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dotnet-desktop-guide/framework/wpf/graphics-multimedia/3-d-transformations-overview.md
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ms.assetid: e45e555d-ac1e-4b36-aced-e433afe7f27f
---
# 3D Transformations Overview
This topic describes how to apply transformations to 3D models in the [!INCLUDE[TLA#tla_winclient](../../../includes/tlasharptla-winclient-md.md)] graphics system. Transformations allow the developer to reposition, resize, and reorient models without changing the base values that define them.
This topic describes how to apply transformations to 3D models in the Windows Presentation Foundation (WPF) graphics system. Transformations allow the developer to reposition, resize, and reorient models without changing the base values that define them.
## 3D Coordinate Space
3D graphics content in [!INCLUDE[TLA#tla_winclient](../../../includes/tlasharptla-winclient-md.md)] is encapsulated in an element, <xref:System.Windows.Controls.Viewport3D>, that can participate in the two-dimensional element structure. The graphics system treats Viewport3D as a two-dimensional visual element like many others in [!INCLUDE[TLA#tla_winclient](../../../includes/tlasharptla-winclient-md.md)]. Viewport3D functions as a window—a viewport—into a three-dimensional scene. More accurately, it is a surface on which a 3D scene is projected. Although you can use Viewport3D with other 2D drawing objects in the same scene graph, you cannot interpenetrate 2D and 3D objects within a Viewport3D. In the following discussion, the coordinate space described is contained by the Viewport3D element.
3D graphics content in Windows Presentation Foundation (WPF) is encapsulated in an element, <xref:System.Windows.Controls.Viewport3D>, that can participate in the two-dimensional element structure. The graphics system treats Viewport3D as a two-dimensional visual element like many others in Windows Presentation Foundation (WPF). Viewport3D functions as a window—a viewport—into a three-dimensional scene. More accurately, it is a surface on which a 3D scene is projected. Although you can use Viewport3D with other 2D drawing objects in the same scene graph, you cannot interpenetrate 2D and 3D objects within a Viewport3D. In the following discussion, the coordinate space described is contained by the Viewport3D element.
The [!INCLUDE[TLA#tla_winclient](../../../includes/tlasharptla-winclient-md.md)] coordinate system for 2D graphics locates the origin in the upper left of the rendering surface (typically the screen). In the 2D system, positive x-axis values proceed to the right and positive y-axis values proceed downward. In the 3D coordinate system, however, the origin is located in the center of the screen, with positive x-axis values proceeding to the right but positive y-axis values proceeding upward instead, and positive z-axis values proceeding outward from the origin, toward the viewer.
The Windows Presentation Foundation (WPF) coordinate system for 2D graphics locates the origin in the upper left of the rendering surface (typically the screen). In the 2D system, positive x-axis values proceed to the right and positive y-axis values proceed downward. In the 3D coordinate system, however, the origin is located in the center of the screen, with positive x-axis values proceeding to the right but positive y-axis values proceeding upward instead, and positive z-axis values proceeding outward from the origin, toward the viewer.
![Coordinate systems](./media/coordsystem-1.png "CoordSystem-1")
Coordinate System Comparison
The space defined by these axes is the stationary frame of reference for 3D objects in [!INCLUDE[TLA#tla_winclient](../../../includes/tlasharptla-winclient-md.md)]. As you build models in this space and create lights and cameras to view them, it's helpful to distinguish this stationary frame of reference, or "world space," from the local frame of reference you create for each model when you apply transformations to it. Remember also that objects in world space might look entirely different, or not be visible at all, depending on light and camera settings, but the position of the camera does not change the location of objects in world space.
The space defined by these axes is the stationary frame of reference for 3D objects in Windows Presentation Foundation (WPF). As you build models in this space and create lights and cameras to view them, it's helpful to distinguish this stationary frame of reference, or "world space," from the local frame of reference you create for each model when you apply transformations to it. Remember also that objects in world space might look entirely different, or not be visible at all, depending on light and camera settings, but the position of the camera does not change the location of objects in world space.
## Transforming Models
When you create models, they have a particular location in the scene. To move those models around in the scene, to rotate them, or to change their size, it's not practical to change the vertices that define the models themselves. Instead, just as in 2D, you apply transformations to models.
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Each model object has a <xref:System.Windows.Media.Media3D.Model3D.Transform%2A> property with which you can move, re-orient, or resize the model. When you apply a transform, you effectively offset all the points of the model by whatever vector or value is specified by the transform. In other words, you've transformed the coordinate space in which the model is defined ("model space"), but you haven't changed the values that make up the model's geometry in the coordinate system of the entire scene ("world space").
## Translation Transformations
3D transformations inherit from the abstract base class <xref:System.Windows.Media.Media3D.Transform3D>; these include the affine transform classes <xref:System.Windows.Media.Media3D.TranslateTransform3D>, <xref:System.Windows.Media.Media3D.ScaleTransform3D>, and <xref:System.Windows.Media.Media3D.RotateTransform3D>. The [!INCLUDE[TLA#tla_winclient](../../../includes/tlasharptla-winclient-md.md)] 3D system also provides a <xref:System.Windows.Media.Media3D.MatrixTransform3D> class that lets you specify the same transformations in more concise matrix operations.
3D transformations inherit from the abstract base class <xref:System.Windows.Media.Media3D.Transform3D>; these include the affine transform classes <xref:System.Windows.Media.Media3D.TranslateTransform3D>, <xref:System.Windows.Media.Media3D.ScaleTransform3D>, and <xref:System.Windows.Media.Media3D.RotateTransform3D>. The Windows Presentation Foundation (WPF) 3D system also provides a <xref:System.Windows.Media.Media3D.MatrixTransform3D> class that lets you specify the same transformations in more concise matrix operations.
