This is a confusing concept, as acknowledged in the paper you cite, "On the definition and computation of rectilinear convex hulls" (Elsevier link).

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          [![WikiImage][1]][1]
          ^{(Image from [Wikipedia](https://en.wikipedia.org/wiki/Orthogonal_convex_hull).)}

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It may help to look at this more modern paper:

Alegría-Galicia, Carlos, Tzolkin Garduño, Areli Rosas-Navarrete, Carlos Seara, and Jorge Urrutia. "Rectilinear convex hull with minimum area." In Computational Geometry, pp. 226-235. Springer Berlin Heidelberg, 2012. (PDF download.)

This is a confusing concept, as acknowledged in the paper you cite, "On the definition and computation of rectilinear convex hulls" (Elsevier link).

---

          [![WikiImage][1]][1]
          ^{(Image from [Wikipedia](https://en.wikipedia.org/wiki/Orthogonal_convex_hull).)}

---

It may help to look at this more modern paper:

Alegría-Galicia, Carlos, Tzolkin Garduño, Areli Rosas-Navarrete, Carlos Seara, and Jorge Urrutia. "Rectilinear convex hull with minimum area." In Computational Geometry, pp. 226-235. Springer Berlin Heidelberg, 2012. (PDF download.)

Excerpt from A-G et al.:

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  [![OrthoHull][2]][2]

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This is a confusing concept, as acknowledged in the paper, "On the definition and computation of rectilinear convex hulls" (Elsevier link).

---

          [![WikiImage][1]][1]
          ^{(Image from [Wikipedia](https://en.wikipedia.org/wiki/Orthogonal_convex_hull).)}

---

It may help to look at this more modern paper:

Alegría-Galicia, Carlos, Tzolkin Garduño, Areli Rosas-Navarrete, Carlos Seara, and Jorge Urrutia. "Rectilinear convex hull with minimum area." In Computational Geometry, pp. 226-235. Springer Berlin Heidelberg, 2012. (PDF download.)

This is a confusing concept, as acknowledged in the paper you cite, "On the definition and computation of rectilinear convex hulls" (Elsevier link).

---

          [![WikiImage][1]][1]
          ^{(Image from [Wikipedia](https://en.wikipedia.org/wiki/Orthogonal_convex_hull).)}

---

It may help to look at this more modern paper:

Alegría-Galicia, Carlos, Tzolkin Garduño, Areli Rosas-Navarrete, Carlos Seara, and Jorge Urrutia. "Rectilinear convex hull with minimum area." In Computational Geometry, pp. 226-235. Springer Berlin Heidelberg, 2012. (PDF download.)