CODEWITHSUNDEEP
c++openglglm-math
Jambon
Jambon

Reputation: 125

LookAt matrix when casting shadows parallel to up vector

I am following the LearnOpenGL tutorials and have been tinkering with shadows casting. So far everything is working correctly but there is this very specific problem where I can't cast shadows that from a purely vertical directional light. Let's add some code. My light space matrix looks like this:

glm::mat4 view = glm::lookAt(-direction, glm::vec3(0.0f), glm::vec3(0.0f, 1.0f, 0.0f));
return glm::ortho(-10.0f, 10.0f, -10.0f, 10.0f, -10.0f, 10.0f) * view;

direction is a vector with as direction the direction of the directional light, of course. Everything works well until that direction vector is set to (0,-1,0), because it is parallel to the up vector (0,1,0). To construct the lookAt matrix, glm is performing the cross product between the up vector and the difference between the center and the eye (so in that case it's basically the direction), but that cross product won't give any result since the two vectors are parallel.

Knowing all of this, my question would be : how should my lookAt view matrix when the up vector and the direction of the light are parallel ?

Edit : Thank you for your answer, I changed my code to this : 

if(abs(direction.x) < FLT_EPSILON && abs(direction.z) < FLT_EPSILON) 
view = glm::lookAt(-direction, glm::vec3(0.0f), glm::vec3(0.0f, 0.0f, 1.0f)); 
else 
view = glm::lookAt(-direction, glm::vec3(0.0f), glm::vec3(0.0f, 1.0f, 0.0f)); 
return glm::ortho(-10.0f, 10.0f, -10.0f, 10.0f, -10.0f, 10.0f) * view;

and now everything works fine !

Upvotes: 1

Views: 715

Answers (1)

Rabbid76
Rabbid76

Reputation: 211135

When the up-vector and the line of sight are parallel, then the view matrix is undefined, because the Cross product is (0, 0, 0).
The view matrix is an Orthogonal matrix, this means each of the 3 axis is perpendicular to plane which is formed by the 2 other axis. Respectively the angele between the axis is 90°.
The view matrix is the inverse matrix of that matrix which defines the viewing position and orientation. This matrix is defined by the parameters to glm::lookAt. 2 of the axis a res specified by the line of sight and the up-vector. The 3rd axis is calculated by the cross product.

This all means, you have to specify the matrix by 2 Orthogonal directions. If the angle between the direction vectors is not exactly (90°) then this is corrected by glm::lookAt. But the algorithm fails to do that if the vectors are parallel. Define a line of sight (direction) vector and a up-vector, with an angle of 90° to each another. If you rotate on of them, then you've to rotate the other vector in the same way.

e.g. Lets assume you've a direction vector (line of sight) and an up-vector:

direction: (0, 0, 1)
up       : (0, 1, 0)

If the direction vector is rotated by 90° then the up-vector has to be rotated by 90°, too:

direction: (0, -1, 0)
up       : (0,  0, 1)

Upvotes: 2

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