Hey guys, I am trying to find a point which is at equal distance from many points in space.. for example if i hava 3 points say A, B, C (say forming a triangle or any shape), i want to tell grasshopper to find a point which is as equal distande from A, B, C.. I dunn want to create a shape out of it, its juss with points.. which shape i just give area command and i get the centre point..
Make Spheres around all 3 points of the same radius. Intersect sphere A with B, which will give a circle. Intersect the circle with sphere C, which will give you 2 points. These are your required points.
Matter of fact, connect these two points to form a line, and any point on this line will always be the same distance from all the 3 points.
Hey Suryansh,
Its a bit confusing.. I didnt understand the Sphere part.. Could u please consider the drawing in 2d for my better understanding.. Its not necessary that there are 3 points, could be more.. If possibe can u post an example please..
Make any 3 points in Rhino, and adjust the radius of the spheres until all 3 touch.
If you have 4 points, intersect the line you get from the above process with the 4th sphere, which will also give you 2 points (both equidistant from the original 4). If you have 5 or more points, I'm not sure if a solution is possible.
Hey Daniel,
How about having 8 points and then finding a common point which is equidistant from all? even in this i am not getting point equidistant to all 3 points.. i dunno whether i have done it correct or not..
1. For any three different points in space the point equally distant from each of them is the center of the circle which passes through those points:
2. For more than three different points in space the solutions exists only if those points lay on a sphere:
However, for any number of points the solution above should give you a point with minimally deviated distances from the given set. In other words - as close as you can get to eqidistant.
I think you might be confusing the centroid point of a point cloud with the concept of an equidistant point, which we've discussed above.
You've mentioned the Area component in your first post, which gives you the centroid of a given shape.
In order to find the centroid of a point cloud you'd need to average the points' xyz coordinates.
Like this, for example:
Or this:
Which is basically the same thing, only more straightforward.