diff --git a/src/angle_defect.cpp b/src/angle_defect.cpp
index 78589fb..5163c6e 100644
--- a/src/angle_defect.cpp
+++ b/src/angle_defect.cpp
@@ -1,9 +1,22 @@
 #include "../include/angle_defect.h"
+#include "internal_angles.h"
+#include <igl/squared_edge_lengths.h>
+#include <math.h>
 
 void angle_defect(
   const Eigen::MatrixXd & V,
   const Eigen::MatrixXi & F,
   Eigen::VectorXd & D)
 {
-  D = Eigen::VectorXd::Zero(V.rows());
+  Eigen::MatrixXd l_sqr;
+  igl::squared_edge_lengths(V, F, l_sqr);
+  Eigen::MatrixXd A;
+  internal_angles(l_sqr, A);
+  
+  D = 2*M_PI*Eigen::VectorXd::Ones(V.rows());
+  for (int fi = 0; fi < F.rows(); fi++) {
+    for (int vi = 0; vi < 3; vi++) {
+      D[F(fi, vi)] -= A(fi, vi);
+    }
+  }
 }
diff --git a/src/internal_angles.cpp b/src/internal_angles.cpp
index 3e14c75..6776272 100644
--- a/src/internal_angles.cpp
+++ b/src/internal_angles.cpp
@@ -1,8 +1,17 @@
 #include "../include/internal_angles.h"
+#include <math.h>
 
 void internal_angles(
   const Eigen::MatrixXd & l_sqr,
   Eigen::MatrixXd & A)
 {
-  // Add with your code
+  A.resize(l_sqr.rows(), 3);
+  for (int i = 0; i < l_sqr.rows(); i++) {
+    double asq = l_sqr(i, 0);
+    double bsq = l_sqr(i, 1);
+    double csq = l_sqr(i, 2);
+    A(i, 0) = acos((bsq + csq - asq) / (2*sqrt(bsq*csq)));
+    A(i, 1) = acos((asq + csq - bsq) / (2*sqrt(asq*csq)));
+    A(i, 2) = acos((asq + bsq - csq) / (2*sqrt(asq*bsq)));
+  }
 }
diff --git a/src/mean_curvature.cpp b/src/mean_curvature.cpp
index 41fce89..f29fb6b 100644
--- a/src/mean_curvature.cpp
+++ b/src/mean_curvature.cpp
@@ -1,10 +1,29 @@
 #include "../include/mean_curvature.h"
+#include <igl/cotmatrix.h>
+#include <igl/massmatrix.h>
+#include <igl/per_vertex_normals.h>
+#include <Eigen/Sparse>
 
 void mean_curvature(
   const Eigen::MatrixXd & V,
   const Eigen::MatrixXi & F,
   Eigen::VectorXd & H)
 {
-  // Replace with your code
-  H = Eigen::VectorXd::Zero(V.rows());
+  Eigen::SparseMatrix<double> L;
+  Eigen::SparseMatrix<double> M;
+  igl::cotmatrix(V, F, L);
+  igl::massmatrix(V, F, igl::MassMatrixType::MASSMATRIX_TYPE_DEFAULT, M);
+  
+  Eigen::MatrixXd Hn = M.cwiseInverse() * L * V;
+  Eigen::MatrixXd N;
+  igl::per_vertex_normals(V, F, N);
+  H.resize(V.rows());
+  
+  for (int i = 0; i < Hn.rows(); i++) {
+    H[i] = Hn.row(i).norm();
+    // make sure sign is correct
+    if (Hn.row(i).dot(N.row(i)) < 0) {
+      H.row(i) *= -1;
+    }
+  }
 }
diff --git a/src/principal_curvatures.cpp b/src/principal_curvatures.cpp
index 6a51d2e..f51bc38 100644
--- a/src/principal_curvatures.cpp
+++ b/src/principal_curvatures.cpp
@@ -1,4 +1,11 @@
 #include "../include/principal_curvatures.h"
+#include <igl/adjacency_list.h>
+#include <igl/per_vertex_normals.h>
+#include <igl/eigs.h>
+#include <igl/pinv.h>
+#include <igl/sort.h>
+#include <igl/colon.h>
+#include <igl/slice.h>
 
