Matrix: transformpoints of GDI + and ry transform C ++

There are a lot of introductions to Baidu's search for ".

 

This is an example in vs2008:

Void example_transpoints (HDC) <br/>{< br/> graphics (HDC); <br/> Pen (color (255, 0, 0,255 )); </P> <p> point points [5] = {<br/> point (50,100), <br/> point (100, 50 ), <br/> point (150,125), <br/> point (200,100), <br/> point (250,150) };</P> <p> matrix (1.0f, 0.0f, 0.0f, 2.0f, 0.0f, 0.0f); </P> <p> graphics. drawcurve (& pen, points, 5); <br/> matrix. transformpoints (points, 5); <br/> graphics. drawcurve (& pen, points, 5); <br/>}< br/>

CodeIn, transformpoints changes the value of points, which is actually an affine transformation. (Here is the transformation in the plane)

Write down the running result and change points:

50,200

100,100

150,250

200,200

250,300

We can see that the result is doubled in the Y axis.

 

For matrix, it is actually a 3*3 matrix:

|1.0f0.0f0.0f| |0.0f2.0f0.0f| |0.0f0.0f1.0f|

 

The first and second parameters of matrix are the first element of the first line of matrix and the second element of the first line;

The third and fourth parameters are the first element of the second row of the matrix and the second element of the second row;

The fifth and sixth parameters are the first element of the third row of the matrix and the second element of the third row;

The matrix constructor is described in msdn.

The third column of the Matrix is always [0 0 1] T, so it is omitted.

Why is the third column omitted? Please refer to Baidu entry

Http://baike.baidu.com/view/954621.htm

Take the Translation Transform as an example (Note: You need to transpose ):

|100| |010| |TXTy1|

The third column of several basic operations of the affinator transformation is [0 0 1] T, so it is omitted.

 

The general form of affine transformation (but it seems that this formula only includes: Translation transformation, Rotation Transformation and scaling transformation, excluding shear transformation ):

 

| (λ x) COS θ (λ x) sin θ 0 | | X1 Y1 1 | = | x Y 1 | * |-(λ y) sin θ (λ y) COS θ 0 | | X0 y0 1 |

 

The transformed coordinates are:

X1 = (λ x) x cosine cos θ-(λ y) x cosine sin θ + x0 Y1 = (λ x) x cosine sin θ + (λ y) y cosine cos θ + y0

Where:

(X0, y0) is the original coordinate origin;

θ is the coordinate rotation angle;

λ x and λ y indicate the shrinkage rate of the Original Coordinate System on the X and Y axes. (Note that λ x is a whole, not λ multiplied by X; λ y is the same)