3D Line Plot for Trajectory Visualization — Pygal

A 3D line plot that displays paths, trajectories, or curves as connected lines in three-dimensional space. Unlike scatter plots that show discrete points, this visualization connects data points sequentially to reveal continuous paths, making it ideal for understanding motion, mathematical curves, and temporal evolution in 3D. Interactive rotation is essential for exploring the spatial structure of complex trajectories.

3D Line Plot for Trajectory Visualization rendered with Pygal

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Python source (Pygal)

""" anyplot.ai
line-3d-trajectory: 3D Line Plot for Trajectory Visualization
Library: pygal 3.1.0 | Python 3.13.13
Quality: 89/100 | Created: 2026-05-16
"""

import os

import matplotlib.pyplot as plt
import numpy as np
import pygal
from matplotlib.colors import Normalize
from pygal.style import Style


THEME = os.getenv("ANYPLOT_THEME", "light")
PAGE_BG = "#FAF8F1" if THEME == "light" else "#1A1A17"
INK = "#1A1A17" if THEME == "light" else "#F0EFE8"
INK_MUTED = "#6B6A63" if THEME == "light" else "#A8A79F"

IMPRINT = ("#009E73", "#C475FD", "#4467A3", "#BD8233", "#AE3030", "#2ABCCD", "#954477")

np.random.seed(42)


# Generate Lorenz attractor trajectory
def lorenz_attractor(dt=0.01, num_steps=3000):
    """Generate Lorenz attractor trajectory."""
    sigma, rho, beta = 10.0, 28.0, 8.0 / 3.0
    x, y, z = 1.0, 1.0, 1.0

    trajectory = np.zeros((num_steps, 3))
    for i in range(num_steps):
        dx = sigma * (y - x)
        dy = x * (rho - z) - y
        dz = x * y - beta * z

        x += dt * dx
        y += dt * dy
        z += dt * dz

        trajectory[i] = [x, y, z]

    return trajectory


# Generate trajectory
trajectory = lorenz_attractor()

# Normalize coordinates for better visualization
x_data = trajectory[:, 0]
y_data = trajectory[:, 1]
z_data = trajectory[:, 2]

# Normalize to [-1, 1] for better scaling
x_norm = (x_data - x_data.mean()) / (x_data.std() + 1e-8)
y_norm = (y_data - y_data.mean()) / (y_data.std() + 1e-8)
z_norm = (z_data - z_data.mean()) / (z_data.std() + 1e-8)

# Create segments with color gradient based on Z progression
num_segments = 30
segment_length = len(x_norm) // num_segments

# Generate color gradient from viridis
cmap = plt.get_cmap("viridis")
norm = Normalize(vmin=0, vmax=num_segments - 1)

custom_style = Style(
    background=PAGE_BG,
    plot_background=PAGE_BG,
    foreground=INK,
    foreground_strong=INK,
    foreground_subtle=INK_MUTED,
    colors=IMPRINT,
    title_font_size=28,
    label_font_size=22,
    major_label_font_size=18,
    legend_font_size=16,
    value_font_size=14,
    stroke_width=2.5,
)

chart = pygal.XY(
    title="line-3d-trajectory · pygal · anyplot.ai",
    x_title="X (Projected)",
    y_title="Y (Projected)",
    width=4800,
    height=2700,
    style=custom_style,
    show_legend=True,
    show_dots=False,
    stroke_dasharray=None,
)

# Add trajectory segments with color progression
for i in range(num_segments):
    start_idx = i * segment_length
    end_idx = start_idx + segment_length if i < num_segments - 1 else len(x_norm)

    segment_x = x_norm[start_idx:end_idx]
    segment_y = y_norm[start_idx:end_idx]

    # Create (x, y) coordinate pairs for this segment
    xy_pairs = [(float(segment_x[j]), float(segment_y[j])) for j in range(len(segment_x))]

    # Get color for this segment (Z progression)
    z_value = z_norm[start_idx : end_idx + 1].mean()
    normalized_z = (z_value + 1) / 2  # Map [-1, 1] to [0, 1]
    rgba = cmap(norm(i))
    color = f"#{int(rgba[0] * 255):02x}{int(rgba[1] * 255):02x}{int(rgba[2] * 255):02x}"

    # Add series
    chart.add(f"Segment {i + 1}", xy_pairs, stroke_style={"width": 2}, color=color)

# Save outputs
chart.render_to_png(f"plot-{THEME}.png")

with open(f"plot-{THEME}.html", "wb") as f:
    f.write(chart.render())

Part of 3D Line Plot for Trajectory Visualization on anyplot.ai.

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