 7 ];
PhiloGL.Quat.$add(q1, q2); //q1 is now [ 5, 7, 9, 11 ].
Substracts the x
, y
, z
, w
components of two Quat
objects. Creates a new Quat
instance and does not modify the original objects.
q1.sub(q2);
PhiloGL.Quat.sub(q1, q2);
Quat
instance.Create two quaternions and substract them.
var q1 = new PhiloGL.Quat(1, 2, 3, 4),
q2 = new PhiloGL.Quat(4, 5, 6, 7);
q1.sub(q2); //q1 and q2 are still the same but a new Quat(-3, -3, -3, -3) was created.
Create two x
, y
, z
, w
objects and substract them.
var q1 = {
x: 1,
y: 2,
z: 3,
w: 4
},
q2 = [ 4, 5, 6, 7 ];
PhiloGL.Quat.sub(q1, q2); //q1 and q2 are still the same but a new Quat(-3, -3, -3, -3) was created.
Substracts the x
, y
, z
, w
components of two Quat
objects. Modifies the original object.
q1.$sub(q2);
PhiloGL.Quat.$sub(q1, q2);
Quat
instance.Create two quaternions and substract them.
var q1 = new PhiloGL.Quat(1, 2, 3, 4),
q2 = new PhiloGL.Quat(4, 5, 6, 7);
q1.$sub(q2); //q1 is now Quat(-3, -3, -3, -3).
Create two x
, y
, z
, w
objects and add them.
var q1 = [ 1, 2, 3, 4 ],
q2 = [ 4, 5, 6, 7 ];
PhiloGL.Quat.$sub(q1, q2); //q1 is now [ -3, -3, -3, -3 ].
Multiplies two quaternions returning a new Quat
instance with the result. The original object is not modified.
q1.mulQuat(q2);
PhiloGL.Quat.mulQuat(q1, q2);
Quat
instance.Create two Quaternions and multiply them.
var q1 = new PhiloGL.Quat(1, 0, 0, 0),
q2 = new PhiloGL.Quat(1, 0, 0, 0);
q1.mulQuat(q2); //q1 is unchanged but a new Quat(-1, 0, 0, 0) is created.
Multiplies two quaternions returning and modifies the receiver with the result.
q1.$mulQuat(q2);
PhiloGL.Quat.$mulQuat(q1, q2);
Quat
instance.Create two Quaternions and multiply them.
var q1 = new PhiloGL.Quat(1, 0, 0, 0),
q2 = new PhiloGL.Quat(1, 0, 0, 0);
q1.$mulQuat(q2); //q1 is now Quat(-1, 0, 0, 0).
Divides two quaternions returning a new Quat
instance with the result. The original object is not modified.
q1.divQuat(q2);
PhiloGL.Quat.divQuat(q1, q2);
Quat
instance.Create two Quaternions and divide them.
var q1 = new PhiloGL.Quat(1, 0, 0, 0),
q2 = new PhiloGL.Quat(1, 0, 0, 0);
q1.divQuat(q2); //q1 is unchanged but a new Quat(1, 0, 0, 0) is created.
Divides two quaternions returning and modifies the receiver with the result.
q1.$divQuat(q2);
PhiloGL.Quat.$divQuat(q1, q2);
Quat
instance.Create two Quaternions and divide them.
var q1 = new PhiloGL.Quat(1, 0, 0, 0),
q2 = new PhiloGL.Quat(1, 0, 0, 0);
q1.$divQuat(q2); //q1 is now Quat(1, 0, 0, 0).
Scales the Quat quaternion by a real number. Creates a new Quat with the scaled components.
q1.scale(s);
PhiloGL.Quat.scale(q1, s);
Create a quaternion and scale it by 2.
var q1 = new PhiloGL.Quat(1, 2, 3, 4);
q1.scale(2); //q1 is unchanged but a new Quat(2, 4, 6, 8) is created.
Create an x
, y
, z
, w
object and scale it by 2.
var q1 = [ 1, 2, 3, 4 ];
PhiloGL.Quat.scale(q1, 2); //q1 is still the same but a new Quat(2, 4, 6, 8) was created.
Scales the Quat quaternion by a real number. Changes the original object.
q1.$scale(s);
PhiloGL.Quat.$scale(q1, s);
Create a quaternion and scale it by 2.
var q1 = new PhiloGL.Quat(1, 2, 3, 4);
q1.$scale(2); //q1 is now Quat(2, 4, 6, 8).
