smallest circumcircle and circumcenter

CMakeLists.txt

diff --git a/CMakeLists.txt b/CMakeLists.txt
index c8e8e13..c12ca18 100644
--- a/CMakeLists.txt
+++ b/CMakeLists.txt
@@ -1,6 +1,6 @@
 cmake_minimum_required(VERSION 3.0.0)
 project(delaunator VERSION 0.1.0)
-set (CMAKE_CXX_STANDARD 11)
+set (CMAKE_CXX_STANDARD 17)
 if (NOT EXISTS "${PROJECT_SOURCE_DIR}/includes")
     execute_process(COMMAND bash "-c" "(cd ${PROJECT_SOURCE_DIR} && ./fetch-includes.sh)")
 endif()

src/delaunator.cpp

diff --git a/src/delaunator.cpp b/src/delaunator.cpp
index e3d37fe..c05b127 100644
--- a/src/delaunator.cpp
+++ b/src/delaunator.cpp
@@ -2,6 +2,7 @@
 #include "delaunator.h"
 #include <cstdio>
 #include <limits>
+#include <tuple>
 
 using namespace std;
 
@@ -37,7 +38,45 @@
         const double x = (ey * bl - dy * cl) * 0.5 / d;
         const double y = (dx * cl - ex * bl) * 0.5 / d;
 
-        return (bl && cl && d && (x * x + y * y)) || max_double;
+        if (bl && cl && d) {
+            return x * x + y * y;
+        } else {
+            return max_double;
+        }
+    }
+
+    double area(
+        const double &px,
+        const double &py,
+        const double &qx,
+        const double &qy,
+        const double &rx,
+        const double &ry
+    ) {
+        return (qy - py) * (rx - qx) - (qx - px) * (ry - qy);
+    }
+
+    tuple<double, double> circumcenter(
+        const double &ax,
+        const double &ay,
+        const double &bx,
+        const double &by,
+        const double &cx,
+        const double &cy
+    ) {
+        const double dx = bx - ax;
+        const double dy = by - ay;
+        const double ex = cx - ax;
+        const double ey = cy - ay;
+
+        const double bl = dx * dx + dy * dy;
+        const double cl = ex * ex + ey * ey;
+        const double d = dx * ey - dy * ex;
+
+        const double x = ax + (ey * bl - dy * cl) * 0.5 / d;
+        const double y = ay + (dx * cl - ex * bl) * 0.5 / d;
+
+        return make_tuple(x, y);
     }
 }
 
@@ -87,5 +126,51 @@
             min_dist = d;
         }
     }
-    // printf("min_dist=%f i1=%lu", min_dist, i1);
+
+    double min_radius = max_double;
+
+    // find the third point which forms the smallest circumcircle with the first two
+    for (unsigned long int i = 0; i < n; i++)
+    {
+        if (i == i0 || i == i1) continue;
+
+        const double r = circumradius(
+            coords[2 * i0], coords[2 * i0 + 1],
+            coords[2 * i1], coords[2 * i1 + 1],
+            coords[2 * i], coords[2 * i + 1]);
+
+        if (r < min_radius)
+        {
+            i2 = i;
+            min_radius = r;
+        }
+    }
+
+    if (min_radius == max_double) {
+        throw No_triangulation();
+    }
+
+    if (
+        area(
+            coords[2 * i0], coords[2 * i0 + 1],
+            coords[2 * i1], coords[2 * i1 + 1],
+            coords[2 * i2], coords[2 * i2 + 1]
+        ) < 0
+    ) {
+        const double tmp = i1;
+        i1 = i2;
+        i2 = tmp;
+    }
+
+    const double i0x = coords[2 * i0];
+    const double i0y = coords[2 * i0 + 1];
+    const double i1x = coords[2 * i1];
+    const double i1y = coords[2 * i1 + 1];
+    const double i2x = coords[2 * i2];
+    const double i2y = coords[2 * i2 + 1];
+
+    tie(center_x, center_y) = circumcenter(i0x, i0y, i1x, i1y, i2x, i2y);
+    // [cx, cy) = center;
+
+    printf("i0x=%f i0y=%f", i0x, i0y);
 };

src/delaunator.h

diff --git a/src/delaunator.h b/src/delaunator.h
index 128f495..bb022bc 100644
--- a/src/delaunator.h
+++ b/src/delaunator.h
@@ -1,9 +1,18 @@
 #pragma once
 #include <vector>
+#include <exception>
 
 using namespace std;
 
 class Delaunator{
     public:
-    Delaunator(const vector<double> &coords);
+        Delaunator(const vector<double> &coords);
+        struct No_triangulation : public exception {
+            const char * what () const throw () {
+                return "No delaunay triangulation";
+            };
+        };
+    private:
+        double center_x;
+        double center_y;
 };