Nearest Point on Surface

https://github.com/nortikin/sverchok/assets/14288520/aeb96cdd-91d3-4ade-aaef-d0b76e61ae46

Dependencies

This node requires SciPy library to work.

Functionality

This node searches for the point on the surface, 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 surface, that will be much faster. This node, on the other hand, is usable in cases when you do not know formulas for your surface - for example, it was received by some approximation.

At the first step of it’s algorithm, this node evaluates the surface in points of a cartesian grid, and selects the closest of them. This point is then used as an initial guess for the more precise algorithm.

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

https://github.com/nortikin/sverchok/assets/14288520/668eebba-dcbb-456b-9bdd-f825bd686af3

Inputs

This node has the following inputs:

  • Surface. The surface to find the nearest point on. This input is mandatory.

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

Parameters

This node has the following parameters:

  • Init Resolution. Number of samples to evaluate the surface in, for the initial guess. The higher this value is, the more precise the initial guess will be, so the less work for the numeric algorithm. The default value is 10. In many simple cases you do not have to change this value.

  • Precise. If checked, then a numeric algorithm will be used to find exact location of the nearest point. Otherwise, the node will return the initial guess. So if this parameter is not checked, the Init Resolution parameter will define the precision of the node. Checked by default.

  • Method. This parameter is available in the N panel only. The algorithm used to find the nearest point. The available algorithms are:

    • L-BFGS-B

    • Conjugate Gradient

    • Truncated Newton

    • SLSQP - Sequential Least SQuares Programming algorithm.

    The default option is L-BFGS-B. In simple cases, you do not have to change this parameter. In more complex cases, you will have to try all algorithms and select the one which fits you the best.

  • Sequential. This parameter is available in the N panel only, and only when Precise parameter is checked. When checked, the node will use result of finding the nearest point from one source point as an initial guess for finding the nearest point for the next source point. This approach can give better results or better performance in case you are, for example, finding nearest points for a series of points generated from one curve. Unchecked by default.

Outputs

This node has the following outputs:

  • Point. The nearest point on the surface, in 3D space.

  • UVPoint. The point in surface’s U/V space, which corresponds to the nearest point. Z coordinate of this output is always zero, X and Y correspond to U and V.

Example of usage

https://github.com/nortikin/sverchok/assets/14288520/377c8839-91d0-4348-863e-0338310618d4 https://github.com/nortikin/sverchok/assets/14288520/e5e6c83f-7c34-4bff-b2fa-97dcaed59e57
https://user-images.githubusercontent.com/284644/87247996-782fc800-c470-11ea-8ccc-e15021b59591.png