Normalize normals to norm 1

Implicit.cpp

@@ -8,11 +8,13 @@ Point ImplicitSurface::normal_at(const Point& pt) const {
     // this is simply the gradient.
     static const double d_dist = 1e-8;
 
-    return Point(
+    Point normal(
             (operator()(pt.x + d_dist, pt.y, pt.z) -
              operator()(pt.x - d_dist, pt.y, pt.z)) / (2. * d_dist),
             (operator()(pt.x, pt.y + d_dist, pt.z) -
              operator()(pt.x, pt.y - d_dist, pt.z)) / (2. * d_dist),
             (operator()(pt.x, pt.y, pt.z + d_dist) -
              operator()(pt.x, pt.y, pt.z - d_dist)) / (2. * d_dist));
+    normal.normalize();
+    return normal;
 }

Mesh.cpp

@@ -91,7 +91,7 @@ void Mesh::compute_normal(size_t vert) {
         normal += e1.cross_prod(e2);
     }
 
-    normal = (1. / ((double) faces_with_vert[vert].size())) * normal;
+    normal.normalize();
     normals[vert].dirty = false;
     normals[vert].vect = normal;
 }

common_structures.hpp

@@ -13,6 +13,17 @@ struct Point {
     Point(double x, double y, double z) : x(x), y(y), z(z) {}
     double x, y, z;
 
+    double norm() const {
+        auto sq = [](double x) { return x * x; };
+        return sqrt(sq(x) + sq(y) + sq(z));
+    }
+    void normalize() {
+        double _norm = norm();
+        x /= _norm;
+        y /= _norm;
+        z /= _norm;
+    }
+
     double operator[](unsigned i) const {
         assert(i < 3);
         switch(i) {