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: letsplot 4.10.1 | Python 3.13.14
Quality: 90/100 | Updated: 2026-06-20
"""
import os
import numpy as np
import pandas as pd
from lets_plot import *
LetsPlot.setup_html()
# Theme tokens — Imprint palette, theme-adaptive chrome
THEME = os.getenv("ANYPLOT_THEME", "light")
PAGE_BG = "#FAF8F1" if THEME == "light" else "#1A1A17"
ELEVATED_BG = "#FFFDF6" if THEME == "light" else "#242420"
INK = "#1A1A17" if THEME == "light" else "#F0EFE8"
INK_SOFT = "#4A4A44" if THEME == "light" else "#B8B7B0"
GRID_COLOR = "#E3E2DB" if THEME == "light" else "#2A2A27"
# Imprint sequential colormap: brand green (t=0) → blue (t=max)
GRAD_LOW = "#009E73" # Imprint position 1 — first series / start
GRAD_HIGH = "#4467A3" # Imprint position 3 — end
# Data — Lissajous figure: x = sin(3t), y = sin(2t), t ∈ [0, 2π]
t_lissajous = np.linspace(0, 2 * np.pi, 1000)
df_lissajous = pd.DataFrame({"x": np.sin(3 * t_lissajous), "y": np.sin(2 * t_lissajous), "t": t_lissajous})
# Data — Archimedean spiral: x = t·cos(t), y = t·sin(t), t ∈ [0, 4π]
t_spiral = np.linspace(0, 4 * np.pi, 1000)
df_spiral = pd.DataFrame({"x": t_spiral * np.cos(t_spiral), "y": t_spiral * np.sin(t_spiral), "t": t_spiral})
anyplot_theme = theme(
plot_background=element_rect(fill=PAGE_BG, color=PAGE_BG),
panel_background=element_rect(fill=PAGE_BG, color=PAGE_BG),
panel_grid_major=element_line(color=GRID_COLOR, size=0.4),
panel_grid_minor=element_blank(),
axis_title=element_text(size=12, color=INK),
axis_text=element_text(size=10, color=INK_SOFT),
axis_line=element_blank(),
axis_ticks=element_blank(),
plot_title=element_text(size=13, color=INK, face="bold"),
legend_text=element_text(size=10, color=INK_SOFT),
legend_title=element_text(size=10, color=INK),
legend_background=element_rect(fill=ELEVATED_BG, color=INK_SOFT),
)
# Plot — Lissajous figure (closed curve: start ≡ end at origin, show only start)
plot_lissajous = (
ggplot(df_lissajous, aes(x="x", y="y", color="t"))
+ geom_path(size=1.5, alpha=0.9, tooltips=layer_tooltips().line("t = @t").format("t", ".2f"))
+ geom_point(data=df_lissajous.iloc[[0]], mapping=aes(x="x", y="y"), color=GRAD_LOW, size=5, shape=16)
+ scale_color_gradient(low=GRAD_LOW, high=GRAD_HIGH, name="t (rad)", format=".1f")
+ coord_fixed()
+ labs(x="x(t) = sin(3t)", y="y(t) = sin(2t)", title="Lissajous Figure · 3:2 frequency ratio, closed")
+ anyplot_theme
)
# Plot — Archimedean spiral (open curve: show both start and end markers)
plot_spiral = (
ggplot(df_spiral, aes(x="x", y="y", color="t"))
+ geom_path(size=1.5, alpha=0.9, tooltips=layer_tooltips().line("t = @t").format("t", ".2f"))
+ geom_point(data=df_spiral.iloc[[0]], mapping=aes(x="x", y="y"), color=GRAD_LOW, size=5, shape=16)
+ geom_point(data=df_spiral.iloc[[-1]], mapping=aes(x="x", y="y"), color=GRAD_HIGH, size=5, shape=17)
+ scale_color_gradient(low=GRAD_LOW, high=GRAD_HIGH, name="t (rad)", format=".1f")
+ coord_fixed()
+ labs(x="x(t) = t·cos(t)", y="y(t) = t·sin(t)", title="Archimedean Spiral · expanding outward")
+ anyplot_theme
)
# Side-by-side layout with overall title
grid_plot = gggrid([plot_lissajous, plot_spiral], ncol=2)
title_str = "line-parametric · python · letsplot · anyplot.ai"
final_plot = (
grid_plot
+ ggsize(800, 450)
+ ggtitle(title_str)
+ theme(
plot_title=element_text(size=16, color=INK, face="bold"),
plot_background=element_rect(fill=PAGE_BG, color=PAGE_BG),
)
)
# Save PNG and interactive HTML
ggsave(final_plot, f"plot-{THEME}.png", path=".", scale=4)
ggsave(final_plot, f"plot-{THEME}.html", path=".")
Part of Parametric Curve Plot on anyplot.ai.