Creates and initializes the Matrix4 to the 4x4 identity matrix.
A column-major list of matrix values.
Read-only flag to check if a given object is of type Matrix.
Read-only flag to check if a given object is of type Matrix4.
Creates a new Matrix4 with identical elements to this one.
A new Matrix4 instance identical this.
Sets this matrix to the transformation composed of position, quaternion and scale.
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The source position
The source quaternion
The source scale
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.
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The output position
The output quaternion
The output vector
Computes and returns the determinant of this matrix.
The determinate.
Test if this matrix and another matrix are value-wise equal.
Returns true if 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)
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Sets the elements of this matrix based on an array in column-major format.
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the array to read the elements from.
offset into the array. Default is 0.
Gets the maximum scale value of the 3 axes.
The maximum scale value.
Resets this matrix to the identity matrix.
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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.
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Set this 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
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Creates an orthographic projection matrix.
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The left coordinate
The right coordinate
The top coordinate
The bottom coordinate
The closest distance.
The distance to horizon
Creates a perspective projection matrix.
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The left coordinate
The right coordinate
The top coordinate
The bottom coordinate
The closest distance.
The distance to horizon
Sets this matrix as rotation transform around axis by theta radians. This is a somewhat controversial but mathematically sound alternative to rotating via Quaternions. See the discussion here
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Rotation axis, should be normalized.
Rotation angle in radians.
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.
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The Euler to update from.
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
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The source quaternion
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
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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
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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
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Rotation angle in radians.
Sets this matrix as scale transform:
x, 0, 0, 0,
0, y, 0, 0,
0, 0, z, 0,
0, 0, 0, 1
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the amount to scale in the X axis.
the amount to scale in the Y axis.
the amount to scale in the Z axis.
Sets this matrix as a shear transform:
1, yx, zx, 0,
xy, 1, zy, 0,
xz, yz, 1, 0,
0, 0, 0, 1
xy - the amount to shear X by Y. xz - the amount to shear X by Z. yx - the amount to shear Y by X. yz - the amount to shear Y by Z. zx - the amount to shear Z by X. zy - the amount to shear Z by Y.
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Sets this matrix as a translation transform:
1, 0, 0, x,
0, 1, 0, y,
0, 0, 1, z,
0, 0, 0, 1
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the amount to translate in the X axis.
the amount to translate in the Y axis.
the amount to translate in the Z axis.
Sets this matrix to a x b.
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Multiplies every component of the matrix by a scalar value s.
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The scalar to multiply
Set the elements of this matrix to the supplied row-major values n11, n12, ... n44.
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Sets the position component for this matrix from vector v, without affecting the rest of the matrix
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
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The position vector.
Sets the position component for this matrix from vector v, without affecting the rest of the matrix
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The X component of position
The Y component of position
The Z component of position
Writes the elements of this matrix to a array[16] in column-major format.
The new array[16].
(optional) array to store the resulting vector in.
(optional) offset in the array at which to put the result.
Transposes this matrix.
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A class representing a 4x4 matrix.
The most common use of a 4x4 matrix in 3D computer graphics is as a Transformation Matrix. For an introduction to transformation matrices as used in WebGL, check out this tutorial. 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.
A Note on Row-Major and Column-Major Ordering 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
will result in the elements array containing:
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 three.js 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.
Extracting position, rotation and scale There are several options available for extracting position, rotation and scale from a Matrix4. Vector3.setFromMatrixPosition: can be used to extract the translation component. Vector3.setFromMatrixScale: can be used to extract the scale component. Quaternion.setFromRotationMatrix, Euler.setFromRotationMatrix or extractRotation can be used to extract the rotation component from a pure (unscaled) matrix. decompose can be used to extract position, rotation and scale all at once.
Example