[geometry] Add function to calculate circumsphere of trinangle

dumux/geometry/circumsphere.hh

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+/*!
+ * \file
+ * \ingroup Geometry
+ * \brief A function to compute the circumsphere of a given geometry
+ * \note The circumscribed sphere (or circumsphere) is a sphere touching all vertices of the geometry
+ *       Therefore it does not necessarily exist for all geometries.
+ */
+#ifndef DUMUX_GEOMETRY_CIRCUMSPHERE_HH
+#define DUMUX_GEOMETRY_CIRCUMSPHERE_HH
+
+#include <type_traits>
+#include <dumux/common/math.hh>
+#include <dumux/geometry/sphere.hh>
+
+namespace Dumux {
+
+/*!
+ * \ingroup Geometry
+ * \brief Computes the circumsphere of a triangle
+ * \note See https://www.ics.uci.edu/~eppstein/junkyard/circumcenter.html
+ */
+template<class Point>
+static inline Sphere<typename Point::value_type, Point::dimension>
+circumSphereOfTriangle(const Point& a, const Point& b, const Point& c)
+{
+    const auto ac = c - a;
+    const auto ab = b - a;
+    const auto n = crossProduct(ab, ac);
+    const auto distCenterToA = (crossProduct(n, ab)*ac.two_norm2() + crossProduct(ac, n)*ab.two_norm2()) / (2.0*n.two_norm2());
+
+    return { a + distCenterToA, distCenterToA.two_norm() };
+}
+
+/*!
+ * \ingroup Geometry
+ * \brief Computes the circumsphere of a triangle
+ */
+template<class Geometry, typename std::enable_if_t<Geometry::mydimension == 2, int> = 0>
+static inline Sphere<typename Geometry::ctype, Geometry::coorddimension>
+circumSphereOfTriangle(const Geometry& triangle)
+{
+    assert(triangle.corners() == 3 && "Geometry is not a triangle.");
+    return circumSphereOfTriangle(triangle.corner(0), triangle.corner(1), triangle.corner(2));
+}
+
+} // end namespace Dumux
+
+#endif