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== The role of "x_gl_mat1" == | == The role of "x_gl_mat1" == | ||
=== x_view === | |||
The following section of code composes the matrix "x_view", which is a subset of "x_gl_mat1". The matrix "x_gl_mat1" consists of multiple translations, scales and one rotation operation. | The following section of code composes the matrix "x_view", which is a major subset of "x_gl_mat1". The matrix "x_gl_mat1" consists of multiple translations, scales and one rotation operation. Hint: A visualization of the individual operation steps is shown in a picture below. | ||
{{Code|Section of axes::properties::update_camera ()"|<syntaxhighlight lang="C" style="font-size:13px"> | {{Code|Section of axes::properties::update_camera ()"|<syntaxhighlight lang="C" style="font-size:13px"> | ||
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</syntaxhighlight>}} | </syntaxhighlight>}} | ||
To visualize the matrix properties, the "x_gl_mat1" matrix is multiplied by the object coordinates. | === x_gl_mat1 === | ||
To visualize the matrix properties, the "x_gl_mat1" matrix is multiplied by the object coordinates. After the transformation, the plot box is aligned with the Z-axis and the view point is at the origin <math display="inline">[0,0,0]</math>. The matrix transforms world coordinates into camera coordinates. The purple planes show the near and far clipping planes. | |||
[[File:Octave_x_gl_mat1_setup.png|center|250px]] | [[File:Octave_x_gl_mat1_setup.png|center|250px]] | ||
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== The role of "x_gl_mat2" == | == The role of "x_gl_mat2" == | ||
=== Bounding box === | |||
The matrix "x_gl_mat2" is composed of the sub matrices "x_viewport" and "x_projection". The purpose of these matrices is to fit the associated 2D image of the above transformation result into a "bounding box". The bounding box is defined as follows: | The matrix "x_gl_mat2" is composed of the sub matrices "x_viewport" and "x_projection". The purpose of these matrices is to fit the associated 2D image of the above transformation result into a "bounding box". The bounding box is defined as follows: | ||
* bb(0), bb(1): Position of the viewport | |||
* bb(2), bb(3): Width and height of the viewport | |||
Hint: If you debug in "update_camera ()", you can print "bb": | Hint: If you debug in "update_camera ()", you can print "bb": | ||
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(gdb) print *bb.rep.data@bb.rep.len | (gdb) print *bb.rep.data@bb.rep.len | ||
Compare the result with the output | Compare the result with the output on the Octave prompt: | ||
hax = axes (); | hax = axes (); | ||
get (hax, "position"); | get (hax, "position"); | ||
=== x_projection === | |||
In the following simplified code section the matrix "x_projection" is assembled. It is used to normalize the image of the above transformation. For this purpose, the field of view (FOV) must be calculated: | In the following simplified code section the matrix "x_projection" is assembled. It is used to normalize the image of the above transformation. For this purpose, the field of view (FOV) must be calculated: | ||
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</syntaxhighlight>}} | </syntaxhighlight>}} | ||
"x_viewport" is a transformation used to place the "normalized" plot box in the center and to | === x_viewport === | ||
"x_viewport" is a transformation used to place the previously "normalized" plot box in the center and to fit it tightly into the bounding box: | |||
{{Code|Section of axes::properties::update_camera ()"|<syntaxhighlight lang="C" style="font-size:13px"> | {{Code|Section of axes::properties::update_camera ()"|<syntaxhighlight lang="C" style="font-size:13px"> | ||