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: bokeh 3.9.1 | Python 3.13.14
Quality: 91/100 | Updated: 2026-06-20
"""
import os
import sys
# Prevent bokeh.py from shadowing the bokeh package (script dir added to sys.path[0])
_here = os.path.dirname(os.path.abspath(__file__))
sys.path = [p for p in sys.path if os.path.abspath(p) != _here]
import time
from pathlib import Path
import numpy as np
from bokeh.io import output_file, save
from bokeh.layouts import gridplot
from bokeh.models import BasicTicker, ColorBar, ColumnDataSource, LinearColorMapper
from bokeh.plotting import figure
from selenium import webdriver
from selenium.webdriver.chrome.options import Options
# Theme tokens
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"
# Imprint sequential colormap — green (#009E73) → blue (#4467A3)
def _lerp_hex(c0, c1, t):
r0, g0, b0 = (int(c0[i : i + 2], 16) for i in (1, 3, 5))
r1, g1, b1 = (int(c1[i : i + 2], 16) for i in (1, 3, 5))
return "#{:02X}{:02X}{:02X}".format(
int(round(r0 + (r1 - r0) * t)), int(round(g0 + (g1 - g0) * t)), int(round(b0 + (b1 - b0) * t))
)
IMPRINT_SEQ256 = [_lerp_hex("#009E73", "#4467A3", i / 255.0) for i in range(256)]
# Data — 1000 points for smooth curves
n_points = 1000
n_seg = n_points - 1
# Lissajous figure: x = sin(3t), y = sin(2t), t ∈ [0, 2π]
t_liss = np.linspace(0, 2 * np.pi, n_points)
x_liss = np.sin(3 * t_liss)
y_liss = np.sin(2 * t_liss)
# Archimedean spiral: x = t·cos(t), y = t·sin(t), t ∈ [0, 4π]
t_spiral = np.linspace(0, 4 * np.pi, n_points)
x_spiral = t_spiral * np.cos(t_spiral)
y_spiral = t_spiral * np.sin(t_spiral)
def make_segment_source(x, y):
n = len(x) - 1
return ColumnDataSource(
data={
"xs": [[x[i], x[i + 1]] for i in range(n)],
"ys": [[y[i], y[i + 1]] for i in range(n)],
"color": [IMPRINT_SEQ256[int(i / (n - 1) * 255)] for i in range(n)],
}
)
seg_liss = make_segment_source(x_liss, y_liss)
seg_spiral = make_segment_source(x_spiral, y_spiral)
# Two panels side-by-side → 1600 + 1600 = 3200 px wide × 1800 px tall
PANEL_W = 1600
PANEL_H = 1800
p1 = figure(
width=PANEL_W,
height=PANEL_H,
title="line-parametric · python · bokeh · anyplot.ai",
x_axis_label="x(t) = sin(3t)",
y_axis_label="y(t) = sin(2t)",
toolbar_location=None,
match_aspect=True,
min_border_bottom=160,
min_border_left=180,
min_border_top=110,
min_border_right=220,
)
p1.multi_line(xs="xs", ys="ys", source=seg_liss, line_color="color", line_width=9)
p1.scatter(
x=[x_liss[0]],
y=[y_liss[0]],
size=30,
fill_color="#009E73",
line_color=PAGE_BG,
line_width=4,
legend_label="Start t = 0",
)
p1.scatter(
x=[x_liss[-1]],
y=[y_liss[-1]],
size=30,
marker="square",
fill_color="#4467A3",
line_color=PAGE_BG,
line_width=4,
legend_label="End t = 2π",
)
liss_cbar = ColorBar(
color_mapper=LinearColorMapper(palette=IMPRINT_SEQ256, low=0, high=round(2 * np.pi, 2)),
ticker=BasicTicker(desired_num_ticks=5),
title="t (rad)",
title_text_font_size="28pt",
title_text_color=INK,
major_label_text_font_size="24pt",
major_label_text_color=INK_SOFT,
label_standoff=14,
width=44,
padding=24,
background_fill_color=PAGE_BG,
border_line_color=INK_SOFT,
)
p1.add_layout(liss_cbar, "right")
p2 = figure(
width=PANEL_W,
height=PANEL_H,
title="Archimedean Spiral · line-parametric · python · bokeh · anyplot.ai",
x_axis_label="x(t) = t·cos(t)",
y_axis_label="y(t) = t·sin(t)",
toolbar_location=None,
