我使用柏林噪声生成了一个 3d 形状。我正在尝试平滑阴影，为此我计算了每个三角形的面法线，然后通过平均它们所属的面的法线并对最终结果进行归一化来计算每个三角形顶点的法线。最终结果看起来很像平面阴影（见附件截图）
法线在我看来是正确的。我不能使用着色器，必须使用旧的不推荐使用的渲染方式。
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);
}
}
我用两个向量之间的简单叉积计算人脸法线：
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);
}
