How to Create a Sphere in OpenGL Without Using gluSphere()?

Drawing a Sphere in OpenGL Without gluSphere()

Many OpenGL tutorials focus on drawing cubes, leaving users seeking alternative methods to create spheres. While gluSphere() is a convenient function, it's beneficial to understand the underlying math to customize and modify spheres as needed.

One approach is to start with a platonic solid like an octahedron, which has triangular faces. By recursively splitting these triangles into smaller ones, you create a set of points that, when normalized to a constant distance from the center, begin to resemble a sphere.

Normalization refers to adjusting the points to maintain the angle between them while varying their distance from a reference point. Consider a 2D example:

[Image of line segment with distances labeled]

Point C is normalized with respect to A and B at a distance of 12 units. The normalization formula is:

function normalize(a, b, length):
    # Calculate new distances and create new point c
    return c

By repeating this process on numerous points with a specified reference point and distance, you create points that lie on an arc of a circle.

In 3D, this technique can be expanded to create a sphere. Adjust the normalization function to include a dz component, resulting in a spherical volume:

[Image of 3D normalized polygons]

With increasing recursion levels, the sphere becomes smoother:

[Image of bulging octahedron at level 1 and 3]

This technique is similar to the dodecahedral shape of Epcot's sphere, where the faces bulge outwards to create a more rounded appearance.

The above is the detailed content of How to Create a Sphere in OpenGL Without Using gluSphere()?. For more information, please follow other related articles on the PHP Chinese website!