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anonymous created 7 days ago Expires in 11 hours 4.5 KB syntax: python

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# -*- coding: utf-8 -*-
"""从一条山脊到一整片大陆.ipynb

Automatically generated by Colab.

Original file is located at
    https://colab.research.google.com/drive/1Huc6gsj8JWXMhVpzBvpS9RDTmPrmqp5f
"""

import numpy as np
import matplotlib.pyplot as plt
from matplotlib.colors import LinearSegmentedColormap
from mpl_toolkits.mplot3d import Axes3D

def diamond_square(iterations=8,
                   initial_displacement=1.0,
                   decay=0.55,
                   seed=7):
    """
    用钻石—正方形算法生成二维山地。

iterations:
        迭代次数。最终网格大小为 (2^iterations + 1) × (2^iterations + 1)

initial_displacement:
        第一次迭代时的随机偏移幅度

decay:
        每轮迭代后，随机偏移缩小的比例

seed:
        随机种子。相同种子会生成相同的山脉
    """

rng = np.random.default_rng(seed)

size = 2 ** iterations + 1
    terrain = np.zeros((size, size))

# 给平面的四个角设置初始高度
    terrain[0, 0] = rng.uniform(-0.2, 0.2)
    terrain[0, -1] = rng.uniform(-0.2, 0.2)
    terrain[-1, 0] = rng.uniform(-0.2, 0.2)
    terrain[-1, -1] = rng.uniform(-0.2, 0.2)

step = size - 1
    displacement = initial_displacement

while step > 1:
        half = step // 2

# -------------------------
        # 第一步：正方形步骤
        # -------------------------
        # 找到每个正方形的中心点，
        # 取四个角高度的平均值，再加入随机偏移
        for y in range(half, size - 1, step):
            for x in range(half, size - 1, step):
                top_left = terrain[y - half, x - half]
                top_right = terrain[y - half, x + half]
                bottom_left = terrain[y + half, x - half]
                bottom_right = terrain[y + half, x + half]

average = (
                    top_left
                    + top_right
                    + bottom_left
                    + bottom_right
                ) / 4

terrain[y, x] = average + rng.uniform(
                    -displacement,
                    displacement
                )

# -------------------------
        # 第二步：钻石步骤
        # -------------------------
        # 找到每个菱形的中心点，
        # 取周围已有点的平均值，再加入随机偏移
        for y in range(0, size, half):
            start_x = half if (y // half) % 2 == 0 else 0

for x in range(start_x, size, step):
                neighbors = []

if y - half >= 0:
                    neighbors.append(terrain[y - half, x])
                if y + half < size:
                    neighbors.append(terrain[y + half, x])
                if x - half >= 0:
                    neighbors.append(terrain[y, x - half])
                if x + half < size:
                    neighbors.append(terrain[y, x + half])

average = np.mean(neighbors)

terrain[y, x] = average + rng.uniform(
                    -displacement,
                    displacement
                )

# 网格尺度缩小
        step //= 2

# 随着尺度变小，随机偏移也逐渐减小
        displacement *= decay

# 把高度归一化到 0～1
    terrain -= terrain.min()
    terrain /= terrain.max()

return terrain

# 生成二维山地
terrain = diamond_square(
    iterations=8,
    initial_displacement=1.0,
    decay=0.55,
    seed=7
)

# 自定义地形颜色：
# 深蓝—浅蓝—绿色—棕色—白色
terrain_colors = LinearSegmentedColormap.from_list(
    "terrain_colors",
    [
        (0.00, "#264653"),
        (0.18, "#4f8a8b"),
        (0.32, "#84a98c"),
        (0.55, "#52734d"),
        (0.72, "#8b6f47"),
        (0.88, "#b8a88a"),
        (1.00, "#f5f5f5")
    ]
)

# 建立平面坐标
size = terrain.shape[0]
x = np.linspace(0, 1, size)
y = np.linspace(0, 1, size)
X, Y = np.meshgrid(x, y)

# 为了让山峰更加明显，对高度稍作非线性处理
Z = terrain ** 1.35

# 绘制三维山脉
fig = plt.figure(figsize=(14, 9))
ax = fig.add_subplot(111, projection="3d")

surface = ax.plot_surface(
    X,
    Y,
    Z,
    cmap=terrain_colors,
    linewidth=0,
    antialiased=True,
    rcount=180,
    ccount=180
)

ax.view_init(elev=42, azim=-125)

# 调整纵向比例，使山脉更有立体感
ax.set_box_aspect((1, 1, 0.38))

ax.set_axis_off()
ax.set_title(
    "Diamond-Square Fractal Mountain",
    fontsize=18,
    pad=10
)

plt.tight_layout()
plt.show()