Create an x
, y
, z
, w
object and scale it by 2.
var q1 = [ 1, 2, 3, 4 ];
PhiloGL.Quat.$scale(q1, 2); //q1 is now [ 2, 4, 6, 8 ].
Conjugates a Quat
. Returns a new instance.
q1.conjugate();
PhiloGL.Quat.conjugate(q1);
Create a quaternion and conjugate it.
var q1 = new PhiloGL.Quat(1, 2, 3, 4);
q1.conjugate(); //q1 is unchanged but a new Quat(-1, -2, -3, 4) is created.
Create an x
, y
, z
, w
object and conjugate it.
var q1 = [ 1, 2, 3, 4 ];
PhiloGL.Quat.conjugate(q1); //q1 is still the same but a new Quat(-1, -2, -3, 4).
conjugates a Quat
. Changes the original object.
q1.$conjugate();
PhiloGL.Quat.$conjugate(q1);
Create a quaternion and conjugate it.
var q1 = new PhiloGL.Quat(1, 2, 3, 4);
q1.$conjugate(); //q1 is now Quat(-1, -2, -3, 4).
Create an x
, y
, z
, w
object and conjugate it.
var q1 = [ 1, 2, 3, 4 ];
PhiloGL.Quat.conjugate(q1); //q1 is now [ -1, -2, -3, 4 ].
Negates a Quat
. Returns a new instance.
q1.neg();
PhiloGL.Quat.neg(q1);
Create a quaternion and negate it.
var q1 = new PhiloGL.Quat(1, 2, 3, 4);
q1.neg(); //q1 is unchanged but a new Quat(-1, -2, -3, -4) is created.
Create an x
, y
, z
, w
object and negate it.
var q1 = [ 1, 2, 3, 4 ];
PhiloGL.Quat.neg(q1); //q1 is still the same but a new Quat(-1, -2, -3, -4).
Negates a Quat
. Changes the original object.
q1.$neg();
PhiloGL.Quat.$neg(q1);
Create a quaternion and negate it.
var q1 = new PhiloGL.Quat(1, 2, 3, 4);
q1.$neg(); //q1 is now Quat(-1, -2, -3, -4).
Create an x
, y
, z
, w
object and negate it.
var q1 = [ 1, 2, 3, 4 ];
PhiloGL.Quat.neg(q1); //q1 is now [ -1, -2, -3, -4 ].
Creates a unit quaternion from the coordinates of Quat
. The original object is not modified.
q1.unit();
PhiloGL.Quat.unit(q1);
Create a quaternion and make a unit quaternion from it.
var q1 = new PhiloGL.Quat(1, 2, 3, 4);
q1.unit(); //q1 is unchanged but a new unit quaternion Quat is created.
Create an x
, y
, z
, w
object and make a unit quaternion from it.
var q1 = [ 1, 2, 3, 4 ];
PhiloGL.Quat.unit(q1); //q1 is still the same but a new Quat that is a unit quaternion is created.
Creates a unit quaternion from the Quat
coordinates. Changes the original object.
q1.$unit();
PhiloGL.Quat.$unit(q1);
Create a quaternion and make a unit quaternion from it.
var q1 = new PhiloGL.Quat(1, 2, 3, 4);
q1.$unit(); //q1 is now a unit quaternion.
Create an x
, y
, z
, w
object and make a unit quaternion from it.
var q1 = [ 1, 2, 3, 4 ];
PhiloGL.Quat.$unit(q1); //q1 is now a unit quaternion vector.
Calculates the norm of Quat
.
q1.norm();
PhiloGL.Quat.norm(q1);
Create a quaternion and calculate its norm.
var q1 = new PhiloGL.Quat(1, 2, 3, 4);
vi.norm(); //returns the real valued norm.
Create an x
, y
, z
, w
object and calculate its norm.
var q1 = [ 1, 2, 3, 4 ];
//A real number with the norm is returned.
var ans = PhiloGL.Quat.norm(q1);
Calculates the squared norm of Quat
.
q1.normSq();
PhiloGL.Quat.normSq(q1);
Create a quaternion and calculate its squared norm.
var q1 = new PhiloGL.Quat(1, 2, 3, 4);
vi.normSq(); //returns the real valued norm.
Create an x
, y
, z
, w
object and calculate its squared norm.
var q1 = [ 1, 2, 3, 4 ];
//A real number with the squared norm is returned.
var ans = PhiloGL.Quat.normSq(q1);
Clones a quaternion.
q1.clone();
PhiloGL.Quat.clone(q1);