# Matrix3D Struct

## Definition

Important

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Represents a 4 x 4 matrix used for transformations in 3-D space.

`public value class Matrix3D : IFormattable`

```
[System.ComponentModel.TypeConverter(typeof(System.Windows.Media.Media3D.Matrix3DConverter))]
[System.Serializable]
public struct Matrix3D : IFormattable
```

```
[System.ComponentModel.TypeConverter(typeof(System.Windows.Media.Media3D.Matrix3DConverter))]
public struct Matrix3D : IFormattable
```

```
[<System.ComponentModel.TypeConverter(typeof(System.Windows.Media.Media3D.Matrix3DConverter))>]
[<System.Serializable>]
type Matrix3D = struct
interface IFormattable
```

```
[<System.ComponentModel.TypeConverter(typeof(System.Windows.Media.Media3D.Matrix3DConverter))>]
type Matrix3D = struct
interface IFormattable
```

```
Public Structure Matrix3D
Implements IFormattable
```

- Inheritance

- Attributes

- Implements

## Examples

```
// Multiplies a Vector3D by a Matrix3D using the static Multiply method.
// Returns a Vector3D.
Vector3D vector1 = new Vector3D(20, 30, 40);
Matrix3D matrix1 = new Matrix3D(10, 10, 10, 0, 20, 20, 20, 0, 30, 30, 30, 0, 5, 10, 15, 1);
Vector3D vectorResult = new Vector3D();
vectorResult = Vector3D.Multiply(vector1,matrix1);
// vector Result is equal to (2000, 2000, 2000)
```

```
' Multiplies a Vector3D by a Matrix3D using the static Multiply method.
' Returns a Vector3D.
Dim vector1 As New Vector3D(20, 30, 40)
Dim matrix1 As New Matrix3D(10, 10, 10, 0, 20, 20, 20, 0, 30, 30, 30, 0, 5, 10, 15, 1)
Dim vectorResult As New Vector3D()
vectorResult = Vector3D.Multiply(vector1,matrix1)
' vector Result is equal to (2000, 2000, 2000)
```

## Remarks

Matrix3D has the following row-vector syntax:

M11 | M12 | M13 | M14 |

M21 | M22 | M23 | M24 |

M31 | M32 | M33 | M34 |

OffsetX | OffsetY | OffsetZ | M44 |

Note that because the fourth column is also accessible, the matrix allows developers to represent affine as well as non-affine transforms.

Matrices can be appended or prepended to other matrices. Appending matrix A to matrix B denotes a transformation by B and then by A:

### XAML Attribute Usage

```
<object property="m11, m12, m13, m21, m22, m23, m31, m32, m33, offsetX, offsetY, offsetZ"/>
- or -
<object property="Identity"/>
```

### XAML Values

*M11*

System.Double

The value in the first row and first column of this Matrix3D. For more information, see the M11 property.

*M12*

System.Double

The value in the first row and second column of this Matrix3D. For more information, see the M12 property.

*M13*

System.Double

The value in the first row and third column of this Matrix3D. For more information, see the M13 property.

*M14*

System.Double

The value in the first row and fourth column of this Matrix3D. For more information, see the M14 property.

*M21*

System.Double

The value in the second row and first column of this Matrix3D. For more information, see the M21 property.

*M22*

System.Double

The value in the second row and second column of this Matrix3D. For more information, see the M22 property.

*M23*

System.Double

The value in the second row and third column of this Matrix3D. For more information, see the M23 property.

*M24*

System.Double

The value in the second row and fourth column of this Matrix3D. For more information, see the M24 property.

*M31*

System.Double

The value in the third row and first column of this Matrix3D. For more information, see the M31 property.

*M32*

System.Double

The value in the third row and second column of this Matrix3D. For more information, see the M32 property.

*M33*

System.Double

The value in the third row and third column of this Matrix3D. For more information, see the M34 property.

*M34*

System.Double

The value in the third row and fourth column of this Matrix3D. For more information, see the M33 property.

*M44*

System.Double

The value in the fourth row and fourth column of this Matrix3D. For more information, see the M44 property.

*offsetX*

System.Double

The value in the fourth row and first column of this Matrix3D. For more information, see the OffsetX property.

*offsetY*

System.Double

The value in the fourth row and second column of this Matrix3D. For more information, see the OffsetY property.

*offsetZ*

System.Double

The value in the fourth row and third column of this Matrix3D. For more information, see the OffsetZ property.

