Matrix3D Struct
Definition
Important
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Represents a 4 × 4 matrix that is used for transformations in a 3-D space. Used as a value for Matrix3DProjection.ProjectionMatrix.
public value class Matrix3D/// [Windows.Foundation.Metadata.ContractVersion(Microsoft.UI.Xaml.WinUIContract, 65536)]
struct Matrix3D[Windows.Foundation.Metadata.ContractVersion(typeof(Microsoft.UI.Xaml.WinUIContract), 65536)]
public struct Matrix3DPublic Structure Matrix3D<Matrix3DProjection ProjectionMatrix="m11, m12, m13, m14,
m21, m22, m23, m24, m31, m32, m33, m34, offsetX, offsetY, offsetZ, m44" />
- or -
<!--xmlns:m3d="using:Windows.UI.Xaml.Media.Media3D"-->
<m3d:Matrix3D>
m11, m12, m13, m14, m21, m22, m23, m24, m31, m32, m33, m34, offsetX, offsetY, offsetZ, m44
</m3d:Matrix3D>
- Inheritance
-
Matrix3D
- Attributes
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 matrices 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;
}
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 UIElement.Projection property). The matrix lets you apply arbitrary model transform matrices and perspective matrices to visual elements.
Matrix3D has this row-vector syntax:
| M11 | M12 | M13 | M14 |
| M21 | M22 | M23 | M24 |
| M31 | M32 | M33 | M34 |
| OffsetX | OffsetY | OffsetZ | M44 |
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: Matrix3DProjection.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 Matrix3DProjection.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 Matrix3DProjection.ProjectionMatrix that uses this same string format.
Fields
| M11 |
The value of the first row and first column of this Matrix3D. |
| M12 |
The value of the first row and second column of this Matrix3D. |
| M13 |
The value of the first row and third column of this Matrix3D. |
| M14 |
The value of the first row and fourth column of this Matrix3D. |
| M21 |
The value of the second row and first column of this Matrix3D. |
| M22 |
The value of the second row and second column of this Matrix3D. |
| M23 |
The value of the second row and third column of this Matrix3D. |
| M24 |
The value of the second row and fourth column of this Matrix3D. |
| M31 |
The value of the third row and first column of this Matrix3D. |
| M32 |
The value of the third row and second column of this Matrix3D. |
| M33 |
The value of the third row and third column of this Matrix3D. |
| M34 |
The value of the third row and fourth column of this Matrix3D. |
| M44 |
The value of the fourth row and fourth column of this Matrix3D. |
| OffsetX |
The value of the fourth row and first column of this Matrix3D. |
| OffsetY |
The value of the fourth row and second column of this Matrix3D. |
| OffsetZ |
The value of the fourth row and third column of this Matrix3D. |