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Joined 29 March 2020
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= OpenGL coordinate systems = | = Investigations on update_camera() = | ||
In the second part of <math display="inline">\rightarrow</math> "axes::properties::update_camera ()" the view transformation "x_gl_mat1" and projection matrix "x_gl_mat2" are put together. The following article illustrates some of the properties of "x_gl_mat1" and "x_gl_mat2". | |||
== OpenGL coordinate systems == | |||
In the Octave plotting backend, we find various OpenGL transformations. Some of the classic OpenGL transformation steps, as well as coordinate systems, are shown in the following picture: | In the Octave plotting backend, we find various OpenGL transformations. Some of the classic OpenGL transformation steps, as well as coordinate systems, are shown in the following picture: | ||
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[[File:Octave_coordinate_systems.png|center|350px]] | [[File:Octave_coordinate_systems.png|center|350px]] | ||
= The Octave coordinate system = | == The Octave coordinate system == | ||
In Octave a plot scene is defined by a "view point", a "camera target" and an "up vector". | In Octave a plot scene is defined by a "view point", a "camera target" and an "up vector". | ||
[[File:Octave_view_point_setup_to_scale.png|center|750px]] | [[File:Octave_view_point_setup_to_scale.png|center|750px]] | ||
== The role of "x_gl_mat1" == | == The role of "x_gl_mat1" == | ||
The following section of code composes the matrix "x_view", which is a | 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. | ||
{{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. The plot box is now 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| | |||
The individual translation, scaling and rotation operations of "x_gl_mat1", are shown in the following figure: | The individual translation, scaling and rotation operations of "x_gl_mat1", are shown in the following figure: | ||
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== The role of "x_gl_mat2" == | == The role of "x_gl_mat2" == | ||
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 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 | |||
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": | ||
(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 in the Octave prompt: | ||
hax = axes (); | hax = axes (); | ||
get (hax, "position") | get (hax, "position"); | ||
In the following simplified code section the matrix "x_projection" is assembled. It is used to scale the image of the above transformation into the bounding box of the window. For this purpose, the field of view (FOV) must be calculated: | |||
In the following simplified code section the matrix "x_projection" is | |||
{{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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v_angle = get_cameraviewangle (); | v_angle = get_cameraviewangle (); | ||
// x_projection | // x_projection = diag([1, 1, 1, 1]) | ||
Matrix x_projection = xform_matrix (); | Matrix x_projection = xform_matrix (); | ||
// Calculate backwards from the angle to the ratio. This step | // Calculate backwards from the angle to the ratio. This step | ||
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</syntaxhighlight>}} | </syntaxhighlight>}} | ||
"x_viewport" is a 2D transformation used to place the "normalized" plot box in the center of the bounding box: | |||
"x_viewport" is a transformation used to place the | |||
{{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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pix = (bb(2) < bb(3) ? bb(2) : bb(3)); | pix = (bb(2) < bb(3) ? bb(2) : bb(3)); | ||
// x_viewport | // x_viewport = diag([1, 1, 1, 1]) | ||
Matrix x_viewport = xform_matrix (); | Matrix x_viewport = xform_matrix (); | ||
// Move to the center of the bounding box inside the figure. | // Move to the center of the bounding box inside the figure. | ||
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</syntaxhighlight>}} | </syntaxhighlight>}} | ||
Note: The matrix | Note: The matrix just scales x, y so that the image fits tightly into the bounding box. The z-coordinate is not modified. | ||