Intersect NURBS Curves

Dependencies

This node requires either SciPy library, or FreeCAD libraries to work.

Functionality

This node tries to find all intersections of provided Curve objects. This node can work only with NURBS or NURBS-like curves.

Inputs

This node has the following inputs:

• Curve1. The first curve. This input is mandatory.

• Curve2. The second curve. This input is mandatory.

Parameters

This node has the following parameters:

• Implementation. Implementation of numeric algorithm to be used. The available options are:

  • FreeCAD. Use implementation from FreeCAD library. This option is available when FreeCAD library is installed.

  • SciPy. Use implementation based on SciPy library. This option is available when SciPy library is installed.

  In general, FreeCAD implementation is considered to be faster, more precise, and better tested. However, it does not allow one to control intersection tolerances, while SciPy implementation does.

  By default, the first available implementation is used.

• Matching. This defines how lists of input curves are matched. The available options are:

  • Longest. The node will use input lists in parallel: first curve from the first list with first curve from the second list, then second curve from first list with second curve from the second list, and so on. In case two lists have different lengths, in the shortest one, the last curve will be repeated as many times as required to match lengths.

  • Cross. The node will use input lists in “each-to-each” mode: first curve from first list with each curve from the second list, then second curve from first list with each curve from the second list, and so on.

  The default option is Longest.

• Find single intersection. If checked, the node will search only one intersection for each pair of input curves. Otherwise, it will search for all intersections. Checked by default.

• Curves do intersect. If checked, then the node will fail if two curves do not intersect. Otherwise, it will just output empty list of intersections. Unchecked by default.

• Split by row. This parameter is available only when Matching parameter is set to Cross. If checked, the node will output a separate list of intersections for each curve from the first list. Otherwise, the node will output a single flat list with all intersections of each curve with each. Checked by default.

• Precision. This parameter is available in the N panel only, and only when Implementation parameter is set to SciPy. This defines the allowed tolerance of numeric method - the maximum allowed distance between curves, which is considered as intersection. The default value is 0.001.

• Numeric method. This parameter is available in the N panel only, and only when Implementation parameter is set to SciPy. This defines numeric method to be used. The available options are: Nelder-Mead, L-BFGS-B, SLSQP, Powell, Trust-Cosntr.

Outputs

This node has the following output:

• Intersections. The list of intersection points.

Example of Usage

Find three intersections of two curves:

Find twelve intersections of two series of curves: