Linear Approximation

Functionality

This node tries to approximate provided set of vertices by either a plane or a straight line. In other words, it searches for such a plane / line, that all provided vertices have the minimum distance to it.

More technically, it searches for a plane or a line A, such that

The plane is represented by a point on the plane and a normal vector.

The line is represented by a point on the line and a direction vector.

That point on line or plane is calculated as a geometrical center of all provided vertices.

Inputs

This node has one input: Vertices - the vertices to be approximated.

Parameters

This node has one parameter - Mode. Two modes are supported:

• Line - approximate vertices by straight line. This is the default mode.

• Plane - approximate vertices by a plane.

Outputs

This node has the following outputs:

• Center - the point on the line or plane. This is geometrical center of all input vertices.

• Normal - the normal vector of a plane. This output is only available in the Plane mode.

• Direction - the direction vector of a line. This output is only available in the Line mode.

• Projections - the projections of input vertices to the line or plane.

• Diffs - difference vectors between the input vertices and their projections to line or plane.

• Distances - distances between the input vertices and their projections to line or plane.

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Examples of usage

The simplest example: approximate 3D curve by a line. Here black curve is a grease pencil, green one - it’s representation in Sverchok, red line - result of linear approximation of green line.

• Generator-> Line

• Number-> Number Range

• Vector-> Vector Interpolation

• Modifiers->Modifier Make-> UV Connection

• Viz-> Viewer Draw

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A simple example with plane.

• Generator-> Plane

• Scene-> Objects In Lite

• Matrix-> Matrix Track To

• Viz-> Viewer Draw

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The node can calculate approximation for several sets of vertices at once:

• Generator-> Plane

• Matrix-> Matrix Track To

• Scene-> Objects In Lite

• Viz-> Viewer Draw

You can also find more examples and some discussion in the development thread.