Drawing a diagonal semicircle in OpenGL - c

Question

I'm trying to draw a diagonal semicircle. So far I've only been able to draw ones that begin and end on a horizontal or vertical axis, like this:
I've tried modifying the code to tilt the circle, but it doesn't work. Can someone please tell me where I've gone wrong, this is infuriating!
float theta, tanTheta, x, y, dx, dy;
int circle_points = 1000, radius = 70;
glBegin(GL_POLYGON);
for(int i = 0; i < circle_points; i++)
{
dx = pts[1].x - pts[0].x;
dy = pts[1].y - pts[0].y;
tanTheta = tan(dy / dx);
// get the inverse
theta = atan(tanTheta);
x = radius * cos(theta);
y = radius * sin(theta);
glVertex2f(x, y);
}
glEnd();

Answer 1

I recommend to calculate the angle to the start point and the angle to the end point by atan2.
Interpolate the angle between the start angle and the end angle and draw a line along the corresponding points on the circe:
float ang_start, ang_end, theta, x, y;
ang_start = atan2( pts[0].y, pts[0].x );
ang_end = atan2( pts[1].y, pts[1].x );
if ( ang_start > ang_end )
ang_start -= 2.0f * M_PI;
glBegin(GL_LINE_STRIP);
for(int i = 0; i <= circle_points; i++)
{
float w = (float)i / (float)circle_points;
float theta = ang_start + w * ( ang_end - ang_start );
x = radius * cos(theta);
y = radius * sin(theta);
glVertex2f(x, y);
}
glEnd();