Study parametric curves using inputs and instant outputs. Inspect motion measures, tangent data, and coordinates. Visualize every path with exports for classwork and verification.
Use cubic component functions: x(t) = a3t3 + a2t2 + a1t + a0, and similarly for y(t) and z(t).
| Example Item | Value |
|---|---|
| x(t) | t3 - 2t |
| y(t) | t2 + 1 |
| z(t) | 0.5t |
| Evaluate at | t = 1 |
| Interval | -2 to 2 |
| Suggested samples | 120 |
This example creates a smooth three-dimensional path. It is useful for checking position, tangent direction, curvature, displacement, and approximate arc length.
A vector curve describes motion or shape using component functions for x, y, and z. Each parameter value gives one point in two-dimensional or three-dimensional space.
They define the cubic polynomial for each coordinate. Changing coefficients changes the path, turning points, growth rate, and overall direction of the curve.
These derivatives describe motion along the curve. Velocity gives direction and rate of travel. Acceleration shows how that motion changes with the parameter.
Curvature measures how sharply the path bends at a chosen point. Larger values mean tighter turning, while smaller values mean a straighter local path.
Yes. Negative values often represent earlier parameter positions. They are valid as long as your curve model makes sense for the interval you choose.
That usually happens when curvature is zero or extremely small. In that case, the curve is locally straight and the radius becomes extremely large.
This page uses numerical approximation from sampled speeds. Increasing the sample count usually improves the estimate and gives a smoother plotted path.
Yes. Set all z(t) coefficients to zero. The calculator will still evaluate the curve correctly and plot it as a flat path in space.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.