Python 脚本快速生成令人惊叹的比安基-平克尔曲面

2024-03-24 22:29:17

用 Python 脚本生成比安基-平克尔曲面

简介

比安基-平克尔曲面以其独特的几何特性而闻名，在数学和计算机图形学领域都有应用。本文将指导你使用 Python 脚本创建这些迷人的曲面。

代码实现

# 导入必要的库
import bpy
import math
from mathutils import Vector
import numpy

# 定义曲面参数
valminu = 0
valmaxu = math.pi * 2
valminv = 0
valmaxv = math.pi * 2
resolutionu = 150
resolutionv = 150
pasu = (valmaxu - valminu) / resolutionu
pasv = (valmaxv - valminv) / resolutionv

# 定义花瓣相关参数
a = 0.93  # 中心花瓣的半径
n = 3  # 花瓣数量
b = 0.36  # 花瓣内侧半径
c = 0
d = 0
k = 15
varu = valminu
varv = valminv

# 定义黄金分割比
goldenRatio = (1 + math.sqrt(5)) / 2

# 定义三角形细分函数
def subdivide(triangles):
    result = []
    for color, A, B, C in triangles:
        if color == 0:
            # 细分红色三角形
            P = A + (B - A) / goldenRatio
            result += [(0, C, P, B), (1, P, C, A)]
        else:
            # 细分蓝色三角形
            Q = B + (A - B) / goldenRatio
            R = B + (C - B) / goldenRatio
            result += [(1, R, C, A), (1, Q, R, B), (0, R, Q, A)]
    return result

# 定义比安基-平克尔曲面创建函数
def createSurfaceBianchiPinkall():
    triangles = []

    for varu in numpy.arange(valminu, valmaxu, pasu):
        for varv in numpy.arange(valminv, valmaxv, pasv):

            # 计算曲面上的点
            gamma = a + b * math.sin(2 * n * varv)
            x = math.cos(varu + varv) * math.cos(gamma)
            y = math.sin(varu + varv) * math.cos(gamma)
            z = math.cos(varu - varv) * math.sin(gamma)
            w = math.sin(varu - varv) * math.sin(gamma)
            r = math.acos(w) / math.pi / math.sqrt(1 - w * w)
            A = Vector((x * r, y * r, z * r))

            # 计算曲面上的下一个点
            varva = varv + pasv
            gamma = a + b * math.sin(2 * n * varva)
            x = math.cos(varu + varva) * math.cos(gamma)
            y = math.sin(varu + varva) * math.cos(gamma)
            z = math.cos(varu - varva) * math.sin(gamma)
            w = math.sin(varu - varva) * math.sin(gamma)
            r = math.acos(w) / math.pi / math.sqrt(1 - w * w)
            B = Vector((x * r, y * r, z * r))

            # 计算曲面上的第三个点
            varua = varu + pasu
            gamma = a + b * math.sin(2 * n * varva)
            x = math.cos(varua + varva) * math.cos(gamma)
            y = math.sin(varua + varva) * math.cos(gamma)
            z = math.cos(varua - varva) * math.sin(gamma)
            w = math.sin(varua - varva) * math.sin(gamma)
            r = math.acos(w) / math.pi / math.sqrt(1 - w * w)
            C = Vector((x * r, y * r, z * r))

            # 构建三角形
            triangles.append((0, A, B, C))

            # 构建额外的三角形
            gamma = a + b * math.sin(2 * n * varv)
            x = math.cos(varua + varv) * math.cos(gamma)
            y = math.sin(varua + varv) * math.cos(gamma)
            z = math.cos(varua - varv) * math.sin(gamma)
            w = math.sin(varua - varv) * math.sin(gamma)
            r = math.acos(w) / math.pi / math.sqrt(1 - w * w)
            D = Vector((x * r, y * r, z * r))
            triangles.append((0, A, C, D))

    return triangles

# 生成曲面网格
listTriangles = createSurfaceBianchiPinkall()
#for x in range(subDivIterations):
# listTriangles = subdivide(listTriangles)

# 创建 Blender 网格对象
mesh = bpy.data.meshes.new("SurfaceBianchiPinkallMesh")
ob = bpy.data.objects.new("SurfaceBianchiPinkall", mesh)
ob.location = Vector((0, 0, 0))
bpy.context.scene.objects.link(ob)

# 填充网格数据
mesh.from_pydata(listVertices, [], listFaces)
mesh.validate(True)