Surface Gauss Curvature¶

https://github.com/nortikin/sverchok/assets/14288520/d52917f6-b86e-46ae-9a3c-8b2ac8b4e727

Functionality¶

This node calculates the Gaussian curvature (see Wikipedia article) at the specified point of the surface.

Here are the main facts about Gaussian curvature that are usually useful:

For points where the surface is shaped like sphere, Gaussian curvature is positive;
For “saddle points” of the surface, Gaussian curvature is negative;
If the surface is “flat” at the given point in one or two directions, then Gaussian curvature is zero;
The more “bent” the surface is at the given point is, the bigger the absolute value of Gaussian curvature will be.

Note that the calculation is done by numerical differentiation, so it may be not very precise in some cases.

This node is a simpler version of the “Surface Curvatures” node.

Inputs¶

This node has the following inputs:

Surface. The surface to analyze. This input is mandatory.
U, V. Values of U and V surface parameters. These inputs are available only when Input mode parameter isset to Separate. The default value is 0.5.
UVPoints. Points at which the surface is to be analyzed. Only two of three coordinates will be used; the coordinates used are defined by the Orientation parameter. This input is available and mandatory if the Input mode parameter is set to Vertices.

Parameters¶

This node has the following parameters:

Input mode. The available options are:
- Separate. The values of U and V surface parameters will be provided in U and V inputs, correspondingly.
- Vertices. The values of U and V surface parameters will be provided in Vertices input; only two of three coordinates of the input vertices will be used.
The default mode is Separate.
Input orientation. This parameter is available only when Input mode parameter is set to Vertices. This defines which coordinates of vertices provided in the Vertices input will be used. The available options are XY, YZ and XZ. For example, if this is set to XY, then the X coordinate of vertices will be used as surface U parameter, and Y coordinate will be used as V parameter. The default value is XY.
Clamp. This defines how the node will process the values of surface U and V parameters which are out of the surface’s domain. The available options are:
- As is. Do not do anything special, just pass the parameters to the surface calculation algorithm as they are. The behaviour of the surface when the values of parameters provided are out of domain depends on specific surface: some will just calculate points by the same formula, others will give an error.
- Clamp. Restrict the parameter values to the surface domain: replace values that are greater than the higher bound with higher bound value, replace values that are smaller than the lower bound with the lower bound value. For example, if the surface domain along U direction is [0 .. 1], and the value of U parameter is 1.05, calculate the point of the surface at U = 1.0.
- Wrap. Wrap the parameter values to be within the surface domain, i.e. take the values modulo domain. For example, if the surface domain along U direction is [0 .. 1], and the value of U parameter is 1.05, evaluate the surface at U = 0.05.
The default mode is As is.