A class representing a 4x4 matrix.
The most common use of a 4x4 matrix in 3D computer graphics is as a Transformation Matrix.
This allows a Vector3 representing a point in 3D space to undergo transformations such as translation, rotation, shear, scale, reflection, orthogonal or perspective projection and so on, by being multiplied by the matrix. This is known as applying the matrix to the vector.
Every Object3D has three associated 4x4 matrices:
Cameras have three additional 4x4:
Note: Object3D.normalMatrix is not a 4x4 matrix, but a 3x3 (Matrix3).
The set() method takes arguments in row-major order, while internally they are stored in the elements array in column-major order.
This means that calling
const m = new v3d.Matrix4();
m.set(11, 12, 13, 14,
21, 22, 23, 24,
31, 32, 33, 34,
41, 42, 43, 44);
will result in the elements array containing:
m.elements = [11, 21, 31, 41,
12, 22, 32, 42,
13, 23, 33, 43,
14, 24, 34, 44];
and internally all calculations are performed using column-major ordering. However, as the actual ordering makes no difference mathematically and most people are used to thinking about matrices in row-major order, the Verge3D documentation shows matrices in row-major order. Just bear in mind that if you are reading the source code, you'll have to take the transpose of any matrices outlined here to make sense of the calculations.
There are several options available for extracting position, rotation and scale from a Matrix4.
Creates and initializes the Matrix4 to the 4x4 identity matrix.
A column-major list of matrix values.
Creates a new Matrix4 with identical elements to this one.
Sets this matrix to the transformation composed of position, quaternion and scale.
Sets this matrix to the transformation composed of position, euler and scale.
Copies the elements of matrix m into this matrix.
Copies the translation component of the supplied matrix m into this matrix's translation component.
Decomposes this matrix into its position, quaternion and scale components.
Note: Not all matrices are decomposable in this way. For example, if an object has a non-uniformly scaled parent, then the object's world matrix may not be decomposable, and this method may not be appropriate.
order — the rotation order in which euler will be decomposed from this matrix. Default is euler._order.
Decomposes this matrix into it's position, euler and scale components.
Computes and returns the determinant of this matrix.
Return true if this matrix and m are equal.
Extracts the basis of this matrix into the three axis vectors provided. If this matrix is:
a, b, c, d,
e, f, g, h,
i, j, k, l,
m, n, o, p
then the xAxis, yAxis, zAxis will be set to:
xAxis = (a, e, i)
yAxis = (b, f, j)
zAxis = (c, g, k)
Extracts the rotation component of the supplied matrix m into this matrix's rotation component.
0.Sets the elements of this matrix based on an array in column-major format.
Inverts this matrix, using the analytic method.
You can not invert with a determinant of zero. If you attempt this, the method produces a zero matrix instead.
Gets the maximum scale value of the 3 axes.
Resets this matrix to the identity matrix.
Constructs a rotation matrix, looking from eye towards target oriented by the up vector.
Sets this matrix as rotation transform around axis by theta radians.
This is a somewhat controversial but mathematically sound alternative to rotating via Quaternions.
Set this materix to the basis matrix consisting of the three provided basis vectors:
xAxis.x, yAxis.x, zAxis.x, 0,
xAxis.y, yAxis.y, zAxis.y, 0,
xAxis.z, yAxis.z, zAxis.z, 0,
0, 0, 0, 1
Creates a perspective projection matrix. This is used internally by PerspectiveCamera.updateProjectionMatrix()
Creates an orthographic projection matrix. This is used internally by OrthographicCamera.updateProjectionMatrix().
Sets the rotation component (the upper left 3x3 matrix) of this matrix to the rotation specified by the given Euler Angle. The rest of the matrix is set to the identity. Depending on the order of the euler, there are six possible outcomes. See this page for a complete list.
Sets the rotation component of this matrix to the rotation specified by q, as outlined here. The rest of the matrix is set to the identity. So, given q = w + xi + yj + zk, the resulting matrix will be:
1-2y²-2z² 2xy-2zw 2xz+2yw 0
2xy+2zw 1-2x²-2z² 2yz-2xw 0
2xz-2yw 2yz+2xw 1-2x²-2y² 0
0 0 0 1
theta — rotation angle in radians.
Sets this matrix as a rotational transformation around the X axis by theta (θ) radians. The resulting matrix will be:
1 0 0 0
0 cos(θ) -sin(θ) 0
0 sin(θ) cos(θ) 0
0 0 0 1
theta — rotation angle in radians.
Sets this matrix as a rotational transformation around the Y axis by theta (θ) radians. The resulting matrix will be:
cos(θ) 0 sin(θ) 0
0 1 0 0
-sin(θ) 0 cos(θ) 0
0 0 0 1
theta — rotation angle in radians.
Sets this matrix as a rotational transformation around the Z axis by theta (θ) radians. The resulting matrix will be:
cos(θ) -sin(θ) 0 0
sin(θ) cos(θ) 0 0
0 0 1 0
0 0 0 1
Sets this matrix as scale transform:
x, 0, 0, 0,
0, y, 0, 0,
0, 0, z, 0,
0, 0, 0, 1
Sets this matrix as a shear transform:
1, yx, zx, 0,
xy, 1, zy, 0,
xz, yz, 1, 0,
0, 0, 0, 1
Sets this matrix as a translation transform:
1, 0, 0, x,
0, 1, 0, y,
0, 0, 1, z,
0, 0, 0, 1
Post-multiplies this matrix by m.
Multiplies every component of the matrix by a scalar value s.
Pre-multiplies this matrix by m.
Multiplies the columns of this matrix by vector v.
Set the elements of this matrix to the supplied row-major values n11, n12, ... n44.
Set the upper 3x3 elements of this matrix to the values of the Matrix3 m.
Sets the position component for this matrix from vector v, without affecting the rest of the matrix - i.e. if the matrix is currently:
a, b, c, d,
e, f, g, h,
i, j, k, l,
m, n, o, p
This becomes:
a, b, c, v.x,
e, f, g, v.y,
i, j, k, v.z,
m, n, o, p
Writes the elements of this matrix to an array in column-major format.
Transposes this matrix.
For more info on how to obtain the source code of this module see this page.