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Let's start by generating all unique vertices. You can then decide whether to index those vertices, or copy them into strips/fans, depending on your needs.

Let's start by generating all unique vertices. You can then decide whether to index those vertices, or copy them into strips/fans, depending on your needs. Here's some example code showing how to organize these vertices into triangles for rendering.

Let's start by generating all unique vertices. You can then decide whether to index those vertices, or copy them into strips/fans, depending on your needs.

Let's start by generating all unique vertices. You can then decide whether to index those vertices, or copy them into strips/fans, depending on your needs.

// One vertex at every latitude-longitude intersection,
// plus one for the north pole and one for the south.
// One meridian serves as a UV seam, so we double the vertices there.
int numVertices = numLatitudeLines * (numLongitudeLines + 1) + 2

vec3[] positions = vec3[numVertices]
vec2[] texcoords = vec2[numVertices]

// North pole.
positions[0] = vec3(0, radius, 0)
texcoords[0] = vec2(0, 1)

// South pole.
positions[numVertices - 1] = vec3(0, -radius, 0)
texcoords[numVertices - 1] = vec2(0, 0)

// +1.0f because there's a gap between the poles and the first parallel.
float latitudeSpacing = 1.0f / (numLatitudeLines + 1.0f)
float latitudeSpacing = 1.0f / (numLongitudeLines)

// start writing new vertices at position 1
int v = 1
for(latitude = 0; latitude < numLatitudeLines; latitude++) {
    for(longitude = 0; longitude <= numLongitudeLines; longitude++) {

      // Scale coordinates into the 0...1 texture coordinate range,
      // with north at the top (y = 1).
      texcoords[v] = vec2(
                        longitude * longitudeSpacing,
                        1.0f - (latitude + 1) * latitudeSpacing                            
                     )

      // Convert to spherical coordinates:
      // theta is a longitude angle (around the equator) in radians.
      // phi is a latitude angle (north or south of the equator).
      float theta = texcoords[v].x * 2.0f * PI
      float phi = (texcoords[v].y - 0.5f) * PI

      // This determines the radius of the ring of this line of latitude.
      // It's widest at the equator, and narrows as phi increases/decreases.
      float c = cos(phi)

      // Usual formula for a vector in spherical coordinates.
      // You can exchange x & z to wind the opposite way around the sphere.
      positions[v] = vec3(
                        c * cos(theta),
                        sin(phi),
                        c * sin(theta)
                      ) * radius
      
      // Proceed to the next vertex.
      v++
    }
}

// One vertex at every latitude-longitude intersection,
// plus one for the north pole and one for the south.
// One meridian serves as a UV seam, so we double the vertices there.
int numVertices = numLatitudeLines * (numLongitudeLines + 1) + 2

vec3[] positions = vec3[numVertices]
vec2[] texcoords = vec2[numVertices]

// North pole.
positions[0] = vec3(0, radius, 0)
texcoords[0] = vec2(0, 1)

// South pole.
positions[numVertices - 1] = vec3(0, -radius, 0)
texcoords[numVertices - 1] = vec2(0, 0)

// +1.0f because there's a gap between the poles and the first parallel.
float latitudeSpacing = 1.0f / (numLatitudeLines + 1.0f)
float longitudeSpacing = 1.0f / (numLongitudeLines)

// start writing new vertices at position 1
int v = 1
for(latitude = 0; latitude < numLatitudeLines; latitude++) {
    for(longitude = 0; longitude <= numLongitudeLines; longitude++) {

      // Scale coordinates into the 0...1 texture coordinate range,
      // with north at the top (y = 1).
      texcoords[v] = vec2(
                        longitude * longitudeSpacing,
                        1.0f - (latitude + 1) * latitudeSpacing                            
                     )

      // Convert to spherical coordinates:
      // theta is a longitude angle (around the equator) in radians.
      // phi is a latitude angle (north or south of the equator).
      float theta = texcoords[v].x * 2.0f * PI
      float phi = (texcoords[v].y - 0.5f) * PI

      // This determines the radius of the ring of this line of latitude.
      // It's widest at the equator, and narrows as phi increases/decreases.
      float c = cos(phi)

      // Usual formula for a vector in spherical coordinates.
      // You can exchange x & z to wind the opposite way around the sphere.
      positions[v] = vec3(
                        c * cos(theta),
                        sin(phi),
                        c * sin(theta)
                      ) * radius
      
      // Proceed to the next vertex.
      v++
    }
}