Matrix3D Matrix3D Matrix3D Struct

Represents a 4 × 4 matrix that is used for transformations in a 3-D space. Used as a value for ProjectionMatrix.

Syntax

Declaration

public struct Matrix3Dpublic struct Matrix3DPublic Structure Matrix3D
<Matrix3DProjection ProjectionMatrix="m11, m12, m13, m14, 
  m21, m22, m23, m24, m31, m32, m33, m34, offsetX, offsetY, offsetZ, m44" />

Remarks

You can use the Matrix3DProjection and Matrix3D types for more complex semi–3-D scenarios than are possible with the PlaneProjection type. Matrix3DProjection provides a complete 3-D transform matrix to apply to any UIElement (you use this as a value for the Projection property). The matrix lets you apply arbitrary model transform matrices and perspective matrices to visual elements.

Matrix3D has this row-vector syntax:

M11M12M13M14
M21M22M23M24
M31M32M33M34
OffsetXOffsetYOffsetZM44

Because the fourth column is accessible, Matrix3D can represent both affine and non-affine transforms.

XAML syntax for Matrix3D

Matrix3D values can be declared in XAML, but the syntax is limited, and different than what you might expect based on how other Windows Runtime structures (like Thickness ) support values for XAML UI:+ The most typical usage for Matrix3D -type properties is to rely on the initialization string behavior that's built-in to the Matrix3D type, and set any value that uses a Matrix3D value as an attribute. You specify a string in the "initialization text" format for constructing a Matrix3D value: 16 separate Double values each separated by comma or space. You can see this format used in the XAML in "Examples" below.

  • There's only one existing property that uses a Matrix3D value: ProjectionMatrix. So that's what's shown as the primary XAML syntax here.
  • The secondary XAML syntax shown has an actual Matrix3D object element. But note that it has a XAML namespace prefix. The Windows.UI.Xaml.Media.Media3D namespace was not included in the set of code namespaces that the Windows Runtime XAML parser uses for the default XAML namespace. In order to use the Matrix3D as an element in XAML, you have to include an xmlns declaration in your XAML that references Windows.UI.Xaml.Media.Media3D by a ** using:** statement. Then qualify the Matrix3D with the xmlns prefix you mapped for the types in Windows.UI.Xaml.Media.Media3D.
  • Even once you do this mapping, the Matrix3D object element can't have attribute values for setting the 16 properties, it's not enabled by the XAML parser (other XAML structures have special-case handling for properties-as-attribute syntax; Matrix3D happens to not have this). You still have to use the initialization text that sets the 16 values as consecutive atoms of a string. In this case the string is contained as the "inner text" / content of the Matrix3D object element.
  • As you can see the object element syntax isn't any easier to read or use than the inline attribute syntax for ProjectionMatrix, so the verbose Matrix3D object element syntax isn't common.

Projection and members of Matrix3D

If you are using a Microsoft .NET language (C# or Microsoft Visual Basic), or in Visual C++ component extensions (C++/CX), then Matrix3D has non-data members available, and its data members are exposed as read-write properties, not fields.

If you are programming with C++ using the Windows Runtime Template Library (WRL), then only the data member fields exist as members of Matrix3D, and you cannot use the utility methods or properties listed in the members table. WRL code can access similar utility methods that exist on the Matrix3DHelper class.

You can't set properties of Matrix3D in XAML with individual XAML attributes. You have to initialize a Matrix3D object element using an initialization string that specifies all 16 values, or use attribute syntax for ProjectionMatrix that uses this same string format.

Examples

This example uses a simple Matrix3D matrix to transform the image in the X and Y directions when you click the image.

<!-- When you click on the image, the projection is applied. -->
<Image PointerPressed="ApplyProjection" x:Name="BeachImage" Source="guy_by_the_beach.jpg"
       Width="200"/>
private void ApplyProjection(Object sender, PointerRoutedEventArgs e)
{
    Matrix3D m = new Matrix3D();

    // This matrix simply translates the image 100 pixels
    // down and 100 pixels right.
    m.M11 = 1.0; m.M12 = 0.0; m.M13 = 0.0; m.M14 = 0.0;
    m.M21 = 0.0; m.M22 = 1.0; m.M23 = 0.0; m.M24 = 0.0;
    m.M31 = 0.0; m.M32 = 0.0; m.M33 = 1.0; m.M34 = 0.0;
    m.OffsetX = 100; m.OffsetY = 100; m.OffsetZ = 0; m.M44 = 1.0;

    Matrix3DProjection m3dProjection = new Matrix3DProjection();
    m3dProjection.ProjectionMatrix = m;

    BeachImage.Projection = m3dProjection;

