Feature request: Perfected blendcrv

Rhino
22

you actually created potential nice logo with this graphics :slight_smile:

23

For a 2D Euler spiral/clothoid if the curvature at the points on the curve is known and the difference in tangent direction between the two points is known:
the arc length between the two points is the difference in tangent direction divided by the average of the curvatures.

Derivation:

  1. The derivative of the tangent direction by the arc length is the curvature.
  2. The change in tangent direction between two points along a curve is the integral of the curvature as a function of arc length between the two points.
  3. For the Euler spiral/clothoid the curvature varies linearly with arc length.
  4. Therefore the integral of the curvature along the curve is average of the curvature at the end points multiplied by the arc length.
  5. Using 2 and 4 and rearranging: the arc length is the difference in tangent direction divided by the average of the curvatures.
24

Ignore previous edit about mistake in the spreadsheet. I confused myself. I will repost.

3 Likes
25

So guys i took effort with my cousin and put together this:

image
image3517×615 273 KB

you can just play around with inputs in gh and moving black points in rhino to have fun
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image933×826 14.3 KB

image
image1327×845 37 KB

clothoidal-transition.gh (34.3 KB)

4 Likes
26

Hello, thank you for the plugin! Unfortunately, I have an issue with the Grasshopper file. Please see the attached image below. This is within the cluster in the middle. Do you know what could be the issue? Thank you in advance.

image
image1194×647 76.8 KB

27

Hi -

When you open that file, you should get the following warning:
image

That’s the component that is missing in your screenshot.
-wim