Geodesic
Constructing the polar cone of a convex polyhedral cone in $\mathbb{R}^3$
Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, no. 4 (2014), pp. 56-63

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In the paper the problem of constructing the polar cone of an acute convex polyhedral cone is considered in three-dimensional Euclidean space. Using Householder transformation the considered cone is placed entirely in the upper half-space. Next on the plane $z=1$ the convex hull spanned by the points of intersection of the given ray of our cone with this plane is constructed. As a result of the sorting algorithm the vertices of the convex hull and the sequence of extreme rays of given cone are determined. After projecting the point $(0,0,1)$ lying the $z$-axis onto the corresponding face the extreme rays of the polar cone are found. Using the Householder transformation again the required cone is obtained. Bibliogr. 9.
Keywords: polyhedral cone, polar cone, convex hull, Householder's transformation. 
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     author = {I. Y. Molchanova and L. N. Polyakova and M. A. Popova},
     title = {Constructing the polar cone of a convex polyhedral cone in $\mathbb{R}^3$},
     journal = {Vestnik Sankt-Peterburgskogo universiteta. Prikladna\^a matematika, informatika, processy upravleni\^a},
     pages = {56--63},
     publisher = {mathdoc},
     number = {4},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VSPUI_2014_4_a5/}
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I. Y. Molchanova; L. N. Polyakova; M. A. Popova. Constructing the polar cone of a convex polyhedral cone in $\mathbb{R}^3$. Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, no. 4 (2014), pp. 56-63. http://geodesic.mathdoc.fr/item/VSPUI_2014_4_a5/