barcode generator source code in c#.net x' = 1 * x + 0 * y + dX y' = 0 * x + 1 * y + dY in Java

Encoder Quick Response Code in Java x' = 1 * x + 0 * y + dX y' = 0 * x + 1 * y + dY

x' = 1 * x + 0 * y + dX y' = 0 * x + 1 * y + dY
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The imaging model
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These formulas scale the coordinate system with factors sX in the X direction and sY in the Y direction:
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x' = sX * x + 0 * y + 0 y' = 0 * x + sY * y + 0
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To rotate the coordinate system with an angle , you need to use the following equations:
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x' = cos( ) * x - sin( ) * y + 0 y' = sin( ) * x + cos( ) * y + 0
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Skewing the coordinates is done like this:
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x' = 1 * x + tan( ) * y + 0 y' = tan( ) * x + 1 * y + 0
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where is the new angle of the X axis and is the new angle of the Y axis. You can use these formulas to compute the values for a, b, c, d, e, and f. For example, if you want to combine a translation (dX, dY), a scaling (sX, sY), and a rotation , you d use these values:
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a b c d e f = = = = = = sX * sY * sX * sY * dX; dY; cos( ); sin( ); -sin( ); cos( );
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If you combine different concatCTM() operations, you can compute the resulting transformation by multiplying the matrices with each other. The order is important when performing transformations one after the other. This can be demonstrated by switching the lines with concatCTM() methods in the sequence between saveState() and restoreState() in listing 14.6.
NOTE
Suppose you want the same result as shown in figure 14.4 but without using concatCTM() directly. In that case, you ll need a version of the addTemplate() method that takes a, b, c, d, e, and f parameters.
ADDING TEMPLATES AND IMAGES
Listing 14.7 is exactly equivalent to listing 14.6. First you add the template without any transformation B in listing 14.7. Then you add two templates, C and D, which are scaled and translated: E skews and translates the template, and F rotates and translates the template. Finally, the template is rotated, scaled, and translated G.
Listing 14.7 TransformationMatrix2.java
canvas.addTemplate(template, canvas.addTemplate(template, canvas.addTemplate(template, canvas.addTemplate(template, canvas.addTemplate(template, canvas.addTemplate(template, 0, 0); 0.5f, 0, 0, 0.5f, -595, 0); 0.5f, 0, 0, 0.5f, -297.5f, 297.5f); 1, 0, 0.4f, 1, -750, -650); 0, -1, -1, 0, 650, 0); 0, -0.2f, -0.5f, 0, 350, 0);
C D E F G
Overview of the graphics state methods
The transformation matrix elements in D are the result of the following multiplication: 1 0 0 0.5 0 1 0 0 595 595 1 595 0 0.5 0 0 0.5 0 0 0 = 0 0.5 0 1 297.5 297.5 1
The parameters in G were computed like this: 0.2 0 0 0.5 0 300 0 0 0 1 1 650 1 0 0 0 0 0 = 0.5 1 350 0.2 0 0 0 0 1
Observe that you get a different result if you switch the order of the multiplication: 0 1 1 0 650 0 0 0.2 0 0 1 0 0 0.5 300 0 0 1 0 = 0.2 130 0.5 0 0 0 0 1
This proves that the order of the concatCTM() methods in listing 14.6 matters. Table 14.9 lists the methods that can be used to add templates and images using iText.
Table 14.9 PDF
PdfTemplate and Image methods in PdfContentByte
Parameters Description The operator Do, preceded by a name of a form XObject, such as /Xf1, paints the XObject. iText will take care of handling the template object, as well as saving the state, performing a transformation of the CTM that s used for adding the XObject, and restoring the state. The operator Do, preceded by a name of an image XObject, such as /img0, paints the image. iText will take care of storing the image stream correctly, as well as saving the state, performing a transformation of the CTM that s used for adding the image, and restoring the state. As discussed in section 3.4.1, images can also be added inline. In that case, there s no Do operator, but the image properties and bytes are added inside a BI and EI sequence.
iText method
addTemplate
(template, e, f) (template, a, b, c, d, e, f)
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