I have written a code for drawing a bezier curve in OpenGL 2.

for example this is my bezier curve that i have drawn:

i can setup my bezier by glMap1f() using my controlPoints and number of controlPoints (which is uOrder)

void MyBezierLine::setup(const GLfloat* controlPoints,
GLint uOrder)
{
    controlpoints = controlPoints;
    uorder = uOrder;
    //setup the bezier
    glMap1f(GL_MAP1_VERTEX_3, //to be generated data
    0.0f, //lower u range
    1.0f, //higher u range
    3, //u control point stride in array
    uorder, //order of u or number of u control point
    controlpoints); //the control points array
    //enabling bezier evaluator
    glEnable(GL_MAP1_VERTEX_3);
}

and i can simply draw them by glMapGrid1f() and glEvalMesh1().

void MyBezierLine::draw(GLenum draw_mode, //GL_LINE or GL_POINT
                        GLint ures)
{
    //setting the 1D grid map containing ures points
    //map to u range 0.0 - 1.0
    glMapGrid1f(ures, 0.0f, 1.0f);
    //evaluate the bezier surface
    glEvalMesh1(draw_mode, 0, ures);
}

what i want to do is try to move an object along this bezier curve which has drawn by purple color.

based on what i have searched over internet, it looks like i have to write the function and calculate the bezier curve by myself to get the position of each point on the line. despite of that, i have to evaluate the rotation of the object based on the position of each point.

do you have any proper way or idea about how can i do this ?

inline void EvaluateBezierLine4 (hkVector4 &pos, hkVector4 &tang, hkVector4 &cp1, hkVector4 &cp2, hkVector4 &cp3, hkVector4 &cp4, hkSimdReal t)
{
	hkSimdReal u = 1.0f - t;		
	
	hkSimdReal vvv = u*u*u;
	hkSimdReal vvu = u*u*t*3;
	hkSimdReal vuu = u*t*t*3;
	hkSimdReal uuu = t*t*t;
	
	pos.setMul4 (vvv, cp1);
	pos.addMul4 (vvu, cp2);
	pos.addMul4 (vuu, cp3);
	pos.addMul4 (uuu, cp4);

	// tangent... 
    vvv = -3*u*u; // opt
    vvu = -6*u*t + 3*u*u; 
    vuu =  6*u*t - 3*t*t; 
    uuu =  3*t*t;

	tang.setMul4 (vvv, cp1);
	tang.addMul4 (vvu, cp2);
	tang.addMul4 (vuu, cp3);
	tang.addMul4 (uuu, cp4);
}