Surface from Net of Curves Node (Gordon Surface)

docs/nodes/curve/curve_index.rst

@@ -54,6 +54,7 @@ Curves
    catenary_curve
    bezier_fit
    circlify
+   intersect_curves
    intersect_curve_plane
    extremes
    interpolate_frame

docs/nodes/curve/intersect_curves.rst

@@ -0,0 +1,97 @@
+Intersect NURBS Curves
+======================
+
+Dependencies
+------------
+
+This node requires either SciPy_ library, or FreeCAD_ libraries to work.
+
+.. _SciPy: https://scipy.org/
+.. _FreeCAD: https://www.freecadweb.org/
+
+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:
+
+.. image:: https://user-images.githubusercontent.com/284644/123548323-c3281580-d77d-11eb-83fb-8216aad82d0f.png
+
+Find twelve intersections of two series of curves:
+
+.. image:: https://user-images.githubusercontent.com/284644/123548414-24e87f80-d77e-11eb-86aa-348b6c7c0322.png
+

docs/nodes/surface/gordon_surface.rst

@@ -0,0 +1,131 @@
+NURBS Surface from Curves Net
+=============================
+
+Functionaltiy
+-------------
+
+Given a net of intersecting curves, this node generates a surface which passes
+through all given curves.
+
+A net of curves is two sets of curves, one set along one direction and one set
+along another. One set of curves is called "U-curves" (curves along U
+direction) and another set of curves is called "V-curves" (curves along V
+direction).
+
+Apart of curves grid, this node requires intersection points of curves provided
+explictly. Intersection points can be calculated by use of "Intersect NURBS
+curves" node. Note: that node uses numeric algorithms to calculate
+intersections, so it can fail to find intersections, or give imprecise results.
+So, if you have intersection points in advance, it's better to use them.
+
+This node generates a NURBS surface from NURBS curves according to algorithm
+known as "Gordon Surface".
+
+"Gordon Surface" algorithm has a number of restrictions:
+
+* All input curves must be NURBS or NURBS-like. More specifically, only
+  non-rational curves are supported - i.e., without weights (or all weights
+  equal).
+* All U-curves must have "the same" direction; all V-curves must also have "the
+  same" direction.
+* There must be N curves along one direction, and M curves along another
+  direction, which must exactly intersect at `N x M` points.
+* Intersection points must be located evenly in parameter spaces of curves. For
+  example, V-Curve `C_v` must intersect all U-curves `C_u` at the same value of
+  U parameter. In other words, intersection points must be located so that
+  given curves would represent iso-curves of some surface, along U and V
+  directions correspondingly.
+* U-curves must be ordered along direction of V-curves, and vice versa. For
+  example, if U-curve `C_u1` intersects V-curve `C_v` at `v = v1`, and another
+  U-curve C_u2 intersects the same V-curve `C_v` at `v = v2`, and `v1 < v2`,
+  then in input curves list, `C_u1` must be provided before `C_u2`.
+
+If some of these requirements are not met exactly, then the resulting surface
+will pass through the curves only approximately.
+
+If intersections of your curves are located arbitrarily in parameter spaces of
+curves, the node can try to reparametrize curves in order to make intersections
+located "even" in parameter spaces. Note that reparametrization algorithm is
+somewhat rude, so it can produce unwanted additional control points, and/or
+create "bad" parametrization of resulting surface. In some cases, it is
+possible to get a better parametrization by manually removing excessive knots.
+
+To clear the issue of intersections location in parameter space, let's draw some pictures.
+
+Good parametrization: (first number is parameter of U-curve at the intersection
+point, the second number is parameter of V-curve at the intersection point):
+
+.. image:: https://user-images.githubusercontent.com/284644/123667069-394a7c00-d853-11eb-86dd-4b7b79bbb827.png
+
+Note that when you move from left to right, U value is changing by the same
+amount at all U-curves. And when you move from bottom to top, V-value is
+changing by the same amount at all V-curves.
+
+"Bad" parametrization:
+
+.. image:: https://user-images.githubusercontent.com/284644/123667108-44051100-d853-11eb-9f68-52529b2278d8.png
+
+Inputs
+------
+
+This node has the following inputs:
+
+* **CurvesU**. Set of curves along U direction. This input is mandatory. At
+  least two U-curves is required to build a proper surface.
+* **CurvesV**. Set of curves along V direction. This input is mandatory. At
+  least two V-curves is required to build a proper surface.
+* **T1**. This input is available and mandatory when **Explicit T values**
+  parameter is checked. For each U-curve, this input should contain a list of T
+  parameter values, at which this curve intersects V-curves.
+* **T2**. This input is available and mandatory when **Explicit T values**
+  parameter is checked. For each V-curve, this input should contain a list of T
+  parameter values, at which this curve intersects U-curves.
+* **Intersections**. Intersection points of curves. For each U-curve, this
+  input must contain a list of points (in 3D space), where this curve
+  intersects V-curves. This input is mandatory.
+
+Parameters
+----------
+
+This node has the following parameters:
+
+* **Explicit T values**. If checked, the node expects the user to provide T
+  parameter values of curve intersections in **T1** and **T2** inputs. In this
+  case, the node will try to automatically reparametrize input curves in order
+  to make intersection points located "evenly" in curve's parameter space (see
+  illustrations above). If not checked, the node will calculate T values of
+  intersections according to **Metric** parameter. Unchecked by default.
+* **Metric**. This node is available in the N panel only, and only when
+  **Explicit T values** parameter is not checked. This defines the metric,
+  which the node should use to calculate T values of curve intersections, when
+  they are not provided by user. The available options are:
+
+   * Manhattan
+   * Euclidian
+   * Points (just number of points from the beginning)
+   * Chebyshev
+   * Centripetal (square root of Euclidian distance).
+
+   The default option is Points. In most cases, this option gives the best results.
+* **Knotvector accuracy**. This parameter is available in the N panel only.
+  Number of decimal digits (after decimal point), to which the node should
+  round values in resulting surface's knot vectors. More decimal digits will
+  give more exact results, but can produce a number of knots / control points
+  located very close to each other, most of them being just an artefact of
+  floating-point precision issues. The default value is 4.
+
+Outputs
+-------
+
+This node has the following output:
+
+* **Surface**. The resulting NURBS surface.
+
+Examples of usage
+-----------------
+
+.. image:: https://user-images.githubusercontent.com/284644/123552408-71888680-d78f-11eb-92b7-904edc5a53bb.png
+
+.. image:: https://user-images.githubusercontent.com/284644/124376217-4e923100-dcbf-11eb-8a50-4c4f2e21442f.png
+
+There are some other examples at github's PR page: https://github.com/nortikin/sverchok/pull/4183

