The mathematical model defining the CHC implemented in the Trough_CHC plug-in is taken from the following article:

William L. Eichhorn,

*"Generalized conic concentrators"*, Appl. Opt. 21, 3887-3890 (1982). http://www.opticsinfobase.org/abstract.cfm?URI=ao-21-21-3887

The plug-in, when added in Tonatiuh as a child to a TShapeKit node, implements one side of a 2D Compound Hyperbolic Concentrator.

From Tonatiuh Blog Figures |

As indicated in the above figure, the geometry is defined by the following 5 parameters:

**r1**, the distance in the x-direction from the origin of the CHC implicit local coordinate system to the middle of the lower border, oriented in the z-direction and centered around the x-axis. In the negative x-direction,**r1**is also de distance in x-axis where the focus of the branch of the hyperbola represented by the plug-in is located (point F in the figure).**p1**, the distance in the x-direction from the origin of the CHC implicit local coordinate system to the middle of the the upper border, oriented in the z-direction and centered around the x-axis.**lengthX1**, the length of the lower border, oriented in the z-direction and centered around the x-axis.**lengthX2**, the length of the upper border,oriented in the z-direction and centered around the x-axis.**height**, the distance in the y-direction between the lower and the upper border.

**lengthX1**and

**lengthX2**appropiately, it is possible to combine several trough CHC plug-ins to represent a large variety of hyperbolic concentrators. As an example, the figure below shows an Hexagonal CHC constructed using six troguh CHC plug-ins.

From Tonatiuh Blog Figures |

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