Fibonacci Sphere Convex Hull

bmesh_tut_18_convex_hull_fib_sphere.py

from bpy import data as D, context as C
import bmesh
import math


def fibonacci_points(count=32, radius=0.5):
    """
    Distributes points on a sphere according to
    the golden ratio, (1.0 + sqrt(5.0)) / 2.0.
    """

    # Validate inputs.
    v_count = max(3, count)
    v_rad = max(0.000001, radius)

    # Approximately 1.618033988749895 .
    golden_ratio = (1.0 + 5.0 ** 0.5) * 0.5
    tau_gr = math.tau * golden_ratio

    to_step = 2.0 / v_count
    i_range = range(0, v_count)

    vs = []
    for i in i_range:
        azimuth = tau_gr * i
        inclination = math.asin(1.0 - i * to_step)
        rho_cos_phi = v_rad * math.cos(inclination)

        # Convert spherical to Cartesian coordinates.
        x = rho_cos_phi * math.cos(azimuth)
        y = rho_cos_phi * math.sin(azimuth)
        z = v_rad * -math.sin(inclination)

        v = (x, y, z)
        vs.append(v)

    return vs


bm = bmesh.new()

count = 1024
fib_points = fibonacci_points(count)
for point in fib_points:
    bm.verts.new(point)
bmesh.ops.convex_hull(bm, input=bm.verts)

mesh_data = D.meshes.new("Sphere")
bm.to_mesh(mesh_data)
bm.free()
mesh_obj = D.objects.new(mesh_data.name, mesh_data)
C.collection.objects.link(mesh_obj)