docs/nodes/surface/interpolate_nurbs_surface.rst

@@ -4,7 +4,7 @@ Interpolate NURBS Surface
 Dependencies
 ------------
 
-This node requires Geomdl_ library to work.
+This node can optionally use Geomdl_ library to work.
 
 .. _Geomdl: https://onurraufbingol.com/NURBS-Python/
 
@@ -45,8 +45,34 @@ Paramters
 
 This node has the following paramters:
 
-* **Centripetal**. This defines whether the node will use centripetal
-  interpolation method. Unchecked by default.
+* **Implementation**. This defines the implementation of NURBS mathematics to
+  be used. The available options are:
+
+  * **Geomdl**. Use Geomdl_ library. This option is available only when Geomdl
+    package is installed.
+  * **Sverchok**. Use built-in Sverchok implementation.
+
+  In general (with large nuber of control points), built-in implementation
+  should be faster; but Geomdl implementation is better tested.
+  The default option is **Geomdl**, when it is available; otherwise, built-in
+  implementation is used.
+
+* **Centripetal**. This parameter is only available when **Implementation**
+  parameter is set to **Geomdl**. Defines whether the node will use
+  centripetal interpolation method. Unchecked by default.
+* **Metric**. This parameter is available only when **Implementation**
+  parameter is set to **Sverchok**. This defines the metric used to calculate
+  surface's U, V parameter values corresponding to specified points. The
+  available values are:
+
+   * Manhattan
+   * Euclidian
+   * Points (just number of points from the beginning)
+   * Chebyshev
+   * Centripetal (square root of Euclidian distance).
+
+   The default value is Euclidian.
+
 * **Input mode**. The available values are:
 
    * **Single list**. The node expects a flat list of points for each surface.

docs/nodes/surface/surface_index.rst

@@ -37,6 +37,7 @@ Surface
    nurbs_loft
    nurbs_sweep
    nurbs_birail
+   gordon_surface
    intersect_curve_surface
    nearest_point
    ortho_project

index.md

@@ -102,6 +102,7 @@
     SvReparametrizeCurveNode
     SvExSurfaceBoundaryNode
     ---
+    SvIntersectNurbsCurvesNode
     SvExNearestPointOnCurveNode
     SvExOrthoProjectCurveNode
     SvExCurveEndpointsNode
@@ -132,6 +133,7 @@
     SvNurbsLoftNode
     SvNurbsSweepNode
     SvNurbsBirailNode
+    SvGordonSurfaceNode
     SvDeconstructSurfaceNode
     ---
     SvExQuadsToNurbsNode