diff --git a/common/mathlib.cc b/common/mathlib.cc
index 94cd7c57..5f53e10a 100644
--- a/common/mathlib.cc
+++ b/common/mathlib.cc
@@ -23,6 +23,7 @@
 #include <assert.h>
 
 #include <tuple>
+#include <map>
 
 #include <glm/glm.hpp>
 #include <glm/ext.hpp>
@@ -654,3 +655,80 @@ float FractionOfLine(const glm::vec3 &v, const glm::vec3 &w, const glm::vec3& p)
     const float t = glm::dot(vp, vw) / l2;
     return t;
 }
+
+// mesh_t
+
+mesh_t buildMesh(const vector<vector<glm::vec3>> &faces)
+{
+    // FIXME: this is ugly
+    using pos_t = tuple<float, float, float>;
+    
+    int nextVert = 0;
+    map<pos_t, int> posToVertIndex;
+    
+    vector<vector<int>> facesWithIndices;
+    for (const auto &face : faces) {
+        vector<int> vertIndices;
+        
+        for (const auto &vert : face) {
+            const pos_t pos = make_tuple(vert[0], vert[1], vert[2]);
+            const auto it = posToVertIndex.find(pos);
+            
+            if (it == posToVertIndex.end()) {
+                posToVertIndex[pos] = nextVert;
+                vertIndices.push_back(nextVert);
+                nextVert++;
+            } else {
+                int vertIndex = it->second;
+                vertIndices.push_back(vertIndex);
+            }
+        }
+        
+        facesWithIndices.push_back(vertIndices);
+    }
+    
+    // convert posToVertIndex to a vector
+    vector<glm::vec3> vertsVec;
+    vertsVec.resize(posToVertIndex.size());
+    for (const auto &posIndex : posToVertIndex) {
+        const pos_t &pos = posIndex.first;
+        vertsVec.at(posIndex.second) = glm::vec3(std::get<0>(pos), std::get<1>(pos), std::get<2>(pos));
+    }
+    
+    mesh_t res;
+    res.verts = vertsVec;
+    res.faces = facesWithIndices;
+    return res;
+}
+
+std::vector<std::vector<glm::vec3>> meshToFaces(const mesh_t &mesh)
+{
+    std::vector<std::vector<glm::vec3>> res;
+    for (const auto &meshFace : mesh.faces) {
+        std::vector<glm::vec3> points;
+        for (int vertIndex : meshFace) {
+            const glm::vec3 point = mesh.verts.at(vertIndex);
+            points.push_back(point);
+        }
+        res.push_back(points);
+    }
+    Q_assert(res.size() == mesh.faces.size());
+    return res;
+}
+
+
+static aabb3 mesh_face_bbox(const mesh_t &mesh, int facenum)
+{
+    const std::vector<int> &face = mesh.faces.at(facenum);
+    
+}
+
+void cleanupMesh(mesh_t &mesh)
+{
+    using facenum_t = int;
+    
+    std::vector<std::pair<aabb3, facenum_t>> faces;
+    
+    octree_node_t<facenum_t> octree = makeOctree(faces);
+    
+}
diff --git a/include/common/mathlib.hh b/include/common/mathlib.hh
index dd864820..40ed2b83 100644
--- a/include/common/mathlib.hh
+++ b/include/common/mathlib.hh
@@ -452,4 +452,19 @@ std::vector<V> PointsAlongLine(const V &start, const V &end, const float step)
     return result;
 }
 
+class mesh_t {
+public:
+    std::vector<glm::vec3> verts;
+    std::vector<std::vector<int>> faces;
+};
+
+// Welds vertices at exactly the same position
+mesh_t buildMesh(const std::vector<std::vector<glm::vec3>> &faces);
+std::vector<std::vector<glm::vec3>> meshToFaces(const mesh_t &mesh);
+
+// Preserves the number and order of faces.
+// doesn't merge verts.
+// adds verts to fix t-juncs
+void cleanupMesh(mesh_t &mesh);
+
 #endif /* __COMMON_MATHLIB_H__ */
diff --git a/light/test_light.cc b/light/test_light.cc
index 1ed9f36b..90ef4fb7 100644
--- a/light/test_light.cc
+++ b/light/test_light.cc
@@ -519,3 +519,76 @@ TEST(mathlib, FractionOfLine) {
     ASSERT_FLOAT_EQ(2, FractionOfLine(vec3(0,0,0), vec3(1,1,1), vec3(2,2,2)));
     ASSERT_FLOAT_EQ(-1, FractionOfLine(vec3(0,0,0), vec3(1,1,1), vec3(-1,-1,-1)));
 }
+
+// mesh_t
+
+TEST(mathlib, meshCreate) {
+    const vector<vec3> poly1 {
+        { 0,0,0 },
+        { 0,64,0 },
+        { 64,64,0 },
+        { 64,0,0 }
+    };
+    const vector<vec3> poly2 {
+        { 64,0,0 },
+        { 64,64,0 },
+        { 128,64,0 },
+        { 128,0,0 }
+    };
+    const vector<vector<vec3>> polys { poly1, poly2 };
+    
+    const mesh_t m = buildMesh(polys);
+    ASSERT_EQ(6, m.verts.size());
+    ASSERT_EQ(2, m.faces.size());
+    ASSERT_EQ(polys, meshToFaces(m));
+}
+
+TEST(mathlib, meshFixTJuncs) {
+    /*
+     
+     poly1
+     
+   x=0 x=64 x=128
+     
+     |---|--| y=64  poly2
+     |   +--| y=32
+     |---|--| y=0   poly3
+     
+     poly1 should get a vertex inserted at the +
+     
+     */
+    const vector<vec3> poly1 {
+        { 0,0,0 },
+        { 0,64,0 },
+        { 64,64,0 },
+        { 64,0,0 }
+    };
+    const vector<vec3> poly2 {
+        { 64,32,0 },
+        { 64,64,0 },
+        { 128,64,0 },
+        { 128,32,0 }
+    };
+    const vector<vec3> poly3 {
+        { 64,0,0 },
+        { 64,32,0 },
+        { 128,32,0 },
+        { 128,0,0 }
+    };
+    
+    const vector<vector<vec3>> polys { poly1, poly2, poly3 };
+    
+    mesh_t m = buildMesh(polys);
+    ASSERT_EQ(8, m.verts.size());
+    ASSERT_EQ(3, m.faces.size());
+    ASSERT_EQ(polys, meshToFaces(m));
+    
+    cleanupMesh(m);
+    
+    const auto newFaces = meshToFaces(m);
+#if 0
+    EXPECT_NE(poly1, newFaces.at(0));
+#endif
+    EXPECT_EQ(poly2, newFaces.at(1));
+    EXPECT_EQ(poly3, newFaces.at(2));
+}