Partworks Curve Tool Help

[archis]

I'm messing around with the curve tool in Partworks 2D and its a little confusing.

For example, I draw a 2 segment line (3 mouse clicks). When I go into node edit I get 1 control point for first and third node and I get two for the node in the middle. When I first move one the control points for the middle node, both control points move in tandem, but it seems I can get it out of that mode by dragging a control point to the node where the control point behavior changed modes.

Sorry for the long winded explanation of my confusion but here are my questions:

1) Is there detailed documentation somewhere for Partsworks that I am missing, the help files I have found are not detailed.

2) Does anybody know exactly what the control points are doing with respect to the curve in mathematical terms? There seems to be a relationship between the two control point but I can' figure it out.

Thanks,
Jim

[dana_swift]

Hello Jim, the control points in Vectric anything (including Partworks) are Bezier-curve control points.

In specific mathematical terms Bezier curves are one member of the family of Bernstein Polynomials. How mathematical do you want to get? I probably have more detail than anybody other than a mathematician would want.

As a user of Bezier curves, the control points define the velocity and direction of a point swept through normalized time (t=0 -> 1), relative to the end point. The point at t=0 starts at end point zero, and moves in the direction of the first control point at the velocity determined by the distance away of the associated control point.

To make two adjacent Bezier curves flow together, the control vectors at the end point of the first curve must be the negative of the control vector at the start of the second curve so Vs = -Ve.

Bezier curves can be N dimensional, so 2d, 3d, or higher Bezier shape definitions make sense mathematically, the are just defined by vectors.

The background behind Bezier curves is interesting, as Pierre Bezier needed a way for the artistic/aesthetic designers at Renault to be able to specify shapes that made sense to them as artists, that a computer could interpret and cut on the brand new technology of CNC.

Excellent documentation of Bezier curves/Bernstein polynomials is available on the web. With a little search I could probably direct you to some if you want to get down into the details.

Hope that helps-

D

[archis]

Dana,

Thanks for your help, they where driving me crazy since I couldn't figure out what they were doing. I'll google those to get a better understanding of how they work.

Jim