How do I set a camera rotation given a rotational matrix M (M is a 4 by 4 matrix)
glLoadMatrix():
Description
glLoadMatrix replaces the current matrix with the one whose elements are specified by m. The current matrix is the projection matrix, modelview matrix, or texture matrix, depending on the current matrix mode (see glMatrixMode).
Related
I want to transform a vector(0,0,0) to a new point with the transformation matrix but if you do the transformation [matrix * v] you would end up at vector(0,0,0) every time. I am thinking there is an added step that I need to do for this to end up working.
Transforming 3D zero-vector with a 3x3 matrix will always result in the zero-vector because 3x3 matrices can only represent linear transforms. But translations are not linear. Therefore, you need to use homogeneous coordinates and a 4x4 matrix. If you have a 4x4 translation matrix, you need to add 1 as the fourth dimension to the vector, so it will get (0, 0, 0, 1) and transform this with your matrix. If the matrix is just a translation (or in general an affine transform), you just need to cut off the fourth dimension to get the final 3D vector.
I am trying to image coordinates to 3D coordinates. Using the solvePnP function (in C++)has given me 3X1 rotation matrix and 3X1 translation matrix. But isn't the [R|t] matrix supposed to be 3X4?
Any help will be greatly appreciated!
From the OpenCV documentation for solvePnP:
"rvec – Output rotation vector (see Rodrigues() ) that, together with tvec , brings points from the model coordinate system to the camera coordinate system."
Following the link to Rodrigues():
src – Input rotation vector (3x1 or 1x3) or rotation matrix (3x3).
dst – Output rotation matrix (3x3) or rotation vector (3x1 or 1x3), respectively.
I'm projecting 3D points with X,Y,Z model coordinates to X,Y image coordinates using a 4x4 perspective view-projection matrix. There is only one model, so it is like a MVP matrix where the M matrix is unity.
Is it possible to extract the coordinates of the position (in model coordinates) of the camera from the view-projection matrix. (i.e. the translation component of the view-matrix)?
Also, what exactly is the meaning of the Z-component in the projected image coordinates (after division by W)? I know it is between -1 and 1 for points between the near and far planes, but is it possible to deduce the distance of the point to the camera (in model coordinates) from it?
The following site says to use the model_view matrix when computing the normal matrix (assuming we are not using the built in gl_NormalMatrix): (site)Light House. I have the following algorithm in my program:
//Calculate Normal matrix
// 1. Multiply the model matrix by the view matrix and then grab the upper left
// corner 3 x 3 matrix.
mat3x3 mv_orientation = glext::orientation_matrix<float, glext::column>(
glext::model_view<float, glext::column>(glext_model_, glext_view_));
// 2. Because openGL matrices use homogeneous coordinate an affine inversion
// should work???
mv_orientation.affine_invert();
// 3. The normal matrix is defined as the transpose of the inverse of the upper
// left 3 X 3 matrix
mv_orientation.transpose();
// 4. Place this into the shader
basic_shader_.set_uniform_3d_matrix("normal_matrix", mv_orientation.to_gl_matrix());
Assuming most statements above are correct in the aforementioned code. Do you not include the projection matrix in the computation of the normal matrix? If not why, does the projection matrix not affect the normals like they do points?
That's because projection is not an affine transformation. Projections don't maintain the inner product and then they don't maintain the angles. And the real angles that have effect on the light diffusion and reflection are the angles in the affine 3d space. So using also the projection matrix would get you different angles, wrong angles, and hence wrong lights.
Do you not include the projection matrix in the computation of the normal matrix?
No. Normals are required for calculations, like illumination, happening in world and/or view space. It doesn't make sense from a mathematical point of you to do this after projection.
If not why, does the projection matrix not affect the normals like they do points?
Because it would make no sense. That normals should not undergo projective transformation was the original reason to have a separate projection matrix. If you'd put normals through the projection they'd loose their meaning and usefullness.
http://www.cs.uaf.edu/2007/spring/cs481/lecture/01_23_matrices.html
I have just finished reading this, but i have 2 questions about multiplications.
gl_Position = gl_ProjectionMatrix*gl_ModelViewMatrix*gl_Vertex
This is the final screen coordinates (x,y) when i multiply them all. What if i only multiply gl_ModelViewMatrix*gl_Vertex or gl_ProjectionMatrix*gl_Vertex ? And what does gl_Vertex mean alone ?
gl_Vertex is the vertex coordinate in world space.
vertices and the eye may be arbitrarily placed and oriented in world space.
After multiplication with ModelViewMatrix, you get a vertex coordinate in 'eye-space', a coordinate system with the eye at 0,0,0. Multiplying by the projection matrix(and doing that homogenous coordinate system division thingy) gives you coordinates in screen space. Those are not pixel-coordinates yet, but some normalized coordinate system with 0,0,0 in the center of the screen/window. Viewport transform is last. It maps the image to window (pixel?) coordinates.
An explanation is given in:
http://www.srk.fer.hr/~unreal/theredbook/
chapter 3.
What if i only multiply gl_ModelViewMatrix*gl_Vertex or gl_ProjectionMatrix*gl_Vertex ?
Then the projection matrix (the 1st case) or model-view matrix (the 2nd case) will not take effect. If they are identity matrices, you will not see effect. If they are not, then your view angle or position might be wrong.
And what does gl_Vertex mean alone ?
gl_Vertex is the vertex coordinate that is passed to the input of the pipeline.