How to rotate a direction

Question

I'm working a spotlight for my deferred renderer and I'm having trouble with matching the mesh to the visual representation of the light. Right now my mesh is a cone, the apex of the cone is at (0,0,0), it has a height of 1 and a radius of 1. The direction of this cone is (0,-1,0) when the rotation is (0,0,0).

The relevant GLSL code:

float spot_alpha = dot(-l,normalize(vec3(0,-1,0) )); // <------
float inner_alpha = cos(light.falloff);
float outer_alpha = cos(light.radius);
float spot = clamp((spot_alpha - outer_alpha) / (inner_alpha - outer_alpha),0.,1.);

As you can see, the GLSL code uses a direction to define the area to be lit, so I could get this direction as a uniform, but I would need to find a rotation from that for the mesh to follow, or I can get the rotation and find a direction, but I don't know how to do either of these things.

Can I rotate a direction? How do I do it? If I can't, is there another solution for this problem?

Answer 1

Assuming C++ with GLM...

C++:

//Construct a rotation matrix to rotate 'degrees' around a certain axis
glm::mat4 rotation = glm::rotate(glm::mat4(1.f), degrees, glm::vec3(/* axis */));

//Upload to shader 'program' as uniform 'rotation'
GLint loc = glGetUniformLocation(program, "rotation");
glUniformMatrix4fv(loc, 1, GL_FALSE, &rotation[0][0]);

GLSL:

uniform mat4 rotation;

...
//Rotate the vector
vec4 result = rotation*vec4(0,-1,0,1);
//Chop off the W component and normalize
vec3 direction = normalize(result.xyz);
//Use the rotated vector
float spot_alpha = dot(-l,direction);
...

Of course, you could also calculate direction entirely in the C++ code and just upload it.