OpenGL calculate circle rotation around a given point

Question

I'm trying to rotate an object around a certain point. If this point is the center of my world space I use the following algorithm:

glm::vec3 center is the center of the current object. Each frame it will get updated.

glm::mat4 transformationMatrix is the 4x4 matrix I am "uploading" to my shader later on. It will get multiplied by the vertex position.

t_point is the point I'd like to rotate around

t_deflection is the impact for each axis (in order to draw ellipses instead of circles)

t_speed is in my case the current time since the game started (e.g. glfwGetTime())

void rotateByPointY( const glm::vec3& t_point, const glm::vec3& t_deflection, const float& t_speed )
{
    float radius = glm::length( t_point - center );

    glm::vec3 newPosition( glm::sin( t_speed ) * radius * t_deflection.x, center.y, glm::cos( t_speed ) * radius * t_deflection.z );

    translationMatrix = glm::translate( glm::mat4( 1.0f ), newPosition );
    center = newPosition;
}

How can I take into account a point other than the center of my world in the calculation?

EDIT:

So my rotateByPointY calculates the translation around the world center. Therefore I am adding the new center vector to my new position:

translationMatrix = glm::translate( glm::mat4( 1.0f ), newPosition + t_point );
center = newPosition + t_point;

That is working now!

Answer 1

You first need to translate the objects, so that the center point falls on (0,0,0), this basically make everything centered around that. Then you can just rotate the object and then translate everything back.