c++ - Opengl平滑着色生成对象

Question

我使用柏林噪声生成了 3D 形状。 我试图平滑它的阴影，为此，我计算了每个三角形的面法线，然后通过对它们所属的面的法线进行平均并标准化最终结果来计算每个三角形顶点的法线。 最终结果看起来很像平面着色(请参阅随附的屏幕截图)

法线对我来说看起来是正确的。 我无法使用着色器，必须使用旧的已弃用的渲染方式。

形状生成器:

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);
  }
}

我使用两个 vector 之间的简单叉积来计算面部法线:

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();
}

每个顶点法线(初始化为 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();
    }
  }
}

最后是绘图部分:

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

解决方案很简单。我很困惑，以为我的边就是顶点。校正后，由于这次新顶点共享正确的点，因此新法线现在是根据 6 个相邻三角形面计算的，并且现在是正确的。生成代码现在也简单得多。

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);
  }
}

其余代码实际上是正确的。结果如下: