Curves Without Inflection points


#1

I frequently find myself having to draw 2D curves tangent to a starting curve then to a point.

For some reason, Rhino appears to always draw such curves with an inflection point making them harder to adjust to shape. Is there any way to get Rhino to draw such a curve without an inflection point?


#2

You could try _BlendCrv with the Point option for the second point, then adjust the handles to taste before setting. Otherwise _Extend > By arc to point will give you an arc extension. Finally you can adjust the already made blend with EndBulge.

–Mitch


(John Brock) #3

When you draw your tangent curve, what command are you using and specifically where are you picking to make the curve?

Can you make a detailed example?
I suspect that process will be enlightening.


(Pascal Golay) #4

Hi Jim - ChangeDegree on that curve to 2. One way to make these is to BlendCrv, with the Point option at one end and blend for tangency. Or just make a 3 point curve from Curve. How are you drawing the curve to begin with?

-Pascal


#5

I am using Interpcrv.

Do the following:

Draw a line in a plane.
Place a point in the plane in the general vicinity of an end of the line.

Interpcrv
S (Start)
Click on the end of the line and make curve tangent to the line.
Click on the point.


(Pascal Golay) #6

I’d use Curve and place three points. OSnaps and Tab direction lock can get you the tangent direction, otherwise Match for tangency when done with the curve.

-Pascal


(John Brock) #7

That’s the problem. Interpcrv forces the curve to pass through the points you pick, so the curve will zig-zag like you saw.

Instead, try the control point curve.
Then use the curvature graph to look at it’s curvature.


(David Cockey) #8

That’s not the problem. The degree 3 curve in the attached file was created using InterpCrv with the StartTangent option and selecting only the end points and the start tangent direction. Inflection.3dm (32.2 KB) The third control point is put in on a straight line from the start to the end curve. That is what causes the inflection. The inflection can be eliminated by moving the third control point.

To duplicate what I did:

InterpCrv with Degree=3
Select StartTangent option
Pick the start of the curve at the end of a line.
Choose the start tangent direction the same as the line.
For next point select the end point.
Enter to finish the command.

Here is the command line history from creating the curve in the attached file:

Command: InterpCrv
Start of curve ( Degree=3 Knots=Uniform PersistentClose=No StartTangent ): StartTangent
Start of curve:
Choose start tangent ( Direction ):
Next point ( Degree=3 Knots=Uniform PersistentClose=No EndTangent Undo ):
Next point. Press Enter when done ( Degree=3 Knots=Uniform PersistentClose=No EndTangent Undo ):