实时渲染技术：LOD与剔除优化

import mathimport random  class Vec3:    """极简三维向量, 仅用于演示."""    def __init__(self, x, y, z):        self.x = x        self.y = y        self.z = z     def dot(self, other):        return self.x * other.x + self.y * other.y + self.z * other.z     def add_scaled(self, other, scale):        return Vec3(            self.x + other.x * scale,            self.y + other.y * scale,            self.z + other.z * scale,        )  class FrustumPlane:    """一个平面: n*p + d = 0, n 朝视锥内部."""    def __init__(self, n, d):        self.n = n        self.d = d     def distance_to_point(self, p):        return self.n.dot(p) + self.d  class Frustum:    """用 6 个平面围成的视锥体."""    def __init__(self, planes):        self.planes = planes     def contains_sphere(self, center, radius):        for plane in self.planes:            if plane.distance_to_point(center) < -radius:                return False        return True  class Mesh:    """网格替身: 只记录三角形数量."""    def __init__(self, name, tri_count):        self.name = name        self.tri_count = tri_count  class SceneObject:    """场景物体: 持有 LOD0 到 LOD3 四档替身."""    def __init__(self, obj_id, center, radius, lods):        self.obj_id = obj_id        self.center = center        self.radius = radius        self.lods = lods     def pick_lod(self, distance):        if distance < 20:            return self.lods[0]        if distance < 60:            return self.lods[1]        if distance < 120:            return self.lods[2]        return self.lods[3]  def build_demo_scene(num_objects=200):    """随机生成场景: 物体散布在 200x200 区域."""    random.seed(42)    scene = []    for i in range(num_objects):        cx = random.uniform(-100, 100)        cz = random.uniform(-100, 100)        radius = random.uniform(1, 3)        lods = [            Mesh("建筑_高模", 20000),            Mesh("建筑_中模", 5000),            Mesh("建筑_低模", 1200),            Mesh("建筑_剪影", 150),        ]        scene.append(SceneObject(i, Vec3(cx, 0, cz), radius, lods))    return scene  def main():    inv_sqrt2 = 1.0 / math.sqrt(2.0)    planes = [        FrustumPlane(Vec3(0, 0, 1), -5),        FrustumPlane(Vec3(0, 0, -1), 200),        FrustumPlane(Vec3(-inv_sqrt2, 0, inv_sqrt2), 0),        FrustumPlane(Vec3(inv_sqrt2, 0, inv_sqrt2), 0),        FrustumPlane(Vec3(0, -inv_sqrt2, inv_sqrt2), 2 * inv_sqrt2),        FrustumPlane(Vec3(0, inv_sqrt2, inv_sqrt2), -2 * inv_sqrt2),    ]    frustum = Frustum(planes)    camera = Vec3(0, 2, -40)    scene = build_demo_scene()     visible_objs = []    total_triangles = 0    for obj in scene:        # 第一步: 视锥剔除, 不在视野内的直接跳过        if not frustum.contains_sphere(obj.center, obj.radius):            continue        dist = (obj.center.add_scaled(camera, -1)).length()        lod = obj.pick_lod(dist)        visible_objs.append((obj.obj_id, lod.name, lod.tri_count))        total_triangles += lod.tri_count     draw_calls = len(visible_objs)    full_cost = len(scene) * 20000    print(f"场景物体总数: {len(scene)}")    print(f"视锥剔除后可见: {draw_calls}")    print(f"经过 LOD 后的三角形总数: {total_triangles}")    print(f"未优化时三角形总数(预估): {full_cost}")    print(f"节省: {(1 - total_triangles / full_cost) * 100:.1f}%")    for obj_id, lod_name, tris in visible_objs[:8]:        print(f"  可见物体 #{obj_id}: 使用{lod_name}, {tris} 三角形")  if __name__ == "__main__":    main()