以前書いたドロネー分割簡易最適化のblender版 (blender 2.82a)

1_simple_delaunay_refinement_for_blender.py

import bpy
import mathutils
import numpy as np
import math

NUM_POINTS = 300   # 点の数
MAX_ITERATION = 100  # 最適化試行回数上限
MAX_ERROR_SQUARED = 1e-4  # 前回の最適化との最大誤差（の２乗）
RADIUS = 5  # 半径

def createDelaunay(points):
    """
    Args:
      points (list of (float,float))
    Returns:
      vertices (list of Vector(2d))
      edges (list of (int,int))
      faces (list of list of int)
    """
    vs = [mathutils.Vector(x) for x in points]
    result = mathutils.geometry.delaunay_2d_cdt(vs, [], [], 0, 0.001)
    vertices, edges, faces = result[:3]
    return vertices, edges, faces

def createDelaunayMesh(points, object_name):
    """
    Args:
      points (list of (float,float))
      object_name (str)
    """
    vertices, edges, faces = createDelaunay(points)
    [v.resize_3d() for v in vertices]
    msh = bpy.data.meshes.new(name=object_name + "_mesh")
    msh.from_pydata(vertices, edges, faces)
    msh.update()
    obj = bpy.data.objects.new(name=object_name, object_data=msh)
    bpy.context.scene.collection.objects.link(obj)

def main():
    # 初期値の点を作成
    points = np.random.randn(NUM_POINTS, 2) * RADIUS
    
    if True:
        points, edges, faces = createDelaunay(points)
        points = np.array(points)
        faces = np.array(faces)
        
        for n in range(MAX_ITERATION):
            if n % 5 == 0:
                print(n, end=" ")

            new_points = []  # 調整後の点のリスト
            ng = False

            # 各点(i=index)について以下を行う
            for i in range(len(points)):
                # 点i
                point = points[i]
                # 点iを含む三角形を抽出
                idxs = faces[(faces == i).any(axis=1)]
                # indexの重複を取り除き、各indexの出現回数を取得
                idxs, counts = np.unique(idxs, return_counts=1)
                # 点iは以下の計算から除外(...しなくてもよい？)
                idxs = idxs[idxs != i]
                # indexに対応する座標を取得
                ps = points.take(idxs, axis=0)
                # 座標の平均値を取得。調整後の点iの位置とする
                avg = np.mean(ps, axis=0)
                
                # 点iが外周上の場合、円周上まで移動させる
                # (出現回数1の点があれば、点iは三角形で囲まれていない)
                if (counts == 1).any():
                    avg = avg / np.sqrt(np.sum(avg**2)) * RADIUS
                # 元の座標との距離(の２乗)が大きければ要再処理とする
                if np.sum((avg - point)**2) > MAX_ERROR_SQUARED:
                    ng = True
                new_points.append(avg)
                
            points, edges, faces = createDelaunay(new_points)
            points = np.array(points)
            faces = np.array(faces)
            
            if not ng:
                print("break:%d / %d" % (n, MAX_ITERATION))
                break
            
    createDelaunayMesh(points, "delaunay")

if __name__=="__main__":
    main()

2_circle_to_half_sphere.py

import bpy
import math

# （続き）円形のメッシュを半球に変形

RADIUS = 5

for v in bpy.data.objects['delaunay'].data.vertices:
    t = v.co.length / RADIUS * math.pi / 2
    v1 = v.co.normalized() * math.sin(t)
    v1.z = math.cos(t)
    v.co = v1 * RADIUS