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CHAPTER 9 GRAPHICS
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points are calculated by multiplying each point (x,y) in the element being transformed by the matrix shown in Figure 9-12.
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Figure 9-12. Transformation matrix to translate ten units to the right In general, the result of multiplying a point (technically a vector) by the matrix is (x * M11 + y * M12 + offsetX), (x * M21 + y * M22 + offsetY). There is a special matrix, known as the identity matrix, where M11 = 1, M12 = 0, M21 = 0, and M22 = 1, and OffsetX and OffsetY are 0. If you multiply any (x,y) point by the identity matrix, you ll get the same point again, provided that OffsetX and OffsetY are 0. (Go ahead and try this on a piece of paper.) This identity matrix is important because it is the default configuration of the matrix. We can skew both coordinates and translate the element at the same time by specifying OffsetX and the M12 and M21 properties as follows: <Rectangle Stroke="Crimson" Fill="Crimson" Width="50" Height="50"> <Rectangle.RenderTransform> <MatrixTransform> <MatrixTransform.Matrix> <Matrix OffsetX="-10" M12="0.5" M21="0.5"/> </MatrixTransform.Matrix> </MatrixTransform> </Rectangle.RenderTransform> </Rectangle> From left to right, Figure 9-13 shows our normal rectangle, the rectangle translated right using a matrix, and the rectangle skewed and translated at the same time.
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Figure 9-13. Using MatrixTransform to translate and skew/translate
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CHAPTER 9 GRAPHICS
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Combining Multiple Transformations
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While you could use the MatrixTransform class to combine multiple transformations into a single transformation, if you want to combine two or more of the directly supported transformations (such as a rotation and a scale), you can use the TransformGroup transform. Figure 9-14 shows the result of combining a ScaleTransform and a RotateTransform together inside a TransformGroup.
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Figure 9-14. Combining transforms using TransformGroup <Rectangle Stroke="Crimson" Fill="Crimson" Width="50" Height="50"> <Rectangle.RenderTransform> <TransformGroup> <ScaleTransform ScaleX="0.75" ScaleY="0.75" CenterX="25" CenterY="25"/> <RotateTransform Angle="45" CenterX="25" CenterY="25"/> </TransformGroup> </Rectangle.RenderTransform> </Rectangle> The TransformGroup class is used in this code to apply multiple transformations simultaneously.
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Composite Transformation
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Silverlight 4 simplifies the code development to implement multiple transforms to an object by adding a CompositeTransform class. The CompositeTransform class provides a simpler way to transform an element, by simply offering a single object to instantiate rather than a group of transforms made for specific transforms. In the previous example, we used the TransformGroup class to combine scale and rotate transformations to the rectangle. Using the single CompositeTransform XAML node (or code-behind), now you can combine scale, skew, rotate, and translate transformation all together. This simplifies the code and makes it more concise, user-friendly, and readable. There is one restriction to apply the composite transformation it follows scale, skew, rotate, and translate transformation order to apply multiple transformations. If you have to follow a different order then you need to use the TransformGroup class. Table 9-8 lists key properties of the CompositeTransform class.
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CHAPTER 9 GRAPHICS
Table 9-8. Key Properties of the System.Windows.Media.CompositeTransform class
Property
CenterX
Type
double
Description
Defines x-coordinate of the center point for all transforms specified by CompositeTransform. Defines y-coordinate of the center point for all transforms specified by the CompositeTransform. Defines angle for clockwise rotation (in degrees). The default value is 0. Defines the x-axis scale factor for stretching or shrinking an object horizontally. The default value is 1 (the object is not scaled in horizontally). A 0 to 1 value decreases the width of the scaled object. A value set to more than 1 increases the width of the scaled object. 0 to -1 value flips the scale object horizontally and decreases its width. -1 value flips the scaled object but does not change the horizontal size. A value less than -1 flips the scale object and increases its width. Defines the y-axis scale factor for stretching or shrinking an object vertically. The default value is 1 (the object is not scaled vertically). A 0 to 1 value decreases the height of the scaled object. A value set to more than 1 increases the height of the scaled object. A 0 to -1 value flips the scale object and decreases its height. A -1 value flips the scaled object but does not change the vertical size. A value less than -1 flips the scale object and increases its height. Defines the x-axis skew angle, which is measured in degrees counterclockwise from the y axis. A skew transform can be useful for creating the illusion of threedimensional depth in a two-dimensional object. The default value is 0. Positive value results in the counterclockwise skew. Negative value results in the clockwise skew. Gets or sets the y-axis skew angle, which is measured in degrees counterclockwise from the x axis. A skew transform can be useful for creating the illusion of threedimensional depth in a two-dimensional object. The default value is 0. Positive value results in the counterclockwise skew. Negative value results in the clockwise skew. Defines the distance to translate along the x axis (in pixels). The default value is 0. Positive value moves the object to the right and negative moves it to the left. Defines the distance to translate (move) an object along the y axis (in pixels). The default value is 0. Positive value moves the object down and negative moves it up.
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