Rotation along a path in opengl - c++

Question

i want to move an object along a path (sine wave), lets suppose object is a roller coaster.
it moves through translate but my problem is that i also want to rotate that object according to the path.
i tried this code before translate but its not working.
if (x = -4.8)
{
glRotatef(89, 1, 1, 0);
}
my code with only translation looks like this.
i want to add rotation here along sine waves
void object()
{ glPushMatrix();
glTranslatef(x, y, 0);
glColor3f(0.0f, 0.0f, 0.0f);//Set drawing color
glBegin(GL_QUADS);
glVertex2f(-0.3, 0.1);
glVertex2f(0.3, 0.1);
glVertex2f(0.3, -0.1);
glVertex2f(-0.3, -0.1);
glEnd();
glFlush();
glPopMatrix();
glFlush();
}
void drawsine()
{
glBegin(GL_LINE_STRIP);//Primitive
glColor3f(255, 0, 0);//Set drawing color
int i = 0;
float x = 0, y = 0;
for (x = -5; x < 6; x = x + 0.1)
{
y = (sin(3.142*x)) / 3.142*x;
glVertex2f(x, y);
//int j= 0;
sinex[i] = x;
siney[i] = y;
i++;
}
glEnd();
glFlush();
}

Answer 1

The angle of rotation depends on the direction vector along the sine wave.
The direction vector can be calculated by the subtraction of 2 positions. Subtract the position before the current position from the positions after the current position, to calcaulte the direction vector. In the following i is the current position of the object:
dx = sinex[i+1] - sinex[i-1];
dy = siney[i+1] - siney[i-1];
The angle of rotation can be calculated by the arcus tangent using atan2, which returns an angle in radians:
float ang_rad = atan2( dy, dx );
Since the angle has to be passed to glRotatef in degrees, the angle has to be converted from radians to degrees, before a rotation around the z axis can be performed.
A full circle in has 360 degrees or 2*Pi radians. So the scale from radians to degrees 180/Pi:
float ang_deg = ang_rad * 180.0f / M_PI;
glRotatef( ang_deg, 0, 0, 1 );
The following cde snippet show how to apply the code. Be aware that there is no bounds check. This means i has to be grater or equal 1 and less than the number of points - 1 (1 <= i < 110):
#define _USE_MATH_DEFINES
#include <math.h>
{
// [...]
drawsine();
x = sinex[i];
y = siney[i];
dx = sinex[i+1] - sinex[i-1];
dy = siney[i+1] - siney[i-1];
object();
// [...]
}
void object()
{
glPushMatrix();
glTranslatef(x, y, 0);
float ang_rad = atan2( dy, dx );
float ang_deg = ang_rad * 180.0f / M_PI;
glRotatef( ang_deg, 0, 0, 1 );
glColor3f(0.0f, 0.0f, 0.0f);
glBegin(GL_QUADS);
glVertex2f(-0.3, 0.1);
glVertex2f(0.3, 0.1);
glVertex2f(0.3, -0.1);
glVertex2f(-0.3, -0.1);
glEnd();
glPopMatrix();
}