Opengl smooth shading generated object

Question

I generated a 3d shape using a perlin noise. I am trying to smooth shade it, to do so I calculated the face normal for each of my triangles and then I calculated the normal of each triangle vertex by averaging the normals of the faces they belong to and normalizing the final result. The final result looks a lot like flat shading (see attached screenshots)

The normals looks correct to me. I cannot use shaders and have to use the old deprecated way of rendering.

The shape generator :

void Island::generateTopTriangles() {
  float xStep = 2 * _xmax / _tess;
  float zStep = 2 * _zmax / _tess;

  PointMap top;
  for (int i = 0; i <= _tess; i++) {
    float z = -_zmax + i * zStep;
    std::vector<Vector3f> rowTop;
    for (int j = 0; j <= _tess; j++) {
      float x = -_xmax + j * xStep;
      rowTop.emplace_back(x, islandPerlin(x, z), z);
    }
    top.emplace_back(rowTop);
  }

  for (int i = 0; i < top.size() - 1; i++) {
    const std::vector<Vector3f> &pointRow = top[i];
    const std::vector<Vector3f> &pointUpRow = top[i + 1];
    std::vector<Triangle> newRow;
    for (int j = 0; j < pointRow.size() - 1; j++) {
      const Vector3f &p1 = pointRow.at(j);
      const Vector3f &p2 = pointRow.at(j + 1);
      const Vector3f &p3 = pointUpRow.at(j);
      const Vector3f &p4 = pointUpRow.at(j + 1);

      Vertex::Ptr v1, v2, v3, v4, v5;
      if (j == 0) {
        v1 = std::make_shared<Vertex>(Vertex(p1, p3, Vector3f()));
      } else { //Retrieve existing Vertex
        v1 = newRow[newRow.size() - 1].v2;
      }
      v2 = std::make_shared<Vertex>(Vertex(p3, p2, Vector3f()));
      if (i == 0) {
        v3 = std::make_shared<Vertex>(Vertex(p2, p1, Vector3f()));
      } else { //Retrieve existing Vertex
        v3 = _triangles[_triangles.size() - 1][j == 0 ? 1 : newRow.size() + 1].v3;
      }
      v4 = std::make_shared<Vertex>(Vertex(p2, p4, Vector3f()));
      v5 = std::make_shared<Vertex>(Vertex(p4, p3, Vector3f()));

      //Create triangles
      newRow.emplace_back(v1, v2, v3, computeNormal(v1->p, v2->p, v3->p));
      newRow.emplace_back(v2, v4, v5, computeNormal(v2->p, v4->p, v5->p).invert());
    }
    _triangles.emplace_back(newRow);
  }
}

I compute face normals with a simple cross product between two vectors :

Vector3f Island::computeNormal(const Vector3f &p1, const Vector3f &p2, const Vector3f &p3) {
  Vector3f u = {p2.x - p1.x,
                p2.y - p1.y,
                p2.z - p1.z};
  Vector3f v = {p3.x - p1.x,
                p3.y - p1.y,
                p3.z - p1.z};
  Vector3f n = {u.y * v.z - u.z * v.y,
                u.z * v.x - u.x * v.z,
                u.x * v.y - u.y * v.x};
  return n.normalize();
}

The per vertex normals (initialized to 0) :

void Island::computePerVertexNormal() {
  for (auto row : _triangles) {
    for (auto t : row) {
      t.v1->n.x += t.n.x;
      t.v1->n.y += t.n.y;
      t.v1->n.z += t.n.z;
      t.v2->n.x += t.n.x;
      t.v2->n.y += t.n.y;
      t.v2->n.z += t.n.z;
      t.v3->n.x += t.n.x;
      t.v3->n.y += t.n.y;
      t.v3->n.z += t.n.z;
    }
  }
  for (auto row : _triangles) {
    for (auto t : row) {
      t.v1->n.normalize();
      t.v2->n.normalize();
      t.v3->n.normalize();
    }
  }
}

And finally the drawing part :

void Island::draw() const {
  glEnable(GL_LIGHTING);
  glEnable(GL_LIGHT0);
  glEnable(GL_BLEND);
  glEnable(GL_COLOR_MATERIAL);

  GLfloat specular[] = {0.1f, 0.1f, 0.1f, 0.0f};
  glMaterialfv(GL_FRONT_AND_BACK, GL_SPECULAR, specular);
  GLfloat diffuse[] = {0.5f, 0.5f, 0.5f, 1.0f};
  glMaterialfv(GL_FRONT_AND_BACK, GL_DIFFUSE, diffuse);
  GLfloat emission[] = {0.0f, 0.0f, 0.0f, 1.0f};
  glMaterialfv(GL_FRONT_AND_BACK, GL_EMISSION, emission);
  GLfloat shininess = 128.0f;
  glMaterialf(GL_FRONT_AND_BACK, GL_SHININESS, shininess);

  glShadeModel(GL_SMOOTH);
  glColor4f(1.0f, 0.5f, 0.0f, 1.0f);
  glBegin(GL_TRIANGLES);
  for (auto &row : _triangles) {
    for (auto &t : row) {
      glNormal3f(t.v1->n.x, t.v1->n.y, t.v1->n.z);
      glVertex3f(t.v1->p.x, t.v1->p.y, t.v1->p.z);
      glNormal3f(t.v2->n.x, t.v2->n.y, t.v2->n.z);
      glVertex3f(t.v2->p.x, t.v2->p.y, t.v2->p.z);
      glNormal3f(t.v3->n.x, t.v3->n.y, t.v3->n.z);
      glVertex3f(t.v3->p.x, t.v3->p.y, t.v3->p.z);
    }
  }
  glEnd();

  glDisable(GL_COLOR_MATERIAL);
  glDisable(GL_BLEND);
  glDisable(GL_LIGHT0);
  glDisable(GL_LIGHTING);
}

Answer 1

The solution was simple. I got confused and thought my edges were the vertices. Once corrected, since the new vertices share the correct points this time, the new normals are now calculated from the 6 adjacent triangle faces and are now correct. the generation code is now much simpler as well.

void Island::generateTopTriangles() {
  float xStep = 2 * _xmax / _tess;
  float zStep = 2 * _zmax / _tess;

  float z;
  for (int i = 0; i <= _tess; i++) {
    z = -_zmax + i * zStep;
    std::vector<Vertex::Ptr> row;
    for (int j = 0; j <= _tess; j++) {
      float x = -_xmax + j * xStep;
      row.emplace_back(std::make_shared<Vertex>(Vector3f(x, islandPerlin(x, z), z)));
    }
    _vertices.emplace_back(row);
  }

  for (int i = 0; i < _vertices.size() - 1; i++) {
    const std::vector<Vertex::Ptr> &pointRow = _vertices[i];
    const std::vector<Vertex::Ptr> &pointUpRow = _vertices[i + 1];
    std::vector<Triangle::Ptr> newRow;
    for (int j = 0; j < pointRow.size() - 1; j++) {
      const Vertex::Ptr p1 = pointRow.at(j);
      const Vertex::Ptr p2 = pointRow.at(j + 1);
      const Vertex::Ptr p3 = pointUpRow.at(j);
      const Vertex::Ptr p4 = pointUpRow.at(j + 1);

      newRow.emplace_back(std::make_shared<Triangle>(p1, p2, p3, computeNormal(p3->p, p2->p, p1->p)));
      newRow.emplace_back(std::make_shared<Triangle>(p3, p2, p4, computeNormal(p4->p, p2->p, p3->p)));
    }
    _triangles.emplace_back(newRow);
  }
}

The rest of the code was actually correct. Here are the results :