diff --git a/src/cgalutils.cc b/src/cgalutils.cc
index b7fbafd3..efc55ee5 100644
--- a/src/cgalutils.cc
+++ b/src/cgalutils.cc
@@ -69,9 +69,9 @@ namespace /* anonymous */ {
 		
 			BOOST_FOREACH(const Polygon &p, ps.polygons) {
 				BOOST_REVERSE_FOREACH(Vector3d v, p) {
-					if (!grid.has(v[0], v[1], v[2])) {
+					if (!grid.has(v)) {
 						// align v to the grid; the CGALPoint will receive the aligned vertex
-						grid.align(v[0], v[1], v[2]) = vertices.size();
+						grid.align(v) = vertices.size();
 						vertices.push_back(CGALPoint(v[0], v[1], v[2]));
 					}
 				}
@@ -91,7 +91,7 @@ namespace /* anonymous */ {
 #endif
 				indices.clear();
 				BOOST_FOREACH(const Vector3d &v, p) {
-					indices.push_back(grid.data(v[0], v[1], v[2]));
+					indices.push_back(grid.data(v));
 				}
 
 				// We perform this test since there is a bug in CGAL's
@@ -275,8 +275,10 @@ static CGAL_Nef_polyhedron *createNefPolyhedronFromPolySet(const PolySet &ps)
 
 	// Since is_convex doesn't work well with non-planar faces,
 	// we tessellate the polyset before checking.
-	PolySet ps_tri(3);
-	PolysetUtils::tessellate_faces(ps, ps_tri);
+	PolySet psq(ps);
+	psq.quantizeVertices();
+    PolySet ps_tri(3);
+	PolysetUtils::tessellate_faces(psq, ps_tri);
 	if (ps_tri.is_convex()) {
 		typedef CGAL::Exact_predicates_inexact_constructions_kernel K;
 		// Collect point cloud
diff --git a/src/grid.h b/src/grid.h
index 23690b3f..f9fe4d0e 100644
--- a/src/grid.h
+++ b/src/grid.h
@@ -1,6 +1,8 @@
 #pragma once
 
 #include "mathc99.h"
+#include "linalg.h"
+
 #ifdef WIN32
 typedef __int64 int64_t;
 #else
@@ -96,10 +98,10 @@ public:
 		res = resolution;
 	}
 
-	T &align(double &x, double &y, double &z) {
-		int64_t ix = (int64_t)round(x / res);
-		int64_t iy = (int64_t)round(y / res);
-		int64_t iz = (int64_t)round(z / res);
+	T &align(Vector3d &v) {
+		int64_t ix = (int64_t)round(v[0] / res);
+		int64_t iy = (int64_t)round(v[1] / res);
+		int64_t iz = (int64_t)round(v[2] / res);
 		if (db.find(std::make_pair(std::make_pair(ix, iy), iz)) == db.end()) {
 			int dist = 10;
 			for (int64_t jx = ix - 1; jx <= ix + 1; jx++) {
@@ -118,14 +120,14 @@ public:
 				}
 			}
 		}
-		x = ix * res, y = iy * res, z = iz * res;
+		v[0] = ix * res, v[1] = iy * res, v[2] = iz * res;
 		return db[std::make_pair(std::make_pair(ix, iy), iz)];
 	}
 
-	bool has(double x, double y, double z) {
-		int64_t ix = (int64_t)round(x / res);
-		int64_t iy = (int64_t)round(y / res);
-		int64_t iz = (int64_t)round(z / res);
+	bool has(const Vector3d &v) {
+		int64_t ix = (int64_t)round(v[0] / res);
+		int64_t iy = (int64_t)round(v[1] / res);
+		int64_t iz = (int64_t)round(v[2] / res);
 		if (db.find(std::make_pair(std::make_pair(ix, iy), iz)) != db.end())
 			return true;
 		for (int64_t jx = ix - 1; jx <= ix + 1; jx++)
@@ -137,19 +139,8 @@ public:
 		return false;
 	}
 
-	bool eq(double x1, double y1, double z1, double x2, double y2, double z2) {
-		align(x1, y1, z1);
-		align(x2, y2, z2);
-		if (fabs(x1 - x2) < res && fabs(y1 - y2) < res && fabs(z1 - z2) < res)
-			return true;
-		return false;
+	T &data(Vector3d v) { 
+		return align(v);
 	}
 
-	T &data(double x, double y, double z) {
-		return align(x, y, z);
-	}
-
-	T &operator()(double x, double y, double z) {
-		return align(x, y, z);
-	}
 };
diff --git a/src/polyset.cc b/src/polyset.cc
index 00ae963f..ec31cd19 100644
--- a/src/polyset.cc
+++ b/src/polyset.cc
@@ -28,6 +28,8 @@
 #include "polyset-utils.h"
 #include "linalg.h"
 #include "printutils.h"
+#include "grid.h"
+
 #include <Eigen/LU>
 #include <boost/foreach.hpp>
 
@@ -174,6 +176,17 @@ void PolySet::resize(Vector3d newsize, const Eigen::Matrix<bool,3,1> &autosize)
 	this->transform(t);
 }
 
+void PolySet::quantizeVertices()
+{
+	Grid3d<int> grid(GRID_FINE);
+	BOOST_FOREACH(Polygon &p, this->polygons) {
+		BOOST_FOREACH(Vector3d &v, p) {
+			// align v to the grid
+			if (!grid.has(v)) grid.align(v);
+		}
+	}
+}
+
 // all GL functions grouped together here
 #ifndef NULLGL
 static void gl_draw_triangle(GLint *shaderinfo, const Vector3d &p0, const Vector3d &p1, const Vector3d &p2, bool e0, bool e1, bool e2, double z, bool mirrored)
diff --git a/src/polyset.h b/src/polyset.h
index 5701137d..d200bf39 100644
--- a/src/polyset.h
+++ b/src/polyset.h
@@ -27,6 +27,7 @@ public:
 	virtual bool isEmpty() const { return polygons.size() == 0; }
 	virtual Geometry *copy() const { return new PolySet(*this); }
 
+	void quantizeVertices();
 	size_t numPolygons() const { return polygons.size(); }
 	void append_poly();
 	void append_vertex(double x, double y, double z = 0.0);