}
<Image Source="guy_by_the_beach.jpg">
    <Image.Projection>
        <Matrix3DProjection  ProjectionMatrix="2, 0, 0, 0,
                                              0, 2, 0, 0,
                                              0, 0, 1, 0,
                                              100, 100, 0, 1"/>
    </Image.Projection>
</Image>
<!-- When you click on the image, the projection is applied. -->
<Image PointerPressed="ApplyProjection" x:Name="BeachImage" Source="guy_by_the_beach.jpg" 
       Width="200"/>
private void ApplyProjection(Object sender, PointerRoutedEventArgs e)
{
    // Translate the image along the negative Z-axis such that it occupies 50% of the
    // vertical field of view.
    double fovY = Math.PI / 2.0;
    double translationZ = -BeachImage.ActualHeight / Math.Tan(fovY / 2.0);
    double theta = 20.0 * Math.PI / 180.0;

    // You can create a 3D effect by creating a number of simple 
    // tranformation Matrix3D matrixes and then multiply them together.
    Matrix3D centerImageAtOrigin = TranslationTransform(
             -BeachImage.ActualWidth / 2.0,
             -BeachImage.ActualHeight / 2.0, 0);
    Matrix3D invertYAxis = CreateScaleTransform(1.0, -1.0, 1.0);
    Matrix3D rotateAboutY = RotateYTransform(theta);
    Matrix3D translateAwayFromCamera = TranslationTransform(0, 0, translationZ);
    Matrix3D perspective = PerspectiveTransformFovRH(fovY,
            LayoutRoot.ActualWidth / LayoutRoot.ActualHeight,   // aspect ratio
            1.0,                                                // near plane
            1000.0);                                            // far plane
    Matrix3D viewport = ViewportTransform(LayoutRoot.ActualWidth, LayoutRoot.ActualHeight);

    Matrix3D m = Matrix3DHelper.Multiply(centerImageAtOrigin,invertYAxis);
    m = Matrix3D.Multiply(m ,rotateAboutY);
    m = Matrix3D.Multiply(m,translateAwayFromCamera);
    m = Matrix3D.Multiply(m,perspective);
    m = Matrix3D.Multiply(m,viewport);

    Matrix3DProjection m3dProjection = new Matrix3DProjection();
    m3dProjection.ProjectionMatrix = m;

    BeachImage.Projection = m3dProjection;
}

private Matrix3D TranslationTransform(double tx, double ty, double tz)
{
    Matrix3D m = new Matrix3D();

    m.M11 = 1.0; m.M12 = 0.0; m.M13 = 0.0; m.M14 = 0.0;
    m.M21 = 0.0; m.M22 = 1.0; m.M23 = 0.0; m.M24 = 0.0;
    m.M31 = 0.0; m.M32 = 0.0; m.M33 = 1.0; m.M34 = 0.0;
    m.OffsetX = tx; m.OffsetY = ty; m.OffsetZ = tz; m.M44 = 1.0;

    return m;
}

private Matrix3D CreateScaleTransform(double sx, double sy, double sz)
{
    Matrix3D m = new Matrix3D();

    m.M11 = sx; m.M12 = 0.0; m.M13 = 0.0; m.M14 = 0.0;
    m.M21 = 0.0; m.M22 = sy; m.M23 = 0.0; m.M24 = 0.0;
    m.M31 = 0.0; m.M32 = 0.0; m.M33 = sz; m.M34 = 0.0;
    m.OffsetX = 0.0; m.OffsetY = 0.0; m.OffsetZ = 0.0; m.M44 = 1.0;

    return m;
}

private Matrix3D RotateYTransform(double theta)
{
    double sin = Math.Sin(theta);
    double cos = Math.Cos(theta);

    Matrix3D m = new Matrix3D();

    m.M11 = cos; m.M12 = 0.0; m.M13 = -sin; m.M14 = 0.0;
    m.M21 = 0.0; m.M22 = 1.0; m.M23 = 0.0; m.M24 = 0.0;
    m.M31 = sin; m.M32 = 0.0; m.M33 = cos; m.M34 = 0.0;
    m.OffsetX = 0.0; m.OffsetY = 0.0; m.OffsetZ = 0.0; m.M44 = 1.0;

    return m;
}

private Matrix3D RotateZTransform(double theta)
{
    double cos = Math.Cos(theta);
    double sin = Math.Sin(theta);

    Matrix3D m = new Matrix3D();
    m.M11 = cos; m.M12 = sin; m.M13 = 0.0; m.M14 = 0.0;
    m.M21 = -sin; m.M22 = cos; m.M23 = 0.0; m.M24 = 0.0;
    m.M31 = 0.0; m.M32 = 0.0; m.M33 = 1.0; m.M34 = 0.0;
    m.OffsetX = 0.0; m.OffsetY = 0.0; m.OffsetZ = 0.0; m.M44 = 1.0;
    return m;
}

private Matrix3D PerspectiveTransformFovRH(double fieldOfViewY, double aspectRatio, double zNearPlane, double zFarPlane)
{
    double height = 1.0 / Math.Tan(fieldOfViewY / 2.0);
    double width = height / aspectRatio;
    double d = zNearPlane - zFarPlane;

