Rebuilding Curve Part 2

Rhino Rhino for Mac
1

I am sorry to bother again. I think this might also help other people searching for a better understanding of generating ‘proper’ surfaces.

I have a profile curve coming from an intersection between a plane tilted 45 degrees and a cube with fillets:

Intersection
Intersection1269×787 120 KB

I am wondering why rhino generates such dense curves on the arched part of my shape. Here you can appreciate a top view of the intersection profile curve oriented parallel to the ground:

Intersection_Curves
Intersection_Curves1246×802 33.9 KB

Why Rhino is building the curves with such a dense and unbalanced amount of control points ?

When I activate the blend curve between the 2 straight lines with the Tangent option activated it seems to be enough to replicate the original curve:

Blend
Blend1230×812 47.9 KB

How can get the same curve (I want to follow my filleted cube ‘original intersection’) with blend. It seems the curve could be replicated exactly with the blend.

I can upload the file in case needed.

Thanks so much. I am sorry again for posting often today. I am trying to solve a furniture that I have in my mind and have been dreaming quite often. Thanks a lot.

2

Try to use the command _Fitcrv
It will simplify your curves as much as possible inside a tolerance. Here an example with 0.01 tolerance settings.

_fitcrv
_fitcrv1294×772 89.3 KB

3

The intersection of two NURBS surfaces, including the situation when one of the surfaces is a plane, usually can not be represented exactly by a NURBS curve. There are special situations where the intersection is exactly a NURBS curve. This is fundamental property of NURBS surfaces and curves, not limited to Rhino. When two surfaces intersect Rhino determines an approximate intersection curve with sufficient number and distribution of control points that the approximate NURBS curve is within the absolute tolerance of the exact intersection curve. (In the Windows version the absolute tolerance set in DocumentProperties > Units > Absolute tolerance; I don’t know how it is set in the Mac version.) Depending on the shapes of the intersecting surfaces and the absolute tolerance the number of control points needed can vary from a few to many. Rhino distributes the control points to minimize the number needed.

In your particular case the straight fillets are portions of a cylinder, and the intersection of a cylinder and a plane is an ellipse. A portion of an ellipse can be represented exactly by a rational NURBS curve with weights other than 1. However Rhino doesn’t have the built-in algorithm to recognize the special case of the intersection, so it just finds a non-rational (weights = 1) curve which is within the absolute tolerance of the intersection curve of the surfaces…

4

Thanks Kiwi. I guess lowering the tolerance will help to get less control points. I will try with .1 Since Its a furniture piece I think its enough. Thanks a lot I will test and come back

5

Not “exact” as in exactly the same at any magnification level. But as @kiwi suggests you can use FitCrv to find a simpler curve which is sufficiently close for your needs.

6

David thanks for your feedback. I read it a few times. I am kind of trying to go in depth with rhino knowledge. I think your reply its weight too far of my understandings. Do you think I can change the weight of the curve? and get it ? Or you think Its kind of not possible ?

Is there anyway to get the blend curve matching the original not manually ?

7

Not easy or simple to do. And for your purposes there is probably no advantage to doing so. Creating surfaces using rational curves can result complications in further operations, or result in a surface which does not exactly match the rational input curve. Usually an approximate non-rational curve is more useful.

8

Ok . David, I am extremely grateful for your insights. Thanks so much.

9

Rhino cannot create intersection curves or trim curves that are simpler (like in ICEM or Catia that both have special tools to simplify degree 3 and 5 curves and higher). The amount of edit points is due to the underlying NURBS math.