Minimal Surface

Dependencies

This node requires SciPy library to work.

Functionality

This node generates a Surface, based on provided points, by use of RBF method. Depending on node parameters, the curve can be either interpolating (go through all points) or only approximating.

The generated surface is not, strictly speaking, guaranteed to be minimal; but in many simple cases it is close enough to the minimal.

This node, in general, searches for a surface as a mapping from (U, V) coordinates to (X, Y, Z). In many simple cases, you will want to provide just a list of points, and tell the node to use their X and Y coordinates as U and V. So, the node will actually only have to find a function which maps (X, Y) to Z. In other cases, you will want to provide a set of (X, Y, Z) points and a set of corresponding (U, V) coordinate pairs.

Inputs

This node has the following inputs:

• Vertices. The points to build minimal surface for. This input is mandatory.

• Epsilon. Epsilon parameter of used RBF function; it affects the shape of generated surface. The default value is 1.0.

  

• Smooth. Smoothness parameter of used RBF function. If this is zero, then the surface will go through all provided points; otherwise, it will be only an approximating surface. The default value is 0.0.

  

• SrcU, SrcV. U and V coordinates for the points specified in the Vertices input. These inputs are available and mandatory if the Surface type is set to UV -> XYZ, and Explicit source UV parameter is checked.

  

  • Generator-> Plane

  • Vector-> Vector Noise

  • A*SCALAR: Number-> Scalar Math

  • Add: Vector-> Vector Math

  • Vector-> Vector Out

  • Matrix-> Matrix In

  • Viz-> Viewer Draw

  • Surfaces-> Evaluate Surface

    SrcU, SrcV: XY->Z

    

    SrcU, SrcV: YZ->X

    

    SrcU, SrcV: ZX->Y

    

    SrcU, SrcV: PHI,Z->XYZ

    

    • Generator-> Cylinder

    • Vector-> Vector Polar Input

    • Vector-> Vector Polar Output

    • Vector-> Vector Noise

    • A*SCALAR, ADD: Vector-> Vector Math

    • Matrix-> Matrix In

    • Viz-> Viewer Draw

    • Surfaces-> Evaluate Surface

    

• Matrix. Matrix used to extract U and V coordinates out of XYZ points. This input is available only if the Surface type is set to XY -> Z. The default is identity matrix.

  

  • Generator-> Plane

  • Vector-> Vector Noise

  • A*SCALAR, ADD: Vector-> Vector Math

  • Matrix-> Matrix In

  • Viz-> Viewer Draw

  • Surfaces-> Evaluate Surface

  

  Align surface with object:

  

  • Generator-> Plane

  • Vector-> Vector Noise

  • A*SCALAR, ADD: Vector-> Vector Math

  • Matrix-> Matrix In

  • Viz-> Viewer Draw

  • Surfaces-> Evaluate Surface

  

Parameters

This node has the following parameters:

• Surface type. This defines which type of function the node will try to find. The available values are:

  • XY -> Z. The node will search for a function, mapping (X, Y) coordinates to Z (or (X, Z) to Y, or (Y, Z) to X,depending on Orientation parameter). So, in this mode the node can generate only surfaces which have a single Z value for each pair of X and Y. X, Y, Z coordinates can be rotated according to the Matrix input.

  • UV -> XYZ. The node will search for a function, mapping arbitrary (U, V) coordinates to (X, Y, Z). This mode is more general, but requires to pass U and V coordinate for each point somehow.

  The default option is XY -> Z.

• Orientation. This parameter is available only if Surface type parameter is set to XY -> Z. This defines which axis will be used as “function value”. Other two axes will be used as U and V parameters. The available values are X, Y and Z. The default option is Z.

• Explicit source UV. This parameter is available only if Surface type parameter is set to UV -> XYZ. This defines whether you want to define U and V parameters for each point in the Vertices input explicitly. If checked, then U and V parameters are expected in SrcU, SrcV inputs. Otherwise, the Vertices input will expect a list of lists of points for each surface, and the node will try to guess U and V coordinates automatically. Checked by default.

• Function. The specific function used by the node. The available values are:

  • Multi Quadric

  • Inverse

  • Gaussian

  • Cubic

  • Quintic

  • Thin Plate

  The default function is Multi Quadric. Scipy RBF Functions

  

Outputs

This node has the following output:

• Surface. The generated Surface object.

Examples of usage

Simple example of XY -> Z mode usage:

• Generator-> NGon

• Surfaces-> Evaluate Surface

• Transform-> Randomize

• Viz-> Viewer Draw

An example of Matrix input usage; rotated and deformed plane is used as input:

• Surfaces-> Evaluate Surface

• Matrix-> Matrix Normal

• Analyzers-> Linear Approximation

• Viz-> Viewer Draw

• Scene-> Objects In Lite

An example where UV -> XYZ mode is required to build a proper surface:

• Generator-> Cylinder

• Surfaces-> Evaluate Surface

• Transform-> Randomize

• Vector-> Vector Polar Output

• Viz-> Viewer Draw