    Matrix3D m = new Matrix3D();
    m.M11 = width; m.M12 = 0; m.M13 = 0; m.M14 = 0;
    m.M21 = 0; m.M22 = height; m.M23 = 0; m.M24 = 0;
    m.M31 = 0; m.M32 = 0; m.M33 = zFarPlane / d; m.M34 = -1;
    m.OffsetX = 0; m.OffsetY = 0; m.OffsetZ = zNearPlane * zFarPlane / d; m.M44 = 0;

    return m;
}

private Matrix3D ViewportTransform(double width, double height)
{
    Matrix3D m = new Matrix3D();

    m.M11 = width / 2.0; m.M12 = 0.0; m.M13 = 0.0; m.M14 = 0.0;
    m.M21 = 0.0; m.M22 = -height / 2.0; m.M23 = 0.0; m.M24 = 0.0;
    m.M31 = 0.0; m.M32 = 0.0; m.M33 = 1.0; m.M34 = 0.0;
    m.OffsetX = width / 2.0; m.OffsetY = height / 2.0; m.OffsetZ = 0.0; m.M44 = 1.0;

    return m;
}

Fields summary

The value of the first row and first column of this Matrix3D.

The value of the first row and second column of this Matrix3D.

The value of the first row and third column of this Matrix3D.

The value of the first row and fourth column of this Matrix3D.

The value of the second row and first column of this Matrix3D.

The value of the second row and second column of this Matrix3D.

The value of the second row and third column of this Matrix3D.

The value of the second row and fourth column of this Matrix3D.

The value of the third row and first column of this Matrix3D.

The value of the third row and second column of this Matrix3D.

The value of the third row and third column of this Matrix3D.

The value of the third row and fourth column of this Matrix3D.

The value of the fourth row and fourth column of this Matrix3D.

The value of the fourth row and first column of this Matrix3D.

The value of the fourth row and second column of this Matrix3D.

The value of the fourth row and third column of this Matrix3D.

Fields

  • M11
    M11
    M11
    M11

    The value of the first row and first column of this Matrix3D.

    public field double M11public field double M11Public Field M11
  • M12
    M12
    M12
    M12

    The value of the first row and second column of this Matrix3D.

    public field double M12public field double M12Public Field M12
  • M13
    M13
    M13
    M13

    The value of the first row and third column of this Matrix3D.

    public field double M13public field double M13Public Field M13
  • M14
    M14
    M14
    M14

    The value of the first row and fourth column of this Matrix3D.

    public field double M14public field double M14Public Field M14
  • M21
    M21
    M21
    M21

    The value of the second row and first column of this Matrix3D.

    public field double M21public field double M21Public Field M21
  • M22
    M22
    M22
    M22

    The value of the second row and second column of this Matrix3D.

    public field double M22public field double M22Public Field M22
  • M23
    M23
    M23
    M23

    The value of the second row and third column of this Matrix3D.

    public field double M23public field double M23Public Field M23
  • M24
    M24
    M24
    M24

    The value of the second row and fourth column of this Matrix3D.

    public field double M24public field double M24Public Field M24
  • M31
    M31
    M31
    M31

    The value of the third row and first column of this Matrix3D.

    public field double M31public field double M31Public Field M31
  • M32
    M32
    M32
    M32

    The value of the third row and second column of this Matrix3D.

    public field double M32public field double M32Public Field M32
  • M33
    M33
    M33
    M33

    The value of the third row and third column of this Matrix3D.

    public field double M33public field double M33Public Field M33
  • M34
    M34
    M34
    M34

    The value of the third row and fourth column of this Matrix3D.

    public field double M34public field double M34Public Field M34
  • M44
    M44
    M44
    M44

    The value of the fourth row and fourth column of this Matrix3D.

    public field double M44public field double M44Public Field M44
  • OffsetX
    OffsetX
    OffsetX
    OffsetX

    The value of the fourth row and first column of this Matrix3D.

    public field double OffsetXpublic field double OffsetXPublic Field OffsetX
  • OffsetY
    OffsetY
    OffsetY
    OffsetY

    The value of the fourth row and second column of this Matrix3D.

    public field double OffsetYpublic field double OffsetYPublic Field OffsetY
  • OffsetZ
    OffsetZ
    OffsetZ
    OffsetZ

    The value of the fourth row and third column of this Matrix3D.

    public field double OffsetZpublic field double OffsetZPublic Field OffsetZ

Device family

Windows 10 (introduced v10.0.10240.0)

API contract

Windows.Foundation.UniversalApiContract (introduced v1)

Attributes

Windows.Foundation.Metadata.WebHostHiddenAttribute
Windows.Foundation.Metadata.ContractVersionAttribute

Details

Assembly

Windows.UI.Xaml.Media.Media3D.dll