Steiner Ellipse¶
Functionality¶
This node can generate either Steiner inellipse (inscribed ellipse) or Steiner ellipse (circumellipse) for each triangular face of the input mesh. For non-tri faces, the node will either skip them or give an error, depending on a setting.
Main properties of the Steiner inellipse are:
It touches each side of the triangle in the midpoint of that side;
The center of the ellipse is the centroid (barycenter) of the triangle.
Main properties of the Steiner circumellipse are:
It touches the triangle in it’s vertices;
The center of the ellipse is the centroid (barycenter) of the triangle.
Inputs¶
This node has the following inputs:
Vertices. The vertices of the input mesh. This input is mandatory.
Faces. The faces of the input mesh. This input is mandatory.
Parameters¶
This node has the following parameters:
Mode. Defines which ellipses should be generated. The available modes are:
Inellipse. Generate Steiner inellipses (inscribed ellipses). This is the default mode.
Circumellipse. Generate Steiner circumellipses.
On non-tri faces. Defines what the node should do if it encounters a non-triangular face. There are following options available:
Skip. Just skip such faces - do not generate inscribed circles for them.
Error. Stop processing and give an error (turn the node red).
The default option is Skip. This parameter is available in the N panel only.
Outputs¶
This node has the following outputs:
Center. Centers of the ellipses.
F1, F2. Focal points of the ellipses.
SemiMajorAxis. Lengths of semi-major axes of the ellipses.
SemiMinorAxis. Lengths of semi-minor axes of the ellipses.
C. Distances from the center of ellipse to it’s focal points.
Eccentricity. Eccentricity values of the ellipses.
Normal. Normals of the planes where ellipses lie; i.e. face normals.
Matrix. For each ellipse, this contains a matrix, Z axis of which points along face normal, and the translation component equals to the center of the ellipse. This output can be used to actually place ellipses at their places.
See also¶
CAD-> Offset
Examples of usage¶
Generator->Generator Extended-> Polygon Grid
Generator->Generator Extended-> Ellipse
Transform-> Noise Displace
Matrix-> Matrix In
Viz-> Viewer Draw
Inscribed ellipses for Delaunay triangulation of some random points:
Generator-> Plane
Generator->Generator Extended-> Ellipse
Spatial-> Delaunay 2D
Matrix-> Matrix In
Viz-> Viewer Draw
Inscribed ellipses for triangulated Suzanne:
Generator-> Suzanne
Generator->Generator Extended-> Ellipse
Modifiers->Modifier Change-> Triangulate Mesh
Matrix-> Matrix In
Matrix-> Matrix In
Viz-> Viewer Draw
Circumellipse of some random triangle:
Generator-> Random Vector
Generator->Generator Extended-> Ellipse
Generator->Generators Extended-> Triangle
Vector-> Vector Rewire
List->List Main-> List Decompose
Viz-> Viewer Draw