diff --git a/src/drawingPass.h b/src/drawingPass.h
index 3d5e2f3..cc99a11 100644
--- a/src/drawingPass.h
+++ b/src/drawingPass.h
@@ -45,9 +45,9 @@ struct DisplayPoint : public DrawingPass {
     inline explicit DisplayPoint(const nanogui::Vector4i &pointColor = {0,0,0,255})
             : DrawingPass(), m_pointColor(pointColor) {}
     void render(const MyView::PointCollection& points, uint8_t*buffer, int w, int h) override{
-        for (const auto&p : points){
-            int i (std::floor(p.x()));
-            int j (std::floor(p.y()));
+        for (const auto&p : points.point_data()){
+            int i (std::floor(p.pos().x()));
+            int j (std::floor(p.pos().y()));
             for (int u = -1; u <= 1; ++u ){
                 for (int v = -1; v <= 1; ++v ){
                     //this is suboptimal: we check multiple time, could be done better.
diff --git a/src/drawingPasses/distanceField.h b/src/drawingPasses/distanceField.h
index 7e38bfa..8599a15 100644
--- a/src/drawingPasses/distanceField.h
+++ b/src/drawingPasses/distanceField.h
@@ -5,14 +5,16 @@
 struct DistanceField : public DrawingPass {
     inline explicit DistanceField() : DrawingPass() {}
     void render(const MyView::PointCollection& points, uint8_t*buffer, int w, int h) override{
+        if(points.point_data().empty()) return;
+
         double normFactor (std::max(w,h));
         for (int j = 0; j < h; ++j ) {
             for (int i = 0; i < w; ++i) {
                 auto *b = buffer + (i + j * w) * 4;
                 int minDist = normFactor; //distance should necessarily be smaller
-                for (const auto &p: points) {
-                    int u(std::floor(p.x()));
-                    int v(std::floor(p.y()));
+                for (const auto &p : points.point_data()) {
+                    int u(std::floor(p.pos().x()));
+                    int v(std::floor(p.pos().y()));
                     auto dist = int(std::sqrt((i-u)*(i-u) + (j-v)*(j-v)));
                     minDist = std::min(dist, minDist);
                 }
@@ -23,3 +25,25 @@ struct DistanceField : public DrawingPass {
         }
     }
 };
+struct DistanceFieldWithKdTree : public DrawingPass {
+    inline explicit DistanceFieldWithKdTree() : DrawingPass() {}
+    void render(const MyView::PointCollection& points, uint8_t*buffer, int w, int h) override{
+        if(points.point_data().empty()) return;
+
+        double normFactor (std::max(w,h));
+        for (int j = 0; j < h; ++j ) {
+            for (int i = 0; i < w; ++i) {
+                auto *b = buffer + (i + j * w) * 4;
+                DataPoint::VectorType query (i, j);
+                auto res = points.nearest_neighbor( query );
+                if(res.begin()!=res.end()) {
+                    auto nei = points.point_data()[res.get()].pos();
+                    float dist = (nei-query).norm();
+                    auto col = uint (255. * dist / normFactor);
+                    b[0] = b[1] = b[2] = col;
+                    b[3] = 255;
+                }
+            }
+        }
+    }
+};
diff --git a/src/main.cpp b/src/main.cpp
index 537a437..8f2f876 100644
--- a/src/main.cpp
+++ b/src/main.cpp
@@ -89,6 +89,7 @@ class ExampleApplication : public Screen {
         m_passes.clear();
         m_passes.push_back( new FillPass( {0,0,0,255}));
         m_passes.push_back( new DistanceField());
+//        m_passes.push_back( new DistanceFieldWithKdTree()); // too slow
         m_passes.push_back( new DisplayPoint({255,0,0,255}));
 
         image_view = new MyView(window);
diff --git a/src/myview.cpp b/src/myview.cpp
index d2d21d2..1fce9be 100644
--- a/src/myview.cpp
+++ b/src/myview.cpp
@@ -23,14 +23,25 @@ MyView::isInsideImage(const Vector2f &lp) const {
     return true;
 }
 
