Hello guys, i am studying opengl for 3 weeks on the red book, at the moment i am in chapter 5 (the lights). I am doing this since it's part of the final work for my degree. Now my teacher wanna me to do a particular thing; i'll past the exacts words: "draw (even in wireframe) a sphere composed by many triangles or quads. If u succeed, try to deform the sphere (matematecally, changing the the calc of the vertices's positions of the triangles) so that the sphere will appear squeezed on the poles. If u wanna amaze me, the sphere has to appear concave on the 2 poles". Ok i have to draw manually the spere, avoiding the use of glut*Sphere. I did it last week using a Icosahedron (it's in chapter 2 of the red book). The verteces of such object are khnown, so i described the verteces thrawning opengl the coords of each vertex, i.e: glBegin (GL_TRIANGLES); ... vertices (in the right order) .... glEnd(); Here there is no math calculation but. What sort of math manipulation can i do here? There is no a function or something like that. So reading what my teacher wrote, i think he wants a different way to draw this sphere. I don't khnow but i.e. it sounds like drawning a circle specifying manually the vertices and drawning a circle with a cicle and sin/cos. Do u agree with me? I think someone with more experience than me can imagin what my teacher's words mean. I hope i have been clear. Bye and thanks guys bro Edit: error in the post title [Edited by - broady on June 26, 2008 5:39:53 AM]

Nice guys,

i will first draw a sphere with sin and cos. Later i will focus on the squeeze.
Thanks

Ciao
If you want to draw a sphere, the simpler way is to use a parametric equation. A common one is the following:

x = R*cos(φ)cos(θ);
y = R*cos(φ)sin(θ);
z = R*sin(φ);

where R is the radius, 0 <= φ < π, 0 <= θ < 2π.

To modify the form of the sphere you can apply a transformation to the sphere or use a function that depends on the angles instead of a constant radius in the formula above.

Edit: You can try working on functions like R(φ) = m + n*sin(φ)k where m,n and k are constants to modulate the point on the sphere. Those functions have a minimum in φ = 0 and and maximum in φ = π/2. When k > 1 the derivatives in 0 and π are k*cos(φ)*sin(φ)k-1 = 0 and the poles look better (if k = 0 the two derivatives have different signs).

[Edited by - apatriarca on June 26, 2008 6:09:28 AM]

Quote:Original post by apatriarca
Ciao
If you want to draw a sphere, the simpler way is to use a parametric equation. A common one is the following:

x = R*cos(φ)cos(θ);
y = R*cos(φ)sin(θ);
z = R*sin(φ);

where R is the radius, 0 <= φ < π, 0 <= θ < 2π.

To modify the form of the sphere you can apply a transformation to the sphere or use a function that depends on the angles instead of a constant radius in the formula above.

Edit: You can try working on functions like R(φ) = m + n*sin(φ)k where m,n and k are constants to modulate the point on the sphere. Those functions have a minimum in φ = 0 and and maximum in φ = π/2. When k > 1 the derivatives in 0 and π are k*cos(φ)*sin(φ)k-1 = 0 and the poles look better (if k = 0 the two derivatives have different signs).

Ciao apatriarca, thanks for the replay!

yeah i am working on that parametrization from this morning. I have some problem connecting the vertices with lines but i will win :D

bye

The best way to understand how to define the polygons is breaking the solid and see it as a set of connected polygons on a piece of paper. If you deform the polygons you should obtains something like that: