diff --git a/src/csg/cgal_helper_polygon.cpp b/src/csg/cgal_helper_polygon.cpp
index 36a214308c1bb61e6cef7f71047a7a9d4c709598..7a24cfd68d9c2705f60a4ee8ec73c7c1339ed0d5 100644
--- a/src/csg/cgal_helper_polygon.cpp
+++ b/src/csg/cgal_helper_polygon.cpp
@@ -1,7 +1,10 @@
 #include "csg_cgal_helper.hpp"
 
+#include <limits>
+
 namespace {
 typedef CGAL::Point_2<cgal_helper::CK> Point;
+typedef cgal_helper::CK::Segment_2 Segment;
 } // namespace
 
 namespace cgal_helper {
@@ -31,4 +34,19 @@ bool inside(const Polygon &polygon, double xx, double yy) {
   return polygon.has_on_bounded_side(Point(xx, yy));
 }
 
+double abs_max_distance(const Polygon &polygon, double xx, double yy,
+                        bool inside) {
+  double dist = -std::numeric_limits<double>::max();
+  auto m = Point(xx, yy);
+
+  double sign = inside ? -1.0 : 1.0;
+
+  for (auto e = polygon.edges_begin(); e != polygon.edges_end(); ++e) {
+    auto d = sign * CGAL::squared_distance(*e, m);
+    dist = std::max(dist, d);
+  }
+
+  return std::fabs(dist);
+}
+
 } // namespace cgal_helper
diff --git a/src/csg/levelset_2d.cpp b/src/csg/levelset_2d.cpp
index b8e0993d7fdd5c9e47e00b9adb943c16553ec1eb..cdfb92caaaad879615cf57a5cc7363b0205f7951 100644
--- a/src/csg/levelset_2d.cpp
+++ b/src/csg/levelset_2d.cpp
@@ -89,8 +89,12 @@ double signed_distance_2d(const Circle &cir, double xx, double yy) {
 
 double signed_distance_2d(const Polygon &polygon, double xx, double yy) {
 
-  // TODO: support signed distance instead of -1.0/1.0
-  return cgal_helper::inside(polygon.cgal_polygon(), xx, yy) ? 1.0 : -1.0;
+  bool inside = cgal_helper::inside(polygon.cgal_polygon(), xx, yy);
+  double sign = inside ? -1.0 : 1.0;
+  double dist =
+      cgal_helper::abs_max_distance(polygon.cgal_polygon(), xx, yy, inside);
+
+  return EXTERNAL_FLOW * sign * dist;
 }
 
 double signed_distance_2d(const Type2D &obj, double xx, double yy) {
diff --git a/src/csg/tests/levelset/extrude.t.cpp b/src/csg/tests/levelset/extrude.t.cpp
index d3574a75448dc11618f3d2a6d6b0170585b17658..e8d7e1b1d05e3e414501bdd85e9d1c38aaa1fc12 100644
--- a/src/csg/tests/levelset/extrude.t.cpp
+++ b/src/csg/tests/levelset/extrude.t.cpp
@@ -10,7 +10,7 @@ TEST_CASE("linear", "[Levelset Extrude]") {
   double height = 100, radius = 10;
   auto my_lin_ext = csg::LinearExtrude{
       .height = 100, .center = false, .scale = {1, 1}, .group = csg::Union2D()};
-  csg::Circle my_cir{.name = std::nullopt, .radius = 10};
+  csg::Circle my_cir{.name = std::nullopt, .radius = radius};
 
   SECTION("Not centered") {
     my_lin_ext.center = false;
@@ -21,15 +21,37 @@ TEST_CASE("linear", "[Levelset Extrude]") {
 
