Question

I am doing some work with opengl es on the iPhone and I am stuck at a particular point. All the code samples on the internet show you how a matrix can be rotated about the x axis, y axis or the z axis but no one talks about how a matrix can be rotated about an arbitrary point?

I am using open gl es 2.0. Any help would be appreciated.

Regards,

Answer 1

It sounds like you’re asking how to construct a matrix that rotates around one of those axes, but at a different point. The way you do that is to first translate to that point, and then apply the rotation for the axis you want. The order of multiplication of matrixes depends on whether you think of it as the axes moving or the geometry.

If you also want to be able to do a rotation of arbitrary x, y, z angle at the same time, you can use the matrix discussed in this article:

static inline void Matrix3DSetRotationByRadians(Matrix3D matrix, GLfloat angle, GLfloat x, GLfloat y, GLfloat z)
{
    GLfloat mag = sqrtf((x*x) + (y*y) + (z*z));
    if (mag == 0.0)
    {
        x = 1.0;
        y = 0.0;
        z = 0.0;
    }
    else if (mag != 1.0)
    {
        x /= mag;
        y /= mag;
        z /= mag;
    }

    GLfloat c = cosf(angle);
    GLfloat s = fastSinf(angle);
    matrix[3] = matrix[7] = matrix[11] = matrix[12] = matrix[13] = matrix[14] = 0.0;
    matrix[15] = 1.0;


    matrix[0] = (x*x)*(1-c) + c;
    matrix[1] = (y*x)*(1-c) + (z*s);
    matrix[2] = (x*z)*(1-c) - (y*s);
    matrix[4] = (x*y)*(1-c)-(z*s);
    matrix[5] = (y*y)*(1-c)+c;
    matrix[6] = (y*z)*(1-c)+(x*s);
    matrix[8] = (x*z)*(1-c)+(y*s);
    matrix[9] = (y*z)*(1-c)-(x*s);
    matrix[10] = (z*z)*(1-c)+c;

}