Nearest Point on Curve

Dependencies

This node requires SciPy library to work.

Functionality

This node searches for the point on the curve, which is the nearest (the closest) to the given point.

Note that the search is implemented with a numeric algorithm, so it may be not very fast. In case you know how to solve this task analytically (with formula) for your particular curve, that will be much faster. This node, on the other hand, is usable in cases when you do not know formulas for your curve - for example, it was received by some approximation.

At the first step of it’s algorithm, this node generates several sample points on the curve with even intervals of T parameter. The nearest of them is selected. This point are then used as initial guess points for the more precise algorithm.

In case there are several points on the curve with equal distance to the original point, the node will return one of them (it is not guaranteed which one).

Inputs

This node has the following inputs:

• Curve. The curve to search the point on. This input is mandatory.

• Point. The point to search the nearest for. The default value is global origin (0, 0, 0).

Parameters

This node has the following parameters:

• Init Resolution. Initial number of segments to subdivide curve in, for the first step of algorithm. The higher values will lead to more precise initial guess, so the precise algorithm will be faster; but that can require more evaluations at the first stage. The default value is 50. In many cases, you do not have to change this value.

  

• Precise. If not checked, then the precise calculation step will not be executed, and the node will just output the nearest point out of points generated at the first step - so it will be “roughly nearest point”. So, if this parameter is not checked, higher values of Init resolution parameter will lead to more precise output. Checked by default.

  

• Method. This parameter is available in the N panel only. This defines the algorithm to be used. In simple cases, all algorithms will give the same result; in more complex cases, you will have to try all and select the one which works for you case. The available values are:

  • Brent. Uses Brent’s algorithm to find a local minimum. The algorithm uses inverse parabolic interpolation when possible to speed up convergence of the golden section method.

  • Bounded. Uses the Brent method to find a local minimum in the interval.

  • Golden. Uses the golden section search technique. It uses analog of the bisection method to decrease the bracketed interval. It is usually preferable to use the Brent method.

Outputs

This node has the following outputs:

• Point. The nearest point in 3D space.

• T. The value of curve’s T parameter corresponding to the nearest point.