calculating a sphere in opengl

Question

I want to calculate all the vertices needed and connect them with lines, so I eventually come up with a sphere. How many ways are there to do it? And also the lines between the vertices, will be straight; how can I make them "curved" I know that I can use glutWireSphere(), but I am interested in actually calculating the vertices. A way that I thought about it, was to put all the vertices manually in an array, but I guess that is not the way it's done.

Answer 1

Copy and Pasting some code I originally wrote in Creating a 3D sphere in Opengl using Visual C++

class SolidSphere
{
protected
    std::vector<GLfloat> vertices;
    std::vector<GLfloat> normals;
    std::vector<GLfloat> texcoords;
    std::vector<GLushort> indices;

public:
    void SolidSphere(float radius, unsigned int rings, unsigned int sectors)
    {
        float const R = 1./(float)(rings-1);
        float const S = 1./(float)(sectors-1);
        int r, s;

        sphere_vertices.resize(rings * sectors * 3);
        sphere_normals.resize(rings * sectors * 3);
        sphere_texcoords.resize(rings * sectors * 2);
        std::vector<GLfloat>::iterator v = sphere_vertices.begin();
        std::vector<GLfloat>::iterator n = sphere_normals.begin();
        std::vector<GLfloat>::iterator t = sphere_texcoords.begin();
        for(r = 0; r < rings; r++) for(s = 0; s < sectors; s++) {
                float const y = sin( -M_PI_2 + M_PI * r * R );
                float const x = cos(2*M_PI * s * S) * sin( M_PI * r * R );
                float const z = sin(2*M_PI * s * S) * sin( M_PI * r * R );

                *t++ = s*S;
                *t++ = r*R;

                *v++ = x * radius;
                *v++ = y * radius;
                *v++ = z * radius;

                *n++ = x;
                *n++ = y;
                *n++ = z;
        }

        sphere_indices.resize(rings * sectors * 4);
        std:vector<GLushort>::iterator i = sphere_indices.begin();
        for(r = 0; r < rings; r++) for(s = 0; s < sectors; s++) {
                *i++ = r * sectors + s;
                *i++ = r * sectors + (s+1);
                *i++ = (r+1) * sectors + (s+1);
                *i++ = (r+1) * sectors + s;
        }
    }

    void draw(GLfloat x, GLfloat y, GLfloat z)
    {
        glMatrixMode(GL_MODELVIEW);
        glPushMatrix();
        glTranslatef(x,y,z);

        glEnableClientState(GL_VERTEX_ARRAY);
        glEnableClientState(GL_NORMAL_ARRAY);
        glEnableClientState(GL_TEXTURE_COORD_ARRAY);

        glVertexPointer(3, GL_FLOAT, 0, &sphere_vertices[0]);
        glNormalPointer(GL_FLOAT, 0, &sphere_normals[0]);
        glTexCoordPointer(2, GL_FLOAT, 0, &sphere_texcoords[0]);
        glDrawElements(GL_QUADS, sphere_indices.size()/4, GL_UNSIGNED_SHORT, sphere_indices);
        glPopMatrix();
    }
}

how can I make them "curved"

You can't. All OpenGL primitives are "affine", i.e. planar or straight. Curvature is emulated by drawing short, straight sections with sufficient resolution.

Answer 2

There's more than one way to do this: a) icosphere generation and b)UV sphere generation. There may be more methods to do this. Some googling got me this excellent post on icosphere generation. I couldn't find UV sphere generation method though.

Answer 3

Paul Bourke actually has a nice introduction to sphere generation. And as for curved lines, there is no such thing in OpenGL. You can only make them appear curved by adding more intermediate connected points.