The line from a point to the closest point on the curve will be perpendicular to that curve whether it is a planar or a space curve.
Remember there are an infinite number of perpendicular lines to a curve at a particular point (all lying on the pla…
The line from a point to the closest point on the curve will be perpendicular to the curve. Are you getting lines which are not perpendicular? If so then something is going wrong. Perhaps you can post an image or definition.
Actually, now I think about it, I guess what I describe above is pretty much the same as David's second method. There's no need to take differences between neighbours, just use the surface normal at each point and ignore the z-component to get the v…
Here's my idea for a possible approach to scripting this:
Treat the surface as a 2D scalar field where the value at each point is the height.
For each point find the values of its 4 neighbours (above,below,left,right) some small distance away.
Def…
My own interest in complex numbers stems from their connection with a long running project of mine - rheotomic surfaces, as I described in this essay.
I'm sharing the grasshopper definition here for the first time. It is in the middle of some chang…
Thanks Vicente.
Yes, I've been following some of the recent developments with this 'Mandelbulb' and it is very interesting indeed. I might try and play around with it a bit over christmas if i get time.
I did start to look at plotting the Hubbard D…
ok, I'll have a go...
With the real numbers any number squared gives a positive answer. eg:
5 * 5 = 25 , -5 * -5 = 25
because a negative multiplied by a negative gives a positive.
The imaginary numbers behave differently from the reals, in that…
Great !!
Many thanks David for all your hard work on this.
If anyone is interested, I'll now be able to share the Rheotomic surface definition I've been working on using the new complex number components
If you mean tangent to 3 lines then this is a special case of Apollonius' problem
In general there are 4 solutions - an incircle and 3 excircles. Here's a def I made a while back to solve this that you might find useful:
That's cool.
I've posted my original method too, in case anyone is interested.
First it extracts the 3 Tait-Bryan angles, then it composes them using Rodrigues' half-angle method.
Hi Again.
Attached you might find a definition that reconstructs the helical movement between two positions of the same Brep. It calculates the angle, the axis and the displacement vector.
Adapting this for any type of geometry must be easy. Just th…
I don't have much time, and I haven't thought of everything, but it may be helpful. Find the plane for each of the two orientations. Get the intersection line between the two planes. Retrieve the same point from each of the two orientations (referre…
Hi, Daniel i want to create a geodesic dome but i have no clue how to strat. i found a topic where you showed your dome but definition doesnt work on my grasshopper. can you send me a picture of this definition?
Hi Daniel, I think I've got a question which is really suitable for you: Do you know if it's possible to generate a Costa Minimal Surface in Grasshopper? I had a look at the function with a mathematician-friend, but he told me it was involving complex numbers (weierstrass function) and grashopper propably can't calculate this. Any ideas?