+//#define USE_KDTREE
 int
 MyView::findPointId(const Vector2f &lp, float epsilon) const{
-    int i = 0;
-    for(const auto&p : m_points)
-    {
-        if(norm((lp-p)) <= epsilon)
-            return i;
-        ++i;
+    if(! m_points.empty()) {
+        int i = 0;
+#ifndef USE_KDTREE
+        for(const auto&p : m_points) {
+            Vector2f query(p.x(), p.y());
+            if (norm((lp - query)) <= epsilon)
+                return i;
+            ++i;
+        }
+#else
+        DataPoint::VectorType query(lp.x(), lp.y());
+        auto res = m_tree.nearest_neighbor(query);
+        if (res.begin() != res.end() &&
+           (query-m_tree.point_data()[res.get()].pos()).norm()<epsilon)
+            return res.get();
+#endif
     }
     return -1;
 }
@@ -45,8 +56,8 @@ MyView::mouse_button_event(const Vector2i &p, int button, bool down, int modifie
         auto pointId = findPointId(lp);
         if (pointId < 0) { // create new point
             std::cout << "MyView::add new point" << std::endl;
-            m_points.push_back( lp );
-            m_updateFunction();
+            m_points.emplace_back( lp.x(), lp.y(), 0, 1 );
+            updateCollection();
             return true;
         } else {
             m_movedPoint = pointId;
@@ -71,13 +82,14 @@ MyView::mouse_drag_event(const nanogui::Vector2i &p, const nanogui::Vector2i &re
                 case 1: //left click
                     // if is on a point
                     std::cout << "Move point by [" << rel << "]" << std::endl;
-                    m_points[m_movedPoint] = lp;
-                    m_updateFunction();
+                    m_points[m_movedPoint].x() = lp.x();
+                    m_points[m_movedPoint].y() = lp.y();
+                    updateCollection();
                     break;
                 case 2: //right click
                     // if is on a point
                     std::cout << "Change normal by [" << rel << "]" << std::endl;
-                    m_updateFunction();
+                    updateCollection();
                     break;
                 default:
                     break;
@@ -85,4 +97,15 @@ MyView::mouse_drag_event(const nanogui::Vector2i &p, const nanogui::Vector2i &re
         }
     }
     return true;
-}
\ No newline at end of file
+}
+
+void
+MyView::updateCollection() {
+    // recompute KdTree
+    if(m_points.empty())
+        m_tree.clear();
+    else
+        m_tree.build(m_points );
+
+    m_updateFunction();
+}
diff --git a/src/myview.h b/src/myview.h
index d5214a4..6e9ae51 100644
--- a/src/myview.h
+++ b/src/myview.h
@@ -3,14 +3,31 @@
 #include <nanogui/imageview.h>
 #include <nanogui/vector.h>
 
+#include <Ponca/SpatialPartitioning>
+
 #include <iostream>
 #include <optional>
 #include <vector>
 
+class DataPoint
+{
+public:
+    enum {Dim = 2};
+    using Scalar = float;
+    using VectorType = Eigen::Vector<Scalar,Dim>;
+    inline const auto& pos() const {return m_pos;}
+    inline const auto& normal() const {return m_normal;}
+    /// \fixme Use maps to avoid duplication
+    explicit inline DataPoint(const nanogui::Vector4f &pn)
+    : m_pos({pn.x(), pn.y()}), m_normal({pn.z(), pn.w()}) {}
+private:
+    VectorType m_pos, m_normal;
+};
+
 
 class MyView : public nanogui::ImageView {
 public:
-    using PointCollection = std::vector<nanogui::Vector2f>;
+    using PointCollection = Ponca::KdTree<DataPoint>;
 
     /// Initialize the widget
     explicit MyView(Widget *parent);
@@ -29,13 +46,17 @@ class MyView : public nanogui::ImageView {
     bool mouse_drag_event(const nanogui::Vector2i &p, const nanogui::Vector2i &rel, int button, int modifiers) override;
 
     /// Read access to point collection
-    inline const PointCollection& getPointCollection() const { return m_points; }
+    inline const PointCollection& getPointCollection() const { return m_tree; }
 
     /// Set Update function, called after each point update
     inline void setUpdateFunction(std::function<void()> &&f) { m_updateFunction = f; }
 
 private:
-    PointCollection m_points;
+    inline void updateCollection();
+
+    using PointContainer  = std::vector<nanogui::Vector4f>; // stores x,y,nx,ny
+    PointContainer m_points;
+    PointCollection m_tree;
     std::function<void()> m_updateFunction {[](){}};
     int m_movedPoint{-1};
 };