calculate sphere in openGL resulted the circle does not aligned - c++

Question

I want to make a sphere without the gluSphere method, and I try to calculate the sphere with this code
void drawCircle(double x, double y, double r)
{
glBegin( GL_QUAD_STRIP );
for(int i=0;i<=360;i++){
glVertex3d(x+sin(i)*r,y+cos(i)*r,-5.0);
}
glEnd();
}
void drawSphere(double x,double y,double r){
glLoadIdentity();
glColor3d(1,0,0);
for(int j=0;j<180;j++){
glTranslated(0,0,r/180);
drawCircle(x,y,r*sin(j));
}
}
The result was like this
But the result was the circle that I made isn't aligned well. Is there any proper calculation so I can make the sphere right?

Answer 1

There is a difference between a Sphere and a Circle. a Circle is a 2 dimensional shape and Sphere is its 3D counterpart. from your code you are not generating points for a sphere but for a cylinder as the z is constant i.e. -0.5. for Sphere all 3 should change within the ranges
if the center is at (xc, yc, zc) then
x => (0-xc) < x < (0+xc)
y => (0-yc) < y < (0+yc)
z => (0-zc) < z < (0+zc)
A sphere may be defined parametrically in terms of (u,v)
x = xo + r cos(theta) cos(phi)
y = yo + r cos(theta) sin(phi)
z = zo + r sin(theta)
Your points should be a the valid combination of x, y z. that means your points can be generated using 3 loops. Only then you would have correct points for sphere.
Also since you ar eusing QuadStrip, the array you pass must have the order of points in counter clockwise or you will not be able to get the correct shape.
Instead of using sin() & cos() you should use the sphere equation: x*x + y*y + z*z = c*c

Answer 2

I agree with #SimpleFellow that another approach would be better. But let me show you what else is not quite how you wanted it in your code.
Your main problem is that you pass degrees to the sin and cos functions instead of radians.
The easiest remedy is to just define a function deg2rad or functions like
double sind(double val){return std::sin(val*M_PI / 180.0);}
double cosd(double val){return std::cos(val*M_PI / 180.0);}
Also, the distance between rings should be
//glTranslated(0,0,r/180); //equidistance will give you something like a pyramid
glTranslated(0, 0, r*(cosd(j)-cosd(j-1));
then the result from your code looks something like this:
When you reduce the sample points you see what's happening:
Then you'll see that you're connecting 4 successive points in a ring to a quad, which is not what you want, so if you change glBegin( GL_QUAD_STRIP ); to glBegin( GL_LINE_STRIP ) you'll see this:
If you increase the points to 360 again then you'll have this:
So now you have a sphere made of circles, but I assume that you wanted a sphere with a surface, for that have a look at this question.