OpenGL - Draw tangent and normal to sine curve

Question

I am trying to draw a moving point on an sine curve and draw the tangent and normal to this point on the curve. I would also like to normalize these lines, but this is not my main concern.

So far I think my tangent is good but I can't find how to draw the normal.

Here is what I have so far : Two defines to avoid typing the in the middle of the code

#define SIN(A, y, x) A * sin(((2 * M_PI) / y) * x)
#define COSDY(A, y, x) A * ((2 * M_PI) / y) * cos(((2 * M_PI) / y) * x)

And those are the drawings I do for the curve, the tangent and then the normal:

glBegin(GL_LINE_STRIP);

for (x = -1.f; x <= 1.f; x += 0.01) {
  glVertex3f(x, SIN(1, 2, x), 1.f);
}

glEnd();

glPointSize(10.0);
glBegin(GL_POINTS);

glVertex3f(position, SIN(1, 2, position), 1.f);

glEnd();
glPointSize(1.0);

float dx = 1;
float dy = COSDY(1, 2, position);

float mag = sqrtf(dx * dx + dy * dy);
dx /= mag;
dy /= mag;

glBegin(GL_LINES);

glVertex3f(position, SIN(1, 2, position), 1.f);
glVertex3f(position + dx, position + dy, 1.f);

glEnd();

glBegin(GL_LINES);

glVertex3f(position, SIN(1, 2, position), 1.f);
glVertex3f(position + dy, position - 1 / dx, 1.f);

glEnd();

As I said the tangent looks ok but the normal is definitely not ok.

Can you see what is the problem in this?

Answer 1

The calculation of the tangent basically looks ok. I don't quite understand the way you draw it, though. If (dx, dy) is your tangent vector, shouldn't your drawing code look like this?

glVertex3f(position, SIN(1, 2, position), 1.f);
glVertex3f(position + dx, SIN(1, 2, position) + dy, 1.f);

In any case, with (dx, dy) being the tangent vector, your two options for the normal vector are (dy, -dx) and (-dy, dx). Remember that the scalar product of the two vectors needs to be zero for the two vectors to be orthogonal. Your normal drawing becomes:

glVertex3f(position, SIN(1, 2, position), 1.f);
glVertex3f(position + dy, SIN(1, 2, position) - dx, 1.f);