Nurbs Curve to Trapezoid Chain

klammax · June 2, 2020, 1:08pm

Hello,

Im trying make a chain of trapezoids following a curbs curve. The input parameters for the trapezoids is a range of width (W) and a range of angles (a) and a height (H) wich should be kept for all trapezoids.

On a straight line, similar trapezoids should alternate like in IMG1

When curvature gets higher. the trapezoids should get slim to handle the curvature. IMG2

The only problem I facing here is that the ends of the trapezoids do not match which is crucial for my application. IMG3

I tried to Use Anemone To use the end Points as start points for the following trapezoid. This doesn’t solve the problem because failiure adds up and The trapezoid chain wont follow the curve anymore.

Is there any other approach to reach a chain of trapezoids within a certain range of angles and widths to discretize a nurbs curve?

Thanks for any Input.
Max

Curve to Trapezoid_MK.gh (19.9 KB)

markz · June 2, 2020, 2:29pm

1- offset curve to both sides
2- project a line using vector normal to curve tangency vector
3- find intersection points of 1 &2
4- draw lines between intersection points
5 - join lines from 4 to for your trapezoid

klammax · June 2, 2020, 2:39pm

Thanks for your answer.

I forgot to Point out that I need symmetrical “Isosceles Trapezoid” which makes it a bit more complicated.

markz · June 2, 2020, 3:11pm

I am thinking that this is geometrically possible only if the original curve is a circle.

Dani_Abalde · June 2, 2020, 3:22pm

That makes it an approximation problem, where the curve is a guide and not a constraint, because you cannot satisfy that criterion for any curve. Create an approximation of the result and then try to satisfy that criterion with Kangaroo.