基于关节角度与肢体段长度的Python人体骨骼绘制方案咨询

核心思路：正向运动学(FK)递推关节坐标 #

不用手动计算每个关节与X轴的夹角，从你设定的根节点（左髋，坐标原点(0,0)）出发，通过正向运动学自动递推所有关节的绝对坐标：

• 以父关节为基准，根据肢体段长度和关节夹角，计算子关节相对于父关节的坐标偏移
• 累加偏移量得到子关节的绝对坐标
• 重复此过程遍历所有关节连接

步骤与Python实现 #

1. 明确关节映射与连接关系 #

先把关节编号对应到身体部位，定义父-子关节对（对应肢体段）：

2. 代码实现（自动计算坐标+绘图） #

使用numpy处理角度计算，matplotlib完成绘图：

import numpy as np
import matplotlib.pyplot as plt

# 输入你的数据
joint_angles = {
    (12, 14, 16): 168.54785591626595,
    (14, 12, 24): 172.77150681015084,
    (24, 12, 11): 54.37272304423055,
    (12, 11, 23): 117.01615512185863,
    (11, 23, 24): 108.6334963772736,
    (23, 11, 13): 45.915788777620314,
    (11, 13, 15): 177.83453548133326,
    (23, 24, 12): 79.97762545663724,
    (26, 24, 23): 163.4421588161629,
    (24, 23, 25): 145.8882059820918,
    (28, 26, 24): 103.70318526501839,
    (23, 25, 27): 178.10520631231438
}

segment_lengths = {
    'hip': 20.4,
    'trunk': 49.3,
    'shoulders': 34.0,
    'forearm': 27.2,
    'upper arm': 29.409999999999997,
    'upper leg': 42.33,
    'lower leg': 42.5
}

# 初始化关节坐标，左髋(23)为原点
joint_coords = {23: np.array([0.0, 0.0])}

# 1. 计算右髋(24)：左髋到右髋沿X轴正方向
joint_coords[24] = joint_coords[23] + np.array([segment_lengths['hip'], 0.0])

# 2. 计算躯干上端(12)：从右髋(24)出发
angle_trunk = np.deg2rad(180 - joint_angles[(23,24,12)])
dx_trunk = segment_lengths['trunk'] * np.cos(angle_trunk)
dy_trunk = segment_lengths['trunk'] * np.sin(angle_trunk)
joint_coords[12] = joint_coords[24] + np.array([dx_trunk, dy_trunk])

# 3. 计算左肩(11)：从躯干上端(12)出发
vec_12_24 = joint_coords[24] - joint_coords[12]
angle_12_24 = np.arctan2(vec_12_24[1], vec_12_24[0])
angle_12_11 = angle_12_24 + np.deg2rad(joint_angles[(24,12,11)])
dx_shoulder_left = 17.0 * np.cos(angle_12_11)
dy_shoulder_left = 17.0 * np.sin(angle_12_11)
joint_coords[11] = joint_coords[12] + np.array([dx_shoulder_left, dy_shoulder_left])

# 4. 计算右肩(14)：从躯干上端(12)出发
angle_12_14 = angle_12_24 - np.deg2rad(180 - joint_angles[(14,12,24)])
dx_shoulder_right = 17.0 * np.cos(angle_12_14)
dy_shoulder_right = 17.0 * np.sin(angle_12_14)
joint_coords[14] = joint_coords[12] + np.array([dx_shoulder_right, dy_shoulder_right])

# 5. 计算左肘(13)：从左肩(11)出发
vec_11_23 = joint_coords[23] - joint_coords[11]
angle_11_23 = np.arctan2(vec_11_23[1], vec_11_23[0])
angle_11_13 = angle_11_23 + np.deg2rad(joint_angles[(23,11,13)])
dx_upper_arm_left = segment_lengths['upper arm'] * np.cos(angle_11_13)
dy_upper_arm_left = segment_lengths['upper arm'] * np.sin(angle_11_13)
joint_coords[13] = joint_coords[11] + np.array([dx_upper_arm_left, dy_upper_arm_left])

# 6. 计算左手(15)：从左肘(13)出发
vec_13_11 = joint_coords[11] - joint_coords[13]
angle_13_11 = np.arctan2(vec_13_11[1], vec_13_11[0])
angle_13_15 = angle_13_11 + np.deg2rad(180 - joint_angles[(11,13,15)])
dx_forearm_left = segment_lengths['forearm'] * np.cos(angle_13_15)
dy_forearm_left = segment_lengths['forearm'] * np.sin(angle_13_15)
joint_coords[15] = joint_coords[13] + np.array([dx_forearm_left, dy_forearm_left])

