pcurve and other FreeCAD concepts.

[onekk]

Hello, I'm stuck with some conceptual things, speaking about BSPline and BSplineSurfaces.

1. What are the concepts behing the BSPline definition used in OCCT. (my fault as someone has tried to explain these things to me, but I missed to note down the post reference)
2. what are pcurves? My fault also here, but a quick search in OCCT documentation gave no proper results, meybe "projected cruves"

TIA and Regards

Carlo D.

[wandererfan]

what are pcurves? My fault also here, but a quick search in OCCT documentation gave no proper results, meybe "projected cruves"

2d parametric curves on the surface underlying the face. Some OCC algos require these.

see: https://opencascade.blogspot.com/2009/0 ... de_12.html

for the other point, maybe B-Splines? More math than OOC though.

[onekk]

what are pcurves? My fault also here, but a quick search in OCCT documentation gave no proper results, meybe "projected cruves"

2d parametric curves on the surface underlying the face. Some OCC algos require these.

see: https://opencascade.blogspot.com/2009/0 ... de_12.html

for the other point, maybe B-Splines? More math than OOC though.

Thanks.

Although I've read recently the article you linked. I've missed:

- Curve C(t) in 3D space, encoded as Geom_Curve. This is considered as a primary representation;
- Curve(s) P(t) in parametric 2D space of a surface underlying each face the edge belongs to. These are often called pcurves and are encoded as Geom2d_Curve;

So P stand for Parametric.

For BSPlines I know the wiki page, mut as there are some peculiarity about the underlying explanation, about poles, knots, and the way they are defined in FC, I don't remember well but @chrisb or @Chris_G once has explained to me the mathematics theory that OCCT follow to define things, like "closed BSpline" and the way you have to specify the knots and similar data that are slightly different from what is the "most found" explanations around.

My fault is not having noted down the forum post reference and probably the linked documents.

Regards

Carlo D.

[chrisb]

@chrisb or @Chris_G once has explained to me the mathematics theory that OCCT follow to define things, like "closed BSpline" and the way you have to specify the knots and similar data that are slightly different from what is the "most found" explanations around.

I have done quite some research on B-splines, but have hardly posted here about it.

[Chris_G]

I think the only thing that OCCT does slightly different from others, is separating the knot sequence into 2 lists (of equal length) :
- knots is the list of unique knots (= not repeated)
- multiplicities (integers) is the list that represent the number of repetition of each knot.

So, a knot sequence that is usually represented like this, for example :
[0.0, 0.0, 0.0, 0.0, 0.3, 0.3, 0.5, 0.5, 0.5, 0.7, 1.0, 1.0, 1.0, 1.0]

will look like this in OCCT / FreeCAD :
knots = [0.0, 0.3, 0.5, 0.7, 1.0]
multiplicities = [4, 2, 3, 1, 4]

[onekk]

...
I have done quite some research on B-splines, but have hardly posted here about it.

Thanks for answering.

Regards

Carlo D.

[onekk]

I think the only thing that OCCT ....

Many thanks, this was the "different" thing I remembered, let me note it down so no more .

Regards

Carlo D.