How to break a spline entity into two separate ones from a point of it if not using command function
@yangguoshe wrote:
.... If I don't use the command function ....
Why not? It's very easy with a Break command, and the coinciding part may not be possible in drawing two new ones. You certainly can't just use the break point as the end of one and start of another -- here the red is the original, and the yellow and green are what happens when you do that:
[Even for a Polyline, that approach becomes challenging if the break point falls on an arc segment.]
Even if one could figure out how to calculate the end tangent directions for use in something like (entmake), that doesn't make it coincide. Here I manually adjusted them for the yellow one as close as I could visually at the ends:
and the shape doesn't coincide in the vicinity of the middle fit point:
I don't even want to think about how you would approach it for a control-point-based one....
Thank your replaying, I want to know if we can deduce the basic function （De Boor’s Algorithm）of each sub segment of the spline curve（AB BC CD DE EF ）, and rely on the basic function to deduce the new control points, and to realize the complete coincidence between the new two segments of the spline curve and the original one
@yangguoshe wrote:
.... I want to deduce the control points from the fitting points. ....
Since you haven't answered the question at the beginning of Message 4, I'll ask it in a different way. For what purpose do you want to deduce the control points? If it's only to make new Splines with something like (entmake), it is infinitely simpler to just get over your irrational fear of the (command) function, and simply Break the original Spline.
Yes, well again, I ask, why do you not want to use the (command) function? It's simpler for Breaking all those other things, too.
If you construct a spline in AutoCAD and do not modify the weight values from 1 for all control vertices then the result will be a B-spline (a special case of the more general NURBS). You can construct a spline in AutoCAD using Fit points or CVs. If you use the Fit Point method then the CVs are automatically determined. In the image below a degree 3 B-spline was constructed using fit points F1 thru F7. The CVs CV1 thru CV9 were determined by AutoCAD's spline software using math beyond this discussion. The red spline was trimmed at the the trim line using the trim command resulting in the green curve (the green curve exactly overlaps the first part of the red curve. The CVs for the trimmed spline (green) are CV1A thru CV5A.
The yellow curve was constructed by using the original fit points F1 thru F3 plus the trim point (the end of the trimmed spline). Note that it is not the same shape as the original curve and thus using the original fit points are of little, if any, benefit.
You could construct a spline using Fit points as discussed here but would need to know the tangent vectors for the ends. I generally consider that once a spline is edited its fit points become irrelevant.
I am aware that you want to avoid using "command" in your code but I think a more practical approach would be to use the commands break or trim to break a spline into two pieces than trying to add the math to calculate the necessary data needed to build the two splines.
@yangguoshe wrote:Thank your replaying, I want to know if we can deduce the basic function （De Boor’s Algorithm）of each sub segment of the spline curve（AB BC CD DE EF ）, and rely on the basic function to deduce the new control points, and to realize the complete coincidence between the new two segments of the spline curve and the original one
Recreating spline segments between Fit Points is a straightforward process. A Fit Point is a knot location so the segment between two consecutive fit points can be recreated as a basic Bezier style curve. And this is true regardless of the Knot Parameterization method.
The tangent direction (acquired via Xline in the screencast) could be retrieved with VisualLisp’s vlax-curve-getFirstDeriv function. The Fit Point location, and the two intersection with the related Control Vertices frame can recreate the segment with perfect fidelity.
Breaking a spline mid span becomes more involved – where the math and/or geometry manipulation increases in complexity. Still doable, if someone were so inclined, but tough to justify with the tools already available – either as a Command call or via the Managed ARX API.
Perhaps one of the programmers versed in both .NET and ALisp could encapsulate the Curve.GetSplitCurves Method.
public virtual DBObjectCollection GetSplitCurves(Point3dCollection point);
