c++ - Sphere Calculations

Question

So I have created all of the correct sphere vertices using this algorithm:

GLint total = 100;
GLfloat radius = 200;
GLfloat sphereVertices[30000];
for (int i = 0; i < total; i++)
{
    float lon = map(i, 0, total, -M_PI, M_PI);
    for (int j = 0; j < total; j++)
    {
        float lat = map(j, 0, total, -M_PI/2, M_PI/2);

        sphereVertices[(i * 300) + (j * 3)] = radius * sin(lon) * cos(lat);
        sphereVertices[(i * 300) + (j * 3) + 1] = radius * sin(lon) * sin(lat);
        sphereVertices[(i * 300) + (j * 3) + 2] = radius * cos(lon);
    }

}

But when I draw it using either GL_TRIANGLES and GL_TRIANGLE_STRIP, I'm produced with this result:

As you can see the only triangles which are being rendered are slicing through the center of the sphere. Is my math wrong? Or am I not plotting my data into my array the correct way for my glVertexAttribPointer function to read the data correctly?

glVertexAttribPointer(0, 3, GL_FLOAT, GL_FALSE, 3 * sizeof(GLfloat), 0);

EDIT 1:

    glBindVertexArray(VAO);
    glBindBuffer(GL_ARRAY_BUFFER, VBO);
    glDrawArrays(GL_TRIANGLES, 0, 10000);

Answer 1

You cant't draw the inices directly by glDrawArrays. You have to bring them in a proper order. Create a triangle index list and use glDrawElements

See also How to map texture to sphere that rendered by parametric equation using points primitive

Further note, that your loop should run from i = 0 to i <= total, because you want to create vertex coordinates on both poles of the sphere.

GLint layers             = 100;
GLint circumferenceTiles = 100;
std::vector<GLfloat> sphereVertices;
va.reserve( (layers+1)*(circumferenceTiles+1)*3 );  // 3 floats: x, y, z 
for ( int i = 0; i <= layers; ++ i )
{
    GLfloat lon     = map(i, 0, layers, -M_PI, M_PI);
    GLfloat lon_sin = std::sin( lon );
    GLfloat lon_cos = std::cos( lon );
    for ( int j = 0; j <= circumferenceTiles; j ++ )
    {
        GLfloat lat     = map(j, 0, circumferenceTiles, -M_PI/2, M_PI/2);
        GLfloat lat_sin = std::sin( lat);
        GLfloat lat_cos = std::cos( lat);

        va.push_back( lon_cos * lat_cos ); // x
        va.push_back( lon_cos * lat_sin ); // y
        va.push_back( lon_sin );           // z
    }
}

You can create triangles by stacking up discs:

// create the face indices 
std::vector<GLuint> ia;
ia.reserve( layers*circumferenceTiles*6 );
for ( GLuint il = 0; il < layers; ++ il )
{
    for ( GLuint ic = 0; ic < circumferenceTiles; ic ++ )
    {
      GLuint i0 = il * (circumferenceTiles+1) + ic;
      GLuint i1 = i0 + 1;
      GLuint i3 = i0 + circumferenceTiles+1;
      GLuint i2 = i3 + 1;

      int faces[]{ i0, i1, i2, i0, i2, i3 };
      ia.insert(ia.end(), faces+(il==0?3:0), faces+(il==layers-1?3:6));
    }
}

Specify the vertex array object:

GLuint vao;
glGenVertexArrays( 1, &vao );
glBindVertexArray( vao );

GLuint vbo;
glGenBuffers( 1, &vbo );
glBindBuffer( GL_ARRAY_BUFFER, vbo );
glBufferData( GL_ARRAY_BUFFER, sphereVertices.size()*sizeof(GLfloat), sphereVertices.data(), 
GL_STATIC_DRAW );

GLuint ibo;
glGenBuffers( 1, &ibo );
glBindBuffer( GL_ELEMENT_ARRAY_BUFFER, ibo );
glBufferData( GL_ELEMENT_ARRAY_BUFFER, ia.size()*sizeof(GLuint), ia.data(), GL_STATIC_DRAW );

GLuint v_attr_inx = 0;
glVertexAttribPointer( v_attr_inx , 3, GL_FLOAT, GL_FALSE, 0, 0 );
glEnableVertexAttribArray( v_attr_inx );

glBindVertexArray( 0 );
glBindBuffer( GL_ARRAY_BUFFER, 0 );
glBindBuffer( GL_ELEMENT_ARRAY_BUFFER, 0 );

Draw the sphere:

glBindVertexArray( vao );
glDrawElements( GL_TRIANGLES, (GLsizei)ia.size(), GL_UNSIGNED_INT, 0 );
glBindVertexArray( 0 );