     SECTION("Outside") {
       CHECK_FALSE(0 < my_levelset(0, radius * 0.99, -0.01 * height));
+      CHECK(Approx(-0.01 * height) ==
+            my_levelset(0, radius * 0.99, -0.01 * height));
+
       CHECK_FALSE(0 < my_levelset(0, radius * 1.01, 0.01 * height));
+      CHECK(Approx((radius) * (radius) - (1.01 * radius) * (1.01 * radius)) ==
+            my_levelset(0, radius * 1.01, 0.01 * height));
+
       CHECK_FALSE(0 < my_levelset(0, radius * 0.99, 1.01 * height));
+      CHECK(Approx(-0.01 * height) ==
+            my_levelset(0, radius * 0.99, 1.01 * height));
+
       CHECK_FALSE(0 < my_levelset(radius * 0.99, 0, 1.01 * height));
+      CHECK(Approx(-0.01 * height) ==
+            my_levelset(radius * 0.99, 0, 1.01 * height));
     }
     SECTION("Inside") {
       CHECK(0 < my_levelset(0, radius * 0.99, 0.01 * height));
+      CHECK(Approx(0.01 * height) ==
+            my_levelset(0, radius * 0.99, 0.01 * height));
+
       CHECK(0 < my_levelset(radius * 0.99, 0, 0.01 * height));
-      CHECK(0 < my_levelset(0, radius * 0.99, 0.99 * height));
-      CHECK(0 < my_levelset(radius * 0.99, 0, 0.99 * height));
+      CHECK(Approx(0.01 * height) ==
+            my_levelset(radius * 0.99, 0, 0.01 * height));
+
+      CHECK(0 < my_levelset(0, radius * 0.99, 0.9 * height));
+      CHECK(Approx((radius) * (radius) - (0.99 * radius) * (0.99 * radius)) ==
+            my_levelset(0, radius * 0.99, 0.9 * height));
+
+      CHECK(0 < my_levelset(radius * 0.99, 0, 0.9 * height));
+      CHECK(Approx((radius) * (radius) - (0.99 * radius) * (0.99 * radius)) ==
+            my_levelset(radius * 0.99, 0, 0.9 * height));
     }
   }
 
@@ -42,15 +64,37 @@ TEST_CASE("linear", "[Levelset Extrude]") {
 
     SECTION("Outside") {
       CHECK_FALSE(0 < my_levelset(0, radius * 0.99, -1.01 * height / 2));
+      CHECK(Approx(-0.01 * height / 2) ==
+            my_levelset(0, radius * 0.99, -1.01 * height / 2));
+
       CHECK_FALSE(0 < my_levelset(0, radius * 1.01, 0.01 * height));
+      CHECK(Approx((radius) * (radius) - (1.01 * radius) * (1.01 * radius)) ==
+            my_levelset(0, radius * 1.01, 0.01 * height));
+
       CHECK_FALSE(0 < my_levelset(0, radius * 0.99, 1.01 * height / 2));
+      CHECK(Approx(-0.01 * height / 2) ==
+            my_levelset(0, radius * 0.99, 1.01 * height / 2));
+
       CHECK_FALSE(0 < my_levelset(radius * 0.99, 0, 1.01 * height / 2));
+      CHECK(Approx(-0.01 * height / 2) ==
+            my_levelset(radius * 0.99, 0, 1.01 * height / 2));
     }
     SECTION("Inside") {
       CHECK(0 < my_levelset(0, radius * 0.99, -0.99 * height / 2));
+      CHECK(Approx(0.01 * height / 2) ==
+            my_levelset(0, radius * 0.99, -0.99 * height / 2));
+
       CHECK(0 < my_levelset(radius * 0.99, 0, 0.01 * height / 2));
+      CHECK(Approx((radius) * (radius) - (0.99 * radius) * (0.99 * radius)) ==
+            my_levelset(radius * 0.99, 0, 0.01 * height / 2));
+
       CHECK(0 < my_levelset(0, radius * 0.99, 0.99 * height / 2));
-      CHECK(0 < my_levelset(radius * 0.99, 0, 0.99 * height / 2));
+      CHECK(Approx(0.01 * height / 2) ==
+            my_levelset(0, radius * 0.99, 0.99 * height / 2));
+
+      CHECK(0 < my_levelset(radius * 0.99, 0, 0.9 * height / 2));
+      CHECK(Approx((radius) * (radius) - (0.99 * radius) * (0.99 * radius)) ==
+            my_levelset(radius * 0.99, 0, 0.9 * height / 2));
     }
   }
 }
@@ -157,19 +201,47 @@ TEST_CASE("Linear extrude of a triangle with hole", "[Levelset Primitives]") {
 
