A parametric curve plot visualizes x(t) and y(t) as functions of a parameter t, tracing smooth curves in 2D space. Unlike standard function plots where y = f(x), parametric curves can loop, self-intersect, and form closed shapes such as Lissajous figures, spirals, and cardioids. This makes them essential for representing trajectories, oscillations, and classical mathematical curves that cannot be expressed as single-valued functions.
""" anyplot.ai
line-parametric: Parametric Curve Plot
Library: pygal 3.1.3 | Python 3.13.14
Quality: 82/100 | Updated: 2026-06-20
"""
import os
import numpy as np
import pygal
from pygal.style import Style
THEME = os.getenv("ANYPLOT_THEME", "light")
# Theme-adaptive chrome tokens
PAGE_BG = "#FAF8F1" if THEME == "light" else "#1A1A17"
INK = "#1A1A17" if THEME == "light" else "#F0EFE8"
INK_MUTED = "#6B6A63" if THEME == "light" else "#A8A79F"
# Imprint categorical palette — canonical order
IMPRINT_PALETTE = (
"#009E73", # 1 brand green — Lissajous start
"#C475FD", # 2 lavender — Lissajous 2nd quarter
"#4467A3", # 3 blue — Lissajous 3rd quarter
"#BD8233", # 4 ochre — Lissajous end
"#AE3030", # 5 matte red — Spiral start
"#2ABCCD", # 6 cyan — Spiral 2nd quarter
"#954477", # 7 rose — Spiral 3rd quarter
"#99B314", # 8 lime — Spiral end
)
# Data
n_points = 800
n_segs = 4
seg_size = n_points // n_segs
# Curve 1: Lissajous (3, 2) — x = sin(3t), y = sin(2t), t in [0, 2pi] — closed curve
t_liss = np.linspace(0, 2 * np.pi, n_points)
liss_x = np.sin(3 * t_liss)
liss_y = np.sin(2 * t_liss)
# Curve 2: Archimedean spiral — x = (t/2pi)*cos(t), y = (t/2pi)*sin(t), t in [0, 2pi]
# Normalised so radius reaches 1.0 at t=2pi, fitting the [-1.2, 1.2] axis range
t_spiral = np.linspace(0, 2 * np.pi, n_points)
spiral_x = (t_spiral / (2 * np.pi)) * np.cos(t_spiral)
spiral_y = (t_spiral / (2 * np.pi)) * np.sin(t_spiral)
font = "DejaVu Sans, Helvetica, Arial, sans-serif"
custom_style = Style(
background=PAGE_BG,
plot_background=PAGE_BG,
foreground=INK,
foreground_strong=INK,
foreground_subtle=INK_MUTED,
colors=IMPRINT_PALETTE,
font_family=font,
title_font_family=font,
title_font_size=66,
label_font_size=56,
major_label_font_size=44,
legend_font_size=44,
value_font_size=36,
tooltip_font_size=36,
tooltip_font_family=font,
opacity=1.0,
stroke_opacity=1.0,
stroke_width=10,
)
chart = pygal.XY(
width=2400,
height=2400,
style=custom_style,
title="line-parametric · python · pygal · anyplot.ai",
x_title="Horizontal Position x(t)",
y_title="Vertical Position y(t)",
show_legend=True,
legend_at_bottom=True,
legend_at_bottom_columns=2,
legend_box_size=24,
stroke=True,
show_dots=False,
show_x_guides=True,
show_y_guides=True,
x_value_formatter=lambda v: f"{v:.1f}",
value_formatter=lambda v: f"{v:.1f}",
js=[],
xrange=(-1.2, 1.2),
range=(-1.2, 1.2),
print_values=False,
min_scale=3,
margin_bottom=440,
margin_left=80,
margin_right=60,
margin_top=60,
truncate_legend=-1,
)
# Segment labels — quarter-period intervals show traversal direction via colour
liss_labels = ["Lissajous 0 to pi/2", "Lissajous pi/2 to pi", "Lissajous pi to 3pi/2", "Lissajous 3pi/2 to 2pi"]
spiral_labels = ["Spiral 0 to pi/2", "Spiral pi/2 to pi", "Spiral pi to 3pi/2", "Spiral 3pi/2 to 2pi"]
# Lissajous (3,2) — solid lines; colour gradient encodes traversal direction
for k in range(n_segs):
start = k * seg_size
end = min((k + 1) * seg_size + 1, n_points)
seg_data = [{"value": (float(liss_x[i]), float(liss_y[i]))} for i in range(start, end)]
chart.add(
liss_labels[k], seg_data, stroke_style={"width": 10, "linecap": "round", "linejoin": "round"}, show_dots=False
)
# Archimedean spiral — dashed lines provide non-colour family disambiguation
# Colour gradient encodes outward growth from origin (red) to radius 1 (lime)
for k in range(n_segs):
start = k * seg_size
end = min((k + 1) * seg_size + 1, n_points)
seg_data = [{"value": (float(spiral_x[i]), float(spiral_y[i]))} for i in range(start, end)]
chart.add(
spiral_labels[k],
seg_data,
stroke_style={"width": 10, "dasharray": "16, 8", "linecap": "round", "linejoin": "round"},
show_dots=False,
)
# Traversal markers — explicit start/end dots for both curves
# Both curves originate at the origin; Lissajous closes at (0,0), spiral ends at (1, 0)
chart.add("● Start t = 0 (both curves)", [{"value": (0.0, 0.0)}], show_dots=True)
chart.add("◆ Spiral end t = 2pi", [{"value": (float(spiral_x[-1]), float(spiral_y[-1]))}], show_dots=True)
# Save — PNG + interactive HTML, both theme-suffixed
chart.render_to_png(f"plot-{THEME}.png")
with open(f"plot-{THEME}.html", "wb") as f:
f.write(chart.render())
Part of Parametric Curve Plot on anyplot.ai.