# 7. 计算左膝(25)：从左髋(23)出发
vec_23_24 = joint_coords[24] - joint_coords[23]
angle_23_24 = np.arctan2(vec_23_24[1], vec_23_24[0])
angle_23_25 = angle_23_24 + np.deg2rad(joint_angles[(24,23,25)])
dx_upper_leg_left = segment_lengths['upper leg'] * np.cos(angle_23_25)
dy_upper_leg_left = segment_lengths['upper leg'] * np.sin(angle_23_25)
joint_coords[25] = joint_coords[23] + np.array([dx_upper_leg_left, dy_upper_leg_left])

# 8. 计算左脚(27)：从左膝(25)出发
vec_25_23 = joint_coords[23] - joint_coords[25]
angle_25_23 = np.arctan2(vec_25_23[1], vec_25_23[0])
angle_25_27 = angle_25_23 + np.deg2rad(180 - joint_angles[(23,25,27)])
dx_lower_leg_left = segment_lengths['lower leg'] * np.cos(angle_25_27)
dy_lower_leg_left = segment_lengths['lower leg'] * np.sin(angle_25_27)
joint_coords[27] = joint_coords[25] + np.array([dx_lower_leg_left, dy_lower_leg_left])

# 9. 计算右膝(26)：从右髋(24)出发
vec_24_23 = joint_coords[23] - joint_coords[24]
angle_24_23 = np.arctan2(vec_24_23[1], vec_24_23[0])
angle_24_26 = angle_24_23 + np.deg2rad(180 - joint_angles[(26,24,23)])
dx_upper_leg_right = segment_lengths['upper leg'] * np.cos(angle_24_26)
dy_upper_leg_right = segment_lengths['upper leg'] * np.sin(angle_24_26)
joint_coords[26] = joint_coords[24] + np.array([dx_upper_leg_right, dy_upper_leg_right])

# 10. 计算右脚(28)：从右膝(26)出发
vec_26_24 = joint_coords[24] - joint_coords[26]
angle_26_24 = np.arctan2(vec_26_24[1], vec_26_24[0])
angle_26_28 = angle_26_24 + np.deg2rad(joint_angles[(28,26,24)])
dx_lower_leg_right = segment_lengths['lower leg'] * np.cos(angle_26_28)
dy_lower_leg_right = segment_lengths['lower leg'] * np.sin(angle_26_28)
joint_coords[28] = joint_coords[26] + np.array([dx_lower_leg_right, dy_lower_leg_right])

# 补充右肘(16)坐标
vec_14_12 = joint_coords[12] - joint_coords[14]
angle_14_12 = np.arctan2(vec_14_12[1], vec_14_12[0])
angle_14_16 = angle_14_12 + np.deg2rad(180 - joint_angles[(12,14,16)])
joint_coords[16] = joint_coords[14] + np.array([segment_lengths['upper arm']*np.cos(angle_14_16), segment_lengths['upper arm']*np.sin(angle_14_16)])

# 绘制骨骼图
plt.figure(figsize=(8, 10))
# 定义骨骼连线
bones = [
    (23,24), (24,12), (12,11), (12,14),
    (11,13), (13,15), (14,16),
    (23,25), (25,27), (24,26), (26,28)
]

for bone in bones:
    x = [joint_coords[bone[0]][0], joint_coords[bone[1]][0]]
    y = [joint_coords[bone[0]][1], joint_coords[bone[1]][1]]
    plt.plot(x, y, 'b-', linewidth=3)
# 绘制关节点
for j_id, coord in joint_coords.items():
    plt.scatter(coord[0], coord[1], c='red', s=50, zorder=5)
    plt.text(coord[0]+1, coord[1]+1, str(j_id), fontsize=10)

plt.gca().set_aspect('equal', adjustable='box')
plt.title('人体骨骼可视化')
plt.xlabel('X坐标(cm)')
plt.ylabel('Y坐标(cm)')
plt.grid(True)
plt.show()

3. 优化建议 #

• 把关节坐标计算逻辑封装成通用函数，比如get_child_coord(parent_coord, ref_angle, joint_angle, seg_len)，避免重复代码
• 如果需要3D可视化，可扩展坐标到三维，使用matplotlib的3D模块，或PyVista、Open3D库
• 若处理时序角度数据，可循环计算每一帧坐标，实现骨骼动画

替代工具 #

• OpenCV：适合实时骨骼绘制，可对接视频流应用
• Blender Python API：生成高精度3D骨骼模型，支持渲染导出
• Maya Python API：专业3D动画流程，适合复杂骨骼绑定需求

内容的提问来源于stack exchange，提问作者Anónimo salvaje