## Constructors

Matrix3D(Double, Double, Double, Double, Double, Double, Double, Double, Double, Double, Double, Double, Double, Double, Double, Double) |
Constructor that sets matrix's initial values. |

## Properties

Determinant |
Retrieves the determinant of this Matrix3D structure. |

HasInverse |
Gets a value that indicates whether this Matrix3D is invertible. |

Identity | |

IsAffine |
Gets a value that indicates whether this Matrix3D structure is affine. |

IsIdentity |
Determines whether this Matrix3D structure is an identity Matrix3D. |

M11 |
Gets or sets the value of the first row and first column of this Matrix3D structure. |

M12 |
Gets or sets the value of the first row and second column of this Matrix3D structure. |

M13 |
Gets or sets the value of the first row and third column of this Matrix3D structure. |

M14 |
Gets or sets the value of the first row and fourth column of this Matrix3D structure. |

M21 |
Gets or sets the value of the second row and first column of this Matrix3D structure. |

M22 |
Gets or sets the value of the second row and second column of this Matrix3D structure. |

M23 |
Gets or sets the value of the second row and third column of this Matrix3D structure. |

M24 |
Gets or sets the value of the second row and fourth column of this Matrix3D structure. |

M31 |
Gets or sets the value of the third row and first column of this Matrix3D structure. |

M32 |
Gets or sets the value of the third row and second column of this Matrix3D structure. |

M33 |
Gets or sets the value of the third row and third column of this Matrix3D structure. |

M34 |
Gets or sets the value of the third row and fourth column of this Matrix3D structure. |

M44 |
Gets or sets the value of the fourth row and fourth column of this Matrix3D structure. |

OffsetX |
Gets or sets the value of the fourth row and first column of this Matrix3D structure. |

OffsetY |
Gets or sets the value of the fourth row and second column of this Matrix3D structure. |

OffsetZ |
Gets or sets the value of the fourth row and third column of this Matrix3D structure. |

## Methods

Append(Matrix3D) |
Appends a specified matrix to the current matrix. |

Equals(Matrix3D) |
Tests equality between two matrices. |

Equals(Matrix3D, Matrix3D) |
Tests equality between two matrices. |

Equals(Object) |
Tests equality between two matrices. |

GetHashCode() |
Returns the hash code for this matrix. |

Invert() |
Inverts this Matrix3D structure. |

Multiply(Matrix3D, Matrix3D) |
Multiplies the specified matrices. |

Parse(String) |
Converts a string representation of a Matrix3D structure into the equivalent Matrix3D structure. |

Prepend(Matrix3D) |
Prepends a specified matrix to the current matrix. |

Rotate(Quaternion) |
Appends a rotation transform to the current Matrix3D. |

RotateAt(Quaternion, Point3D) | |

RotateAtPrepend(Quaternion, Point3D) |
Prepends a rotation about a specified center Point3D to this Matrix3D structure. |

RotatePrepend(Quaternion) |
Prepends a rotation specified by a Quaternion to this Matrix3D structure. |

Scale(Vector3D) |
Appends the specified scale Vector3D to this Matrix3D structure. |

ScaleAt(Vector3D, Point3D) |
Scales this Matrix3D structure by the specified Vector3D about the specified Point3D. |

ScaleAtPrepend(Vector3D, Point3D) |
Prepends the specified scale transformation about the specified Point3D to this Matrix3D structure. |

ScalePrepend(Vector3D) |
Prepends the specified scale Vector3D to the current Matrix3D structure. |

SetIdentity() |
Changes this Matrix3D structure into an identity matrix. |

ToString() |
Creates a string representation of this Matrix3D structure. |

ToString(IFormatProvider) |
Creates a string representation of this Matrix3D structure. |

Transform(Point3D) |
Transforms the specified Point3D by the Matrix3D and returns the result. |

Transform(Point3D[]) |
Transforms the specified Point3D objects in the array by the Matrix3D. |

Transform(Point4D) |
Transforms the specified Point4D by the Matrix3D and returns the result. |

Transform(Point4D[]) |
Transforms the specified Point4D objects in the array by the Matrix3D and returns the result. |

Transform(Vector3D) | |

Transform(Vector3D[]) |
Transforms the specified Vector3D objects in the array by this Matrix3D. |

Translate(Vector3D) |
Appends a translation of the specified offset to the current Matrix3D structure. |

TranslatePrepend(Vector3D) |
Prepends a translation of the specified offset to this Matrix3D structure. |

## Operators

Equality(Matrix3D, Matrix3D) |
Compares two Matrix3D instances for exact equality. |

Inequality(Matrix3D, Matrix3D) |
Compares two Matrix3D instances for exact inequality. |

Multiply(Matrix3D, Matrix3D) |
Multiplies the specified matrices. |

## Explicit Interface Implementations

IFormattable.ToString(String, IFormatProvider) |
Formats the value of the current instance using the specified format. |