Коммит e41b4c2a создал по автору Ilya Portnov's avatar Ilya Portnov
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Update documentation.

владелец a5dc101f
...@@ -96,6 +96,16 @@ for reference. ...@@ -96,6 +96,16 @@ for reference.
in which distance between neighbour knots is different in different places. in which distance between neighbour knots is different in different places.
For example, ``0 0 0.5 0.6 1.5 1.7 1.9 2 2 2`` is a non-uniform (and clamped) For example, ``0 0 0.5 0.6 1.5 1.7 1.9 2 2 2`` is a non-uniform (and clamped)
knot vector. knot vector.
* **Node values**, **Node points**. Also known as Greville abscissaes and
Greville points, average knot values, or simply edit points. The values of
NURBS curve's T parameter, defined as: ``t[i] = sum(u[i+j] for j from 1 to p)
/ p``, where ``u`` is curve's knotvector, and ``p`` is curve's degree. NURBS
curve *node points* (or Greville points) are points at the curve at parameter
values equal to node values. The number of curve's nodes is equal to the
number of curve's control points. Node points of the curve are positioned on
the curve near corresponding control points. So in many NURBS algorithms,
node points are used to define the shape of NURBS curve, instead of control
points.
.. _Book: https://www.springer.com/gp/book/9783642973857 .. _Book: https://www.springer.com/gp/book/9783642973857
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...@@ -5,7 +5,7 @@ Functionality ...@@ -5,7 +5,7 @@ Functionality
------------- -------------
This node calculates so-called *node* points (also known as Greville points or This node calculates so-called *node* points (also known as Greville points or
average knot points) of the NURBS curve. average knot points, or simply edit points) of the NURBS curve.
NURBS curve *nodes* (or Greville abscissaes) are defined as: NURBS curve *nodes* (or Greville abscissaes) are defined as:
``t[i] = sum(u[i+j] for j from 1 to p) / p``, where ``u`` is curve's knotvector, and ``t[i] = sum(u[i+j] for j from 1 to p) / p``, where ``u`` is curve's knotvector, and
``p`` is curve's degree. ``p`` is curve's degree.
...@@ -34,3 +34,7 @@ This node has the following outputs: ...@@ -34,3 +34,7 @@ This node has the following outputs:
Example of Usage Example of Usage
---------------- ----------------
Orange is curve's control polygon; dark blue are curve's node points (Greville points):
.. image:: https://user-images.githubusercontent.com/284644/186223165-72a48126-b290-4eb9-a3cc-262fd23bf426.png
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