match_aspect=True,
min_border_bottom=160,
min_border_left=180,
min_border_top=110,
min_border_right=220,
)
p2.multi_line(xs="xs", ys="ys", source=seg_spiral, line_color="color", line_width=9)
p2.scatter(
x=[x_spiral[0]],
y=[y_spiral[0]],
size=30,
fill_color="#009E73",
line_color=PAGE_BG,
line_width=4,
legend_label="Start t = 0",
)
p2.scatter(
x=[x_spiral[-1]],
y=[y_spiral[-1]],
size=30,
marker="square",
fill_color="#4467A3",
line_color=PAGE_BG,
line_width=4,
legend_label="End t = 4π",
)
spiral_cbar = ColorBar(
color_mapper=LinearColorMapper(palette=IMPRINT_SEQ256, low=0, high=round(4 * np.pi, 2)),
ticker=BasicTicker(desired_num_ticks=5),
title="t (rad)",
title_text_font_size="28pt",
title_text_color=INK,
major_label_text_font_size="24pt",
major_label_text_color=INK_SOFT,
label_standoff=14,
width=44,
padding=24,
background_fill_color=PAGE_BG,
border_line_color=INK_SOFT,
)
p2.add_layout(spiral_cbar, "right")
# Theme-adaptive chrome for both panels
for p in [p1, p2]:
p.background_fill_color = PAGE_BG
p.border_fill_color = PAGE_BG
p.outline_line_color = None # L-shaped frame: axes provide the bottom+left boundary
p.title.text_color = INK
p.title.text_font_size = "36pt"
p.title.text_font_style = "normal"
p.xaxis.axis_label_text_color = INK
p.yaxis.axis_label_text_color = INK
p.xaxis.axis_label_text_font_size = "32pt"
p.yaxis.axis_label_text_font_size = "32pt"
p.xaxis.axis_label_text_font_style = "italic"
p.yaxis.axis_label_text_font_style = "italic"
p.xaxis.major_label_text_color = INK_SOFT
p.yaxis.major_label_text_color = INK_SOFT
p.xaxis.major_label_text_font_size = "26pt"
p.yaxis.major_label_text_font_size = "26pt"
p.xaxis.axis_line_color = INK_SOFT
p.yaxis.axis_line_color = INK_SOFT
p.xaxis.major_tick_line_color = INK_SOFT
p.yaxis.major_tick_line_color = INK_SOFT
p.axis.minor_tick_line_color = None
p.xgrid.grid_line_color = INK
p.ygrid.grid_line_color = INK
p.xgrid.grid_line_alpha = 0.12
p.ygrid.grid_line_alpha = 0.12
p.legend.background_fill_color = ELEVATED_BG
p.legend.border_line_color = INK_SOFT
p.legend.label_text_color = INK_SOFT
p.legend.label_text_font_size = "26pt"
p.legend.glyph_width = 36
p.legend.glyph_height = 36
p.legend.location = "top_right"
p.legend.padding = 14
p.legend.spacing = 8
# Layout
grid = gridplot([[p1, p2]], merge_tools=False, toolbar_location=None)
# Save interactive HTML
html_path = Path(f"plot-{THEME}.html")
output_file(str(html_path))
save(grid)
# Strip default body margin so the plot fills the Selenium viewport exactly
html = html_path.read_text()
html = html.replace("<body>", f'<body style="margin:0;padding:0;overflow:hidden;background:{PAGE_BG};">', 1)
html_path.write_text(html)
# Screenshot with headless Chrome (Selenium) at canvas dimensions
W, H = 3200, 1800
opts = Options()
for arg in (
"--headless=new",
"--no-sandbox",
"--disable-dev-shm-usage",
"--disable-gpu",
f"--window-size={W},{H}",
"--hide-scrollbars",
):
opts.add_argument(arg)
driver = webdriver.Chrome(options=opts)
driver.set_window_size(W, H)
# Compensate for any browser chrome that reduces the actual viewport
actual_h = driver.execute_script("return window.innerHeight")
if actual_h < H:
driver.set_window_size(W, H + (H - actual_h))
driver.get(f"file://{html_path.resolve()}")
time.sleep(3)
driver.save_screenshot(f"plot-{THEME}.png")
driver.quit()
Part of Parametric Curve Plot on anyplot.ai.