Plot parametric equations x(t) and y(t) with animated trace, adjustable parameter ranges, and multiple curve overlay.
This tool draws the curve traced by two independent expressions, x(t) and y(t), evaluated together as t sweeps across a range you set, then connects the resulting points and can animate a marker moving along them. Because the curve is defined by a shared parameter rather than y as a function of x, it can draw loops, cusps, and self-crossing paths no single y=f(x) graph could show. Several x(t)/y(t) pairs can be overlaid with independent t ranges for comparison. The most common surprise: the shape depends entirely on the chosen t interval, so a range that stops early truncates the curve before it closes, and one that runs too long retraces the same path on top of itself.
A concrete input and expected output from the current implementation.
Input
x(t) = cos(t), y(t) = sin(2t), t from 0 to 2*pi
Expected output
A figure-eight lying along the x-axis, bounded within x in [-1,1] and y in [-1,1]. It starts and ends at (1,0), and crosses itself at the origin (0,0) at t = pi/2 and t = 3*pi/2.
x has period 2*pi while y = sin(2t) has period pi, so the point returns to y = 0 twice as often as x completes its cycle; at t = pi/2 and 3*pi/2, x = 0 and y = 0 coincide, producing the self-intersection at the origin that gives this Lissajous curve its figure-eight shape.
The plotter evaluates x(t) and y(t) at a series of t values spaced across the range you supply, then connects consecutive (x,y) points with line segments. It does not solve for an algebraic relation between x and y. Curves with sharp cusps, tight loops, or high-frequency oscillation (like Lissajous figures with large ratios) need a range with enough samples per cycle or the plotted path looks faceted instead of smooth.
Each curve you add carries its own x(t), y(t), and t range, so curves with different periods or domains can be compared on one canvas without forcing a shared scale. The animated trace replays the same sampled points in order as t increases, which is why reversing or narrowing the t range changes what the animation shows, not just the static plot.
Yes, but you have to convert it yourself first: set x(t) = (1 + cos(t)) * cos(t) and y(t) = (1 + cos(t)) * sin(t), then plot t over the range that closes the curve (0 to 2*pi for this one). The tool doesn't accept r(theta) directly.
No. The description covers plotting, animated tracing, adjustable ranges, and overlay of multiple curves - it does not mention computing derived quantities like arc length, curvature, or self-intersection coordinates, so treat any of those as something you'd need to work out separately.
The example and behavioral notes were checked against the browser implementation. Standards and primary references below define the relevant format, formula, or platform behavior.
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