GlOrtho矩阵的开罗矩阵等价物？

Question

Given that I do something like this:

void glOrtho(   GLdouble    left, 
    GLdouble    right, 
    GLdouble    bottom, 
    GLdouble    top, 
    GLdouble    nearVal, 
    GLdouble    farVal);

and the result is: http://www.opengl.org/sdk/docs/man/xhtml/glOrtho.xml w could I achieve a matrix like this:

http://cairographics.org/manual/cairo-matrix.html

I tried this:

cairo_matrix_t mat;
            mat.xx = 2 / (right - left);
            mat.yx = 0;
            mat.xy =  2 / (top - bottom);
            mat.yy = 0;
            mat.x0 = 0;
            mat.y0 = 0;

cairo_set_matrix(cr,&mat);

But it did not work. How could I acheive the same matrix that GlOrtho makes in Cairo? Thanks

Answer 1

I don't know Cairo so I'll delete my answer if a better one comes.

According to the docs of Cairo:

x_new = xx * x + xy * y + x0;
y_new = yx * x + yy * y + y0;

When you use OpenGL, the formula is like: ( m being the matrix)

x_new = m(1,1) * x + m(1,2) * y + m(1,3) * z + m(1,4)
y_new = m(2,1) * x + m(2,2) * y + m(2,3) * z + m(2,4)
z_new = m(3,1) * x + m(3,2) * y + m(3,3) * z + m(3,4)

(note that for the sake of simplicity I did not mention the fourth coordinate)

So what you have to do is simply match the two formulas:

mat.xx = 2 / (right - left);
mat.yy = 2 / (top - bottom);
mat.xy = 0;
mat.yx = 0;
mat.x0 = -(right + left) / (right - left);
mat.y0 = -(top + bottom) / (top - bottom);

Please try this