複数の質点のトータル重量重心位置をPythonで３Dプロットする

どんな工作物でも，各パーツの重量と重心位置のバランスは大切です！

何を設計するに際しても，（例えばアームロボットなど）
工作物の重量を把握し，全体の重量バランスを検討する必要があります．

下図のように，Pythonでサクッと計算・可視化して確認できるといいですよね．

このプログラムでのポイントは，
１．最初に何個の質量の総和を求めたいのか，個数を指定できる
２．質量と３次元空間の座標値をダイアログボックスにて入力できる
３．３次元プロットで可視化
　①個別の質量は，青丸印で表示
　②トータルの質量は，赤丸印で表示
　③質量に応じて丸印の大きさが異なる
　④質量と重心位置の座標値をプロット内に表示

実行方法は，コマンドプロンプト（Macではターミナル）で以下を実行

python3 calc_total_cg.py

calc_total_cg.py

# coding: utf-8
import tkinter as tk
from tkinter import simpledialog, messagebox
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D

def get_mass_points_from_dialog():
    """
    Accepts mass point information as input from dialog boxes.
    Returns:
        list: A list of [mass, x, y, z] for each mass point.
    """
    mass_points = []
    while True:
        try:
            # Ask the user for the number of mass points
            num_points_str = simpledialog.askstring("Mass Point Input", "Enter the number of mass points (e.g., 3):")
            if num_points_str is None: # If canceled
                return None
            num_points = int(num_points_str)
            if num_points <= 0:
                raise ValueError("The number of mass points must be a positive integer.")
            break
        except ValueError as e:
            messagebox.showerror("Input Error", str(e))
        except TypeError: # If NoneType (e.g., Cancel button pressed)
            return None

    for i in range(num_points):
        while True:
            try:
                # Enter mass and coordinates for each mass point
                input_str = simpledialog.askstring(f"Mass Point {i+1} Input",
                                                    f"Enter mass (kg) and coordinates (x, y, z) for mass point {i+1}, separated by commas.\nExample: 10, 1.0, 2.0, 3.0")
                if input_str is None: # If canceled
                    return None
                parts = [float(p.strip()) for p in input_str.split(',')]
                if len(parts) != 4:
                    raise ValueError("Please enter 4 values: mass and 3 coordinates (x, y, z).")
                mass, x, y, z = parts
                if mass < 0:
                    raise ValueError("Mass cannot be negative.")
                mass_points.append([mass, x, y, z])
                break
            except ValueError as e:
                messagebox.showerror("Input Error", str(e))
            except Exception as e:
                messagebox.showerror("Error", f"An unexpected error occurred: {e}")
    return mass_points

def calculate_center_of_gravity(mass_points):
    """
    Calculates the center of gravity for multiple mass points.
    Args:
        mass_points (list): A list of [mass, x, y, z] for each mass point.
    Returns:
        tuple: (Total Mass, CoG_x, CoG_y, CoG_z)
               or None (if no input).
    """
    if not mass_points:
        return None

    total_mass = sum(mp[0] for mp in mass_points)
    if total_mass == 0:
        messagebox.showwarning("Calculation Warning", "Total mass is 0, so CoG cannot be calculated.")
        return 0, 0, 0, 0 # If total mass is 0, return origin or handle as an error

    sum_mx = sum(mp[0] * mp[1] for mp in mass_points)
    sum_my = sum(mp[0] * mp[2] for mp in mass_points)
    sum_mz = sum(mp[0] * mp[3] for mp in mass_points)

    cog_x = sum_mx / total_mass
    cog_y = sum_my / total_mass
    cog_z = sum_mz / total_mass

    return total_mass, cog_x, cog_y, cog_z

def plot_3d_points(mass_points, cog_info):
    """
    Plots mass points and the center of gravity in 3D space.
    Args:
        mass_points (list): A list of [mass, x, y, z] for each mass point.
        cog_info (tuple): (Total Mass, CoG_x, CoG_y, CoG_z).
    """
    fig = plt.figure(figsize=(10, 8))
    ax = fig.add_subplot(111, projection='3d')

    # Calculate max individual mass for scaling reference
    max_individual_mass = max(mp[0] for mp in mass_points) if mass_points else 1

    # Plot each mass point
    for i, mp in enumerate(mass_points):
        mass, x, y, z = mp
        # Scale blue marker size relative to its mass.
        # Max marker size for individual points is about 200, min is 20.
        # This makes sure smaller points are still visible.
        marker_size = max(20, (mass / max_individual_mass) * 200)
        ax.scatter(x, y, z, color='blue', s=marker_size, label=f'Mass Point {i+1}' if i == 0 else "", alpha=0.7)
        ax.text(x, y, z, f'M: {mass}kg\n({x:.1f},{y:.1f},{z:.1f})', color='blue')

    # Plot the total center of gravity
    if cog_info:
        total_mass, cog_x, cog_y, cog_z = cog_info
        # Scale red marker size based on total mass, significantly larger than individual points.
        # This uses the total mass relative to the max individual mass for a more intuitive scale.
        # Minimum size 100, larger points will be scaled up from there.
        cog_marker_size = max(100, (total_mass / max_individual_mass) * 300)
        ax.scatter(cog_x, cog_y, cog_z, color='red', marker='o', s=cog_marker_size, label='Center of Gravity', edgecolor='black', linewidth=0.8)
        ax.text(cog_x, cog_y, cog_z, f'Total Mass: {total_mass:.2f}kg\nCoG: ({cog_x:.2f},{cog_y:.2f},{cog_z:.2f})', color='red', fontsize=10, ha='right')

    ax.set_xlabel('X-axis')
    ax.set_ylabel('Y-axis')
    ax.set_zlabel('Z-axis')
    ax.set_title('Mass Points and Center of Gravity in 3D Space')
    ax.legend()
    ax.grid(True)
    plt.show()

# Hide the Tkinter root window
root = tk.Tk()
root.withdraw()

# Get mass point data
mass_points_data = get_mass_points_from_dialog()

if mass_points_data:
    # Calculate CoG
    center_of_gravity_info = calculate_center_of_gravity(mass_points_data)

    if center_of_gravity_info is not None:
        # Plot the results
        plot_3d_points(mass_points_data, center_of_gravity_info)
    else:
        messagebox.showinfo("Information", "No mass point data entered. Exiting process.")