Superformula

superformula.md

Steps

1. Clone the gist
2. Install ASDF from https://asdf-vm.com
3. Install python plugin and the latest python version

asdf plugin-add python
asdf list-all python
asdf install python 3.11.0
asdf global python 3.11.0

4. Install requirements

pip install -r superformula.txt

5. Run the script

./superformula.py

Further reading: https://github.com/mate-h/supershape

superformula.py

#!/usr/bin/env python3

import plotly.express as px
import pandas as pd
import numpy as np
import math
import progressbar


def generate_dataset():
    # Define the parameter ranges (adjust these as needed)
    m_values = np.linspace(0, 10, 11)
    n1_values = np.linspace(1, 5, 5)
    n2_values = np.linspace(1, 5, 5)
    n3_values = np.linspace(1, 5, 5)
    angle_values = np.linspace(0, 2 * math.pi, 360*2)
    dataset = []
    total_iterations = len(m_values) * len(n1_values) * \
        len(n2_values) * len(n3_values) * len(angle_values)
    green_text = "\033[32m"
    end_color = "\033[0m"
    progress_bar = progressbar.ProgressBar(
        max_value=total_iterations,
        widgets=[
            progressbar.Bar(marker="━",
                            left="["+green_text, right=end_color+"]"),
            progressbar.Percentage(),
            " ",
            progressbar.ETA(),
        ],
    )

    # Use nested loops to calculate the superformula for each combination of parameter values
    for m in m_values:
        for n1 in n1_values:
            for n2 in n2_values:
                for n3 in n3_values:
                    for angle in angle_values:
                        a = 1
                        b = 1
                        # n2 = 5
                        # n3 = 5
                        # n1 = 5
                        # m = 4
                        radius = superformula(
                            a, b, m, n1, n2, n3, angle)
                        row = [a, b, m, n1, n2, n3, angle, radius]
                        dataset.append(row)
                        progress_bar.update(progress_bar.value + 1)

    progress_bar.finish()

    # Convert the dataset to a NumPy array
    dataarr = np.array(dataset)
    df = pd.DataFrame(dataarr, columns=[
        "a", "b", "m", "n1", "n2", "n3", "angle", "radius"])

    print("Dataset shape: ", dataarr.shape)
    print("Dataset size: ", dataarr.size)
    print("Dataset dtype: ", dataarr.dtype)

    return df


def superformula(a, b, m, n1, n2, n3, angle):
    # Calculate the superformula
    return math.pow(
        math.pow(math.fabs(math.cos(m * angle / 4) / a), n2) +
        math.pow(math.fabs(math.sin(m * angle / 4) / b), n3),
        -1 / n1
    )


def show_plot():
    # Create a DataFrame with column labels
    df = generate_dataset()
    df["angle"] = df["angle"] * 180 / math.pi
    fig = px.line_polar(df, r="radius", theta="angle",
                        line_close=True, color="m")
    # remove elements from the plot except the lines
    fig.update_layout(
        showlegend=False,
        polar=dict(
            radialaxis=dict(
                visible=False,
            ),
            angularaxis=dict(
                visible=False,
            ),
            bgcolor="rgba(0,0,0,0)",
        ),
        margin=dict(l=0, r=0, t=0, b=0),
    )
    fig.update_traces(line_width=.33)
    # set page background color
    fig.update_layout(
        paper_bgcolor="#212121",
    )

    # Show the plot
    fig.show()


if __name__ == "__main__":
    show_plot()

superformula.txt

numpy
plotly
pandas
packaging
progressbar2