Surface Frame

https://github.com/nortikin/sverchok/assets/14288520/3e76ce84-cbb1-440d-b416-9b5dfc5ddd68

Functionality

This node outputs information about normals and tangents of the surface at given points, together with a matrix giving reference frame according to surface normals.

https://github.com/nortikin/sverchok/assets/14288520/588ffb4c-9caf-45a4-9e17-3afd4910e1c2

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.

    https://github.com/nortikin/sverchok/assets/14288520/b533e68e-dee5-4fe5-a1d0-3d60c971e3fc

  • 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.

Outputs

This node has the following outputs:

  • Normal. Unit normal vectors of the surface at the specified points.

    https://github.com/nortikin/sverchok/assets/14288520/817ea4da-bbfa-442f-a8c0-e1a9334b7355

  • TangentU. Unit tangent vectors of the surface at the specified points along the U direction; more precisely, if the surface is defined by P = F(u, v), then this is dF/du vector divided by it’s length.

  • TangentV. Unit tangent vectors of the surface at the specified points along the V direction; more precisely, if the surface is defined by P = F(u, v), then this is dF/dv vector divided by it’s length.

  • AreaStretch. Coefficient of the stretching of the surface area in the mapping of areas in the UV space to 3D space, in the provided points. This equals to |dF/du| * |dF/dv| (norm of derivative by U multiplied by norm of derivative by V). So, AreaStretch is always equal to product of StretchU by StretchV.

  • StretchU. Coefficient of stretching the surface along the U direction; this equals to |dF/du|.

  • StretchV. Coefficient of stretching the surface along the V direction; this equals to |dF/dv|.

    https://github.com/nortikin/sverchok/assets/14288520/abfa65dc-40c6-417c-be56-19982032ff72

  • Matrix. Reference frame at the surface point, defined by the surface’s normal and parametric tangents: it’s Z axis is looking along surface normal; it’s X axis is looking along TangentU, and it’s Y axis is looking along TangentV.

  • Matrix-> Matrix In

  • Matrix Multiply: Matrix-> Matrix Math

  • Viz-> Viewer Draw

Examples of Usage

Visualize Matrix outputfor some formula-defined surface:

https://github.com/nortikin/sverchok/assets/14288520/25a59ce8-5a83-44cc-adf9-8707589ede3d https://github.com/nortikin/sverchok/assets/14288520/8f2a3747-e78c-459a-91d4-e0527ecf621f

Use that matrices to place cubes, oriented accordingly:

https://github.com/nortikin/sverchok/assets/14288520/9aa259ed-b40d-4aff-8ff0-4aabadaa616d https://github.com/nortikin/sverchok/assets/14288520/4b61b97f-ee5a-4268-940f-c082d6953588

As you can see, the surface in areas that are far from the center, so that cubes are put sparsely. Let’s use StretchU and StretchV outputs to scale them:

https://user-images.githubusercontent.com/284644/81722582-03a1d280-949b-11ea-8e99-9d9354f5e906.png