Rotate an object given only by its points?

Question

I was recently writing a simple 3D maze FPP game. Once I was done fiddling with planes in OpenGL, I wanted to add support for importing Blender objects. The approach I used was triangulization of the object, then using Three.js to export the points to plaintext and then parsing the result JSON in my app.

The example file can be seen here: https://github.com/d33tah/tinyfpp/blob/master/Data/Models/cross.txt The numbers represent x,y,z,u,v of a single vertex, which combined in three make a triangle.

Then I rendered such an object triangle-by-triangle and played with it. I could move it back and forth and sideways, but I still have no idea how to rotate it by some axis. Let's say I'd like to rotate all the points by five degrees to the left, how would a code doing it look like?

Answer 1

I think the easiest way to rotate a vertex around an axis is using the Rodrigues Rotation Formula.

Here is my implementation of it using C++ and the library GLM:

(Note: it may not be the most efficient way, but I use it for learning purpose :3. Also, I'm using row major order (not the way GLM do things), so the multiplication is inverse later. Also, rotation are counter-clockwise :3)

glm::mat3 rodriguesMatrix(const double degrees, const glm::vec3& axis) {
glm::mat3 v = glm::mat3(
    axis.x*axis.x, axis.x*axis.y, axis.x*axis.z,
    axis.x*axis.y, axis.y*axis.y, axis.y*axis.z,
    axis.x*axis.z, axis.y*axis.z, axis.z*axis.z
    );

glm::mat3 v2 = glm::mat3(
    0, -axis.z, axis.y,
    axis.z, 0, -axis.x,
    -axis.y, axis.x, 0
    );

glm::mat3 rotation = cos(degrees * M_PI/180.f) * glm::mat3(1.0f) + (1-cos(degrees * M_PI/180.f)) * v + sin(degrees * M_PI/180.f) * v2;

return rotation;
}

So, let's say you want to rotate the vertice (3.866185 -0.996761 -1.366355)(first of your example) by 5 degress along the y axis. You can do it by doing something like:

glm::vec3 y_unit = glm::vec3(0, 1.f, 0);

glm::mat3 rotationMatrix = rodriguesMatrix(5, y_unit);

glm::vec3 myVertice = glm::vec3(3.866185,-0.996761,-1.366355);

glm::vec3 myVerticeRotated = myVertice*rotationMatrix;

Answer 2

glPushMatrix();

// Translate our object in  (x,y,z) position
glTranslatef(x, y, z); 

// Rotates the object around a rotation axis
// i.e. glRotatef(45.0, 0.0, 1.0, 0.0) rotates 45 degrees around the y-axis
glRotatef(angle, rot_axis_x, rot_axis_y, rot_axis_z);  

// Create a function for drawing the object
Draw();   

glPopMatrix();

---

You need to draw you're object preferably in the origin, because every rotation that you apply will be done around a position vector (vector that starts from the origin), and than you can translate it. OpenGl will first rotate your object and then it will translate it, so it will call the functions in reverse order. If you change the order, you will first translate the object and then rotate it around the position vector.