<xref:System.Windows.Media.Media3D.TranslateTransform3D> moves all the points in the Model3D in the direction of the offset vector you specify with the <xref:System.Windows.Media.Media3D.TranslateTransform3D.OffsetX%2A>, <xref:System.Windows.Media.Media3D.TranslateTransform3D.OffsetY%2A>, and <xref:System.Windows.Media.Media3D.TranslateTransform3D.OffsetZ%2A> properties. For example, given one vertex of a cube at (2,2,2), an offset vector of (0,1.6,1) would move that vertex (2,2,2) to (2,3.6,3). The cube's vertex is still (2,2,2) in model space, but now that model space has changed its relationship to world space so that (2,2,2) in model space is (2,3.6,3) in world space.
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[!code-xaml[animation3dgallery_snip#Rotate3DUsingAxisAngleRotation3DExampleWholePage](~/samples/snippets/csharp/VS_Snippets_Wpf/Animation3DGallery_snip/CS/Rotat3DUsingAxisAngleRotation3DExample.xaml#rotate3dusingaxisanglerotation3dexamplewholepage)]
Note:[!INCLUDE[TLA#tla_winclient](../../../includes/tlasharptla-winclient-md.md)] 3D is a right-handed system, which means that a positive angle value for a rotation results in a counter-clockwise rotation about the axis.
Note:Windows Presentation Foundation (WPF) 3D is a right-handed system, which means that a positive angle value for a rotation results in a counter-clockwise rotation about the axis.
Axis-angle rotations assume rotation about the origin if a value is not specified for the <xref:System.Windows.Media.Media3D.RotateTransform3D.CenterX%2A>, <xref:System.Windows.Media.Media3D.RotateTransform3D.CenterY%2A>, and <xref:System.Windows.Media.Media3D.RotateTransform3D.CenterZ%2A> properties on RotateTransform3D. As with scaling, it's helpful to remember that the rotation transforms the model's entire coordinate space. If the model was not created about the origin, or has been translated previously, the rotation might "pivot" about the origin instead of rotating in place.
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When building a scene, it's common to apply more than one transformation to a model. Add transforms to the <xref:System.Windows.Media.Media3D.Transform3DGroup.Children%2A> collection of the <xref:System.Windows.Media.Media3D.Transform3DGroup> class to group transforms conveniently to apply to various models in the scene. It's often convenient to reuse a transformation in several different groups, in much the way that you can reuse a model by applying a different set of transforms to each instance. Note that order in which the transformations are added to the collection is significant: transforms in the collection are applied from first to last.
## Animating Transformations
The [!INCLUDE[TLA#tla_winclient](../../../includes/tlasharptla-winclient-md.md)] 3D implementation participates in the same timing and animation system as 2D graphics. In other words, to animate a 3D scene, animate the properties of its models. It's possible to animate properties of primitives directly, but it's typically easier to animate transformations that change the position or appearance of models. Because transformations can be applied to <xref:System.Windows.Media.Media3D.Model3DGroup> objects as well as individual models, it's possible to apply one set of animations to the children of a Model3Dgroup and another set of animations to a group of objects. For background information on the [!INCLUDE[TLA#tla_winclient](../../../includes/tlasharptla-winclient-md.md)] timing and animation system, see [Animation Overview](animation-overview.md) and [Storyboards Overview](storyboards-overview.md).
The Windows Presentation Foundation (WPF) 3D implementation participates in the same timing and animation system as 2D graphics. In other words, to animate a 3D scene, animate the properties of its models. It's possible to animate properties of primitives directly, but it's typically easier to animate transformations that change the position or appearance of models. Because transformations can be applied to <xref:System.Windows.Media.Media3D.Model3DGroup> objects as well as individual models, it's possible to apply one set of animations to the children of a Model3Dgroup and another set of animations to a group of objects. For background information on the Windows Presentation Foundation (WPF) timing and animation system, see [Animation Overview](animation-overview.md) and [Storyboards Overview](storyboards-overview.md).
To animate an object in [!INCLUDE[TLA#tla_winclient](../../../includes/tlasharptla-winclient-md.md)], create a timeline, define an animation (which is really a change in some property value over time), and specify the property to which to apply the animation. This property must be a property of a FrameworkElement. Because all the objects in a 3D scene are children of Viewport3D, the properties targeted by any animation you want to apply to the scene are properties of properties of Viewport3D. It's important to work out the property path for the animation carefully, because the syntax can be verbose.
To animate an object in Windows Presentation Foundation (WPF), create a timeline, define an animation (which is really a change in some property value over time), and specify the property to which to apply the animation. This property must be a property of a FrameworkElement. Because all the objects in a 3D scene are children of Viewport3D, the properties targeted by any animation you want to apply to the scene are properties of properties of Viewport3D. It's important to work out the property path for the animation carefully, because the syntax can be verbose.
Suppose you want to rotate an object in place, but also to apply a swinging motion to expose more of the object to view. You might choose to apply a RotateTransform3D to the model, and animate the axis of its rotation from one vector to another. The following code example demonstrates applying a <xref:System.Windows.Media.Animation.Vector3DAnimation> to the Axis property of the transformation's Rotation3D, assuming the RotateTransform3D to be one of several transforms applied to the model with a <xref:System.Windows.Media.TransformGroup>.