Trisected Perimeter Point

A triangle center which has a Triangle Center Function

$$\alpha=bc(v-c+a)(v-a+b),$$

where $v$ is the unique Real Root of

$2x^3-3(a+b+c)x^2+(a^2+b^2+c^2+8bc+8ca+8ab)x$
$-(b^2c+c^2a+a^2b+5bc^2+5ca^2+5ab^2+9abc)=0.$

References

Kimberling, C. ``Central Points and Central Lines in the Plane of a Triangle.'' Math. Mag. 67, 163-187, 1994.