How to determine if two points are approximate

Rhino Developer
1

Given two ON_3dPoint2, how can I determine if they (within the error range) are the same point?

2

You mean, if the distance between them is smaller than a given tolerance?

3

Its usually called „EpsilonEquals“, but implementing that on your own is not hard either as you pointed out. Distance smaller than tolerance, although there are some slight variations out there.

4

yes, It is not hard to implementing.
I have used eigen before, which supports determining whether two vectors are similar by its internal Epsilon.

Eigen::Vector3d v1,v2;
if(v1.isApprox(v2)){
  // do something
}

So I wonder if Rhino has a similar method?
As I know, there are different types of tolerance in Rhino, so I don’t know which one is more suitable for me.

5

in Rhinocommon - yes - search for EpsilonEquals in the docs…

https://developer.rhino3d.com/api/rhinocommon/rhino.geometry.arc/epsilonequals?search=EpsilonEquals

most basic geometry offers the searched functionality.

are you using opennurbs ? rhinocommon ? c++ or c# ?

6

Hi @Liu2 ,
There are many ways to reach your goal
Simplest solution would be

def points_are_equal(pt1, pt2, tolerance):
    distance = pt1.DistanceTo(pt2)
    return distance <= tolerance

Or you could consider just each axis by itself

def points_are_equal(pt1, pt2, tolerance):
    def almost_equal(a, b, tol):
        return abs(a - b) <= tol
    x_equal = almost_equal(pt1.X, pt2.X, tolerance)
    y_equal = almost_equal(pt1.Y, pt2.Y, tolerance)
    z_equal = almost_equal(pt1.Z, pt2.Z, tolerance)
    return x_equal and y_equal and z_equal

The most accurate method would be the first.
Hope this helps,
Farouk

7

This is really simple… :hear_no_evil:

 public static bool EpsilonEquals(Point3d p1, Point3d p2, double epsilon = 0.00001)
 {
     return Math.Abs(p1.X - p2.X) <= epsilon &&
            Math.Abs(p1.Y - p2.Y) <= epsilon &&
            Math.Abs(p1.Z - p2.Z) <= epsilon;
 }
8

Thank you for your reply!
I am using opennurbs in c++.

What I am most concerned about is not how to implement this method, but how to use the correct tolerance.
I want to make sure my tolerance is same to Rhino default.

This is my current code, and I have no idea which tolerance should I use.

bool isApprox(const ON_3dPoint& p1, const ON_3dPoint& p2, int epsilon=ON_EPSILON){
  if(p1.DistanceTo(p2)<epsilon)
    return true;
  return false;
}
9

my guess:

ON_ZERO_TOLERANCE
?
from the documentation:
…
In cases when an absolute “zero” tolerance / is required to compare model space coordinates,
…

10

Note if you use DistanceTo you compute the full distance every-time. If you choose my/Farouks approach by using the Math.Abs, your computation will be more efficient, because it will return false if the x is already out of bounds, before even computing the y and z distance. On top you don’t need the if clause. Just return the statement in the if, otherwise you branch the code for no reason.

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11

There is no one correct tolerance. You must decide, based on the problem you are trying to solve, what tolerance is sufficient.

– Dale

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