 void principal_curvatures(
   const Eigen::MatrixXd & V,
@@ -8,9 +15,88 @@ void principal_curvatures(
   Eigen::VectorXd & K1,
   Eigen::VectorXd & K2)
 {
-  // Replace with your code
-  K1 = Eigen::VectorXd::Zero(V.rows());
-  K2 = Eigen::VectorXd::Zero(V.rows());
-  D1 = Eigen::MatrixXd::Zero(V.rows(),3);
-  D2 = Eigen::MatrixXd::Zero(V.rows(),3);
+  K1.resize(V.rows());
+  K2.resize(V.rows());
+  D1.resize(V.rows(),3);
+  D2.resize(V.rows(),3);
+  
+  std::vector<std::vector<int>> adj;
+  igl::adjacency_list(F, adj);
+  
+  Eigen::MatrixXd N;
+  igl::per_vertex_normals(V, F, N);
+  
+  Eigen::SelfAdjointEigenSolver<Eigen::MatrixXd> es;
+  
+  for (int i = 0; i < V.rows(); i++) {
+  
+    // gather the vertices in the two-ring of vi into a matrix P
+    std::vector<int> two_ring;
+    for (int u : adj[i]) {
+      if (find(two_ring.begin(), two_ring.end(), u) == two_ring.end())
+        two_ring.push_back(u);
+      for (int w : adj[u]) {
+        if (find(two_ring.begin(), two_ring.end(), w) == two_ring.end())
+          two_ring.push_back(w);
+      }
+    }
+    
+    int k = two_ring.size();
+    Eigen::MatrixXd P(k, 3);
+    for (int j = 0; j < k; j++) {
+      P.row(j) = V.row(two_ring[j]) - V.row(i);
+    }
+    
+    // do PCA on Q = P'P
+    es.compute(P.transpose() * P);
+    Eigen::VectorXd Q_evals, Q_inds;
+    igl::sort(es.eigenvalues(), 1, false, Q_evals, Q_inds);
+    Eigen::MatrixXd Q_evecs;
+    igl::slice(es.eigenvectors(), Q_inds, 2, Q_evecs);
+    
+    // w should be consistently oriented
+    Q_evecs.col(2) *= Q_evecs.col(2).dot(N.row(i)) > 0 ? 1 : -1;
+    
+    // [Sc|B] = (Q_evecs'*P')' = P*Q_evecs
+    Eigen::MatrixXd Q_uv(3, 2);
+    Q_uv << Q_evecs.col(0), Q_evecs.col(1);
+    Eigen::MatrixXd Sc = P * Q_uv;
+    Eigen::VectorXd B = P * Q_evecs.col(2);
+    
+    // use least squares to fit a quadratic function to the k points (in the above basis)
+    Eigen::MatrixXd A(k, 5);
+    for (int i = 0; i < Sc.rows(); i++) {
+      double u = Sc(i, 0);
+      double v = Sc(i, 1);
+      A.row(i) << u, v, u*u, u*v, v*v;
+    }
+    Eigen::VectorXd quad_coeffs = (A.transpose() * A).ldlt().solve(A.transpose() * B);
+    double a1 = quad_coeffs[0];
+    double a2 = quad_coeffs[1];
+    double a3 = quad_coeffs[2];
+    double a4 = quad_coeffs[3];
+    double a5 = quad_coeffs[4];
+    
+    // compute shape operator
+    Eigen::Matrix2d F1, F2, S;
+    F1 << 1 + a1*a1, a1*a2, a1*a2, 1+a2*a2;
+    F2 << 2*a3, a4, a4, 2*a5;
+    F2 /= sqrt(a1*a1+1+a2*a2);
+    
+    S = -F2 * F1.inverse();
+    
+    // do PCA on S
+    es.compute(S);
+    Eigen::VectorXd S_evals, S_inds;
+    igl::sort(es.eigenvalues(), 1, false, S_evals, S_inds);
+    Eigen::MatrixXd S_evecs;
+    igl::slice(es.eigenvectors(), S_inds, 2, S_evecs);
+    
+    // finally we have the principal curvatures and directions
+    K1[i] = S_evals[0];
+    K2[i] = S_evals[1];
+    
+    D1.row(i) = Q_uv * S_evecs.col(0);
+    D2.row(i) = Q_uv * S_evecs.col(1);
+  }
 }