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| from manim import *
import numpy as np
class ThreeDWorldDemo(ThreeDScene):
def construct(self):
# 设置相机视角
self.set_camera_orientation(phi=45 * DEGREES, theta=-35 * DEGREES)
# 创建坐标系
axes = ThreeDAxes(
x_range=[-4, 4, 1],
y_range=[-4, 4, 1],
z_range=[-4, 4, 1],
x_length=8,
y_length=8,
z_length=8,
).add_coordinates()
# 创建球体
sphere = Sphere(
radius=3,
resolution=(60, 80),
stroke_width=0.5,
stroke_color=BLUE
).set_color(BLUE).set_opacity(0.3)
# 创建示例数据 - 模拟ggb中的点集合
# 这里创建两个示例曲线：一个螺旋线和一个圆形
# 曲线1: 螺旋线
list1 = []
for i in np.linspace(0, 2*np.pi, 50):
# (r, theta, phi) - 使用弧度制
r = 3.0 # 固定半径
theta = i # 经度角
phi = i * 0.5 # 纬度角，创建螺旋效果
if phi > np.pi: # 限制phi在[0, π]范围内
phi = np.pi - (phi - np.pi)
list1.append((r, theta, phi))
# 曲线2: 赤道上的圆
list2 = []
for i in np.linspace(0, 2*np.pi, 50):
r = 2.8 # 稍微小于球体半径
theta = i # 经度角变化
phi = np.pi/2 # 固定phi在π/2，表示赤道
list2.append((r, theta, phi))
# 定义球极坐标转三维坐标的函数
def polar_to_vector(r, theta, phi):
"""将球坐标(r, theta, phi)转换为笛卡尔坐标(x, y, z)"""
x = r * np.sin(phi) * np.cos(theta)
y = r * np.sin(phi) * np.sin(theta)
z = r * np.cos(phi)
return np.array([x, y, z])
# 转换坐标点
list_point1 = [polar_to_vector(r, theta, phi) for r, theta, phi in list1]
list_point2 = [polar_to_vector(r, theta, phi) for r, theta, phi in list2]
# 创建路径
path1 = VMobject()
path1.set_points_smoothly([*list_point1, list_point1[0]]) # 闭合曲线
path1.set_stroke(color=RED, width=3)
path1.set_fill(color=RED, opacity=0.2)
path2 = VMobject()
path2.set_points_smoothly([*list_point2, list_point2[0]]) # 闭合曲线
path2.set_stroke(color=GREEN, width=3)
path2.set_fill(color=GREEN, opacity=0.2)
# 添加标签
title = Text("球极坐标可视化", font_size=36, color=WHITE).to_edge(UP)
label1 = Text("螺旋路径", font_size=24, color=RED).next_to(path1, UP, buff=0.5)
label2 = Text("赤道圆", font_size=24, color=GREEN).next_to(path2, DOWN, buff=0.5)
# 添加参考网格
sphere_grid = Sphere(
radius=3,
resolution=(30, 30),
stroke_width=0.2,
stroke_color=BLUE,
fill_opacity=0
)
# 添加坐标轴标签
axes_labels = axes.get_axis_labels(
Tex("X").scale(0.7),
Tex("Y").scale(0.7),
Tex("Z").scale(0.7)
)
# 动画序列
self.begin_ambient_camera_rotation(rate=0.1) # 缓慢旋转相机
# 显示标题
self.add_fixed_in_frame_mobjects(title)
self.play(Write(title))
self.wait(0.5)
# 显示坐标系
self.play(Create(axes), Write(axes_labels))
self.wait(0.5)
# 显示球体和网格
self.play(
Create(sphere_grid),
Create(sphere)
)
self.wait(1)
# 显示第一条路径
self.play(Create(path1))
self.add_fixed_in_frame_mobjects(label1)
self.play(Write(label1))
self.wait(1)
# 显示第二条路径
self.play(Create(path2))
self.add_fixed_in_frame_mobjects(label2)
self.play(Write(label2))
self.wait(2)
# 停止相机旋转，然后围绕场景旋转查看
self.stop_ambient_camera_rotation()
self.move_camera(
phi=60 * DEGREES,
theta=-45 * DEGREES,
run_time=3
)
self.wait(2)
# 展示坐标转换点
# 从每条路径中选择几个点进行高亮显示
highlight_points1 = []
highlight_points2 = []
for i in range(0, len(list_point1), 10): # 每10个点取一个
point = Dot3D(point=list_point1[i], color=YELLOW, radius=0.05)
highlight_points1.append(point)
for i in range(0, len(list_point2), 10):
point = Dot3D(point=list_point2[i], color=PURPLE, radius=0.05)
highlight_points2.append(point)
highlight_group1 = VGroup(*highlight_points1)
highlight_group2 = VGroup(*highlight_points2)
self.play(
LaggedStart(
*[Create(point) for point in highlight_points1],
lag_ratio=0.1
),
LaggedStart(
*[Create(point) for point in highlight_points2],
lag_ratio=0.1
)
)
self.wait(2)
# 清理高亮点
self.play(
FadeOut(highlight_group1),
FadeOut(highlight_group2),
FadeOut(label1),
FadeOut(label2)
)
self.wait(1)
# 最终视图，缓慢旋转展示
self.begin_ambient_camera_rotation(rate=0.05)
self.wait(8)
self.stop_ambient_camera_rotation()
# 淡出所有元素
self.play(
FadeOut(title),
FadeOut(sphere_grid),
FadeOut(sphere),
FadeOut(path1),
FadeOut(path2),
FadeOut(axes),
FadeOut(axes_labels)
)
|
