Sketch A Curve with The Following Properties Calculator

This calculator helps you sketch a curve by defining control points, tangents, and interpolation methods. Whether you're working with Bézier curves, splines, or other parametric curves, this tool provides a visual representation of your curve based on the properties you specify.

How to Use This Calculator

To sketch a curve with specific properties:

Enter the coordinates of your control points in the "Control Points" field.
Specify the tangent vectors at each point if needed.
Choose the interpolation method (e.g., Bézier, Catmull-Rom, or Hermite).
Click "Calculate" to generate the curve.
Review the result and adjust parameters as needed.

For best results, ensure your control points are ordered sequentially along the curve. The calculator supports up to 10 control points.

Formula Used

The calculator uses parametric equations to generate the curve. The general form is:

For Bézier curves:

P(t) = Σ [n choose i] (1-t)^(n-i) t^i P_i, where i ranges from 0 to n

For Catmull-Rom splines:

P(t) = 0.5 * [(2t^3 - 3t^2 + 1)P_i + (-2t^3 + 3t^2)P_{i+1} + (t^3 - 2t^2 + t)P_{i+2} + (t^3 - t^2)P_{i+3}]

The exact formula used depends on the interpolation method selected.

Worked Example

Let's create a Bézier curve with these control points:

Point	X Coordinate	Y Coordinate
P0	0	0
P1	1	2
P2	2	1
P3	3	3

The resulting curve will smoothly connect these points with a single continuous tangent at each control point.

Frequently Asked Questions

What interpolation methods are supported?: The calculator supports Bézier curves, Catmull-Rom splines, and Hermite interpolation.
How many control points can I use?: You can use up to 10 control points. More points will create a more complex curve.
Can I export the curve data?: Currently, the calculator displays the curve visually but does not support exporting data.
What if my curve doesn't look right?: Check your control points and tangents. Adjusting these values can significantly change the curve's shape.