   SECTION("Outside") {
     CHECK_FALSE(0 < my_levelset(0.5 * thick, 0.5 * thick, 1.01 * (ht / 2)));
+    CHECK(Approx(-0.01 * ht / 2) ==
+          my_levelset(0.5 * thick, 0.5 * thick, 1.01 * (ht / 2)));
+
     CHECK_FALSE(0 < my_levelset(0.5 * thick, 0.5 * thick, -1.01 * (ht / 2)));
-    CHECK_FALSE(0 < my_levelset(2 * thick, 2 * thick, 0.0));
-    CHECK_FALSE(0 < my_levelset(4 * thick, 2 * thick, 0.0));
+    CHECK(Approx(-0.01 * ht / 2) ==
+          my_levelset(0.5 * thick, 0.5 * thick, -1.01 * (ht / 2)));
+
+    CHECK_FALSE(0 < my_levelset(1.5 * thick, 1.5 * thick, 0.0));
+    CHECK(Approx(-(0.5 * thick) * (0.5 * thick)) ==
+          my_levelset(1.5 * thick, 1.5 * thick, 0.0));
+
     CHECK_FALSE(0 < my_levelset(1.01 * outer, 0.5 * thick, 0.0));
+    CHECK(Approx(-(1.01 * outer) * (1.01 * outer)) ==
+          my_levelset(1.01 * outer, 0.5 * thick, 0.0));
+
     CHECK_FALSE(0 < my_levelset(0.5 * thick, 1.01 * outer, 0.0));
+    CHECK(Approx(-(1.01 * outer) * (1.01 * outer)) ==
+          my_levelset(0.5 * thick, 1.01 * outer, 0.0));
+
     CHECK_FALSE(0 < my_levelset(inner, inner, 0.0));
+    CHECK(Approx(-inner * inner) == my_levelset(inner, inner, 0.0));
   }
   SECTION("Inside") {
     CHECK(0 < my_levelset(0.5 * thick, 0.5 * thick, 0.99 * (ht / 2)));
+    CHECK(Approx(0.01 * ht / 2) ==
+          my_levelset(0.5 * thick, 0.5 * thick, 0.99 * (ht / 2)));
+
     CHECK(0 < my_levelset(0.5 * thick, 0.5 * thick, -0.99 * (ht / 2)));
-    CHECK(0 < my_levelset(0.5 * thick, 0.5 * thick, 0.0));
-    CHECK(0 < my_levelset(0.7 * outer, 0.5 * thick, 0.0));
+    CHECK(Approx(0.01 * ht / 2) ==
+          my_levelset(0.5 * thick, 0.5 * thick, -0.99 * (ht / 2)));
+
+    CHECK(0 < my_levelset(0.1 * thick, 0.5 * thick, 0.0));
+    CHECK(Approx((0.1 * thick) * (0.1 * thick)) ==
+          my_levelset(0.1 * thick, 0.5 * thick, 0.0));
+
+    CHECK(0 < my_levelset(0.7 * outer, 0.1 * thick, 0.0));
+    CHECK(Approx((0.1 * thick) * (0.1 * thick)) ==
+          my_levelset(0.7 * outer, 0.1 * thick, 0.0));
+
     CHECK(0 < my_levelset(0.5 * thick, 0.7 * outer, 0.0));
+    CHECK(Approx(ht / 2) == my_levelset(0.5 * thick, 0.7 * outer, 0.0));
   }
 }
 
diff --git a/src/csg/tests/levelset/transform.t.cpp b/src/csg/tests/levelset/transform.t.cpp
index 99bf3ef1cf19b2be9b253a969086738b9bf5c2cb..8e48f5c2a34d7d4e07cd96f5983e043e0abd6247 100644
--- a/src/csg/tests/levelset/transform.t.cpp
+++ b/src/csg/tests/levelset/transform.t.cpp
@@ -3,8 +3,8 @@
 #include "catch2/catch.hpp"
 
 #include <csg.hpp>
-#include <csg_types.hpp>
 #include <csg_matrix_functions.hpp>
+#include <csg_types.hpp>
 
 namespace {
 
diff --git a/src/csg_cgal_helper.hpp b/src/csg_cgal_helper.hpp
index f4cc6883e3632696a0880956da95ed7c1352a38f..3eb6463a5f8c206349cba8be9371c4b65d49c31b 100644
--- a/src/csg_cgal_helper.hpp
+++ b/src/csg_cgal_helper.hpp
@@ -23,6 +23,9 @@ bool inside(const Polyhedron &polyhedron, double xx, double yy, double zz);
 
 bool inside(const Polygon &polygon, double xx, double yy);
 
+double abs_max_distance(const Polygon &ploygon, double xx, double yy,
+                        bool inside);
+
 } // namespace cgal_helper
 
 #endif
diff --git a/src/inputs/tests/solver.t.cpp b/src/inputs/tests/solver.t.cpp
index 580175235de25288e89016897517a2c8f5be2b9a..8797121abf9ff07e873266c2af857990eaaa999b 100644
--- a/src/inputs/tests/solver.t.cpp
+++ b/src/inputs/tests/solver.t.cpp
@@ -1,7 +1,7 @@
 #include "catch2/catch.hpp"
 
-#include <solver_inputs.hpp>
 #include <solver_impl.hpp>
+#include <solver_inputs.hpp>
 
 TEST_CASE("GeometrySettings", "[]") {
   solver::InputInfo ii;