python - 近距离 3D 显示困惑

Question

我复制了 YouTube 的一段代码，关于在 Python 中在屏幕上显示 3d 立方体，而不使用外部模块(如 PyOpenGL)。它工作得很好，但是当你进入两个立方体之间时，显示就会变得困惑。这是我的代码:

import pygame, sys, math, random

def rotate2d(pos, rad): x,y=pos; s,c = math.sin(rad),math.cos(rad); return x*c-y*s,y*c+x*s

class Cam:
    def __init__(self, pos=(0,0,0),rot=(0,0)):
        self.pos = list(pos)
        self.rot = list(rot)

    def events(self, event):
        if event.type == pygame.MOUSEMOTION:
            x, y = event.rel; x/=200; y/=200
            self.rot[0]+=y; self.rot[1]+=x

    def update(self, dt, key):
        s = dt*10

        if key[pygame.K_q]: self.pos[1]+=s
        if key[pygame.K_e]: self.pos[1]-=s

        x,y = s*math.sin(self.rot[1]),s*math.cos(self.rot[1])
        if key[pygame.K_w]: self.pos[0]+=x; self.pos[2]+=y
        if key[pygame.K_s]: self.pos[0]-=x; self.pos[2]-=y
        if key[pygame.K_a]: self.pos[0]-=y; self.pos[2]+=x
        if key[pygame.K_d]: self.pos[0]+=y; self.pos[2]-=x
        if key[pygame.K_r]: self.pos[0]=0; self.pos[1]=0;\
                                         self.pos[2]=-5; self.rot[0]=0; self.rot[1]=0


class Cube:
    faces = (0,1,2,3),(4,5,6,7),(0,1,5,4),(2,3,7,6),(0,3,7,4),(1,2,6,5)
    colors = (255,0,0),(255,128,0),(255,255,0),(255,255,255),(0,0,255),(0,255,0)
    def __init__(self,pos=(0,0,0),color=None,v0=(-1,-1,-1),v1=(1,-1,-1),v2=(1,1,-1),v3=(-1,1,-1),v4=(-1,-1,1),v5=(1,-1,1),v6=(1,1,1),v7=(-1,1,1)):
        if color != None:
            if len(color) == 3 or len(color) == 4:
                self.colors = tuple((color for i in range(6)))
            if len(color) == 6:
                self.colors = color
        self.vertices = (v0,v1,v2,v3,v4,v5,v6,v7)
        x,y,z = pos
        self.verts = [(x+X/2,y+Y/2,z+Z/2) for X,Y,Z in self.vertices]


pygame.init()
w,h = 400,400; cx,cy = w//2, h//2
screen = pygame.display.set_mode((w,h))
clock = pygame.time.Clock()
cam = Cam((0,0,-5))
pygame.event.get(); pygame.mouse.get_rel()
pygame.mouse.set_visible(0); pygame.event.set_grab(1)
occupied = []

cube1 = Cube((0,0,0))
cube2 = Cube((0,0,2))
objects = [cube1, cube2]

while True:
    dt = clock.tick()/1000

    for event in pygame.event.get():
        if event.type == pygame.QUIT: pygame.quit(); sys.exit()
        if event.type == pygame.KEYDOWN:
            if event.key == pygame.K_ESCAPE: pygame.quit(); sys.exit()
        cam.events(event)

    screen.fill((0,0,0))

    face_list = []; face_color = []; depth = []

    for obj in objects:

        vert_list = []; screen_coords = []
        for x,y,z in obj.verts:
            x-= cam.pos[0]; y-=cam.pos[1];z-=cam.pos[2]
            x,z = rotate2d((x,z),cam.rot[1])
            y,z = rotate2d((y,z),cam.rot[0])
            vert_list += [(x,y,z)]

            f = 200/z
            x,y = x*f,y*f
            screen_coords+=[(cx+int(x),cy+int(y))]

        for f in range(len(obj.faces)):
            face = obj.faces[f]

            on_screen = False
            for i in face:
                x,y = screen_coords[i]
                if vert_list[i][2]>0 and x>0 and x<w and y>0 and y<h: on_screen = True; break

            if on_screen:
                coords = [screen_coords[i] for i in face]
                face_list += [coords]
                face_color += [obj.colors[f]]
                depth += [sum(sum(vert_list[j][i]**2 for i in range(3)) for j in face) / len(face)]

    order = sorted(range(len(face_list)),key=lambda i:depth[i],reverse=1)

    for i in order:
        try: pygame.draw.polygon(screen,face_color[i],face_list[i])
        except: pass

    key = pygame.key.get_pressed()
    pygame.display.flip()
    cam.update(dt,key)

当您尝试在两个多维数据集之间导航时，会发生以下情况:

有人可以建议对代码进行编辑，以防止当 cam.pos 靠近立方体时立方体变形吗？

Answer 1

当一个面(原始面，立方体的一侧)的一部分位于眼睛位置的后面而另一部分位于眼睛位置的前面时，应用程序无法正确绘制几何图形。如果变换后的 z 坐标 (vert_list += [(x,y,z)]) 对于某些顶点为正，对于形成图元(面)的其他一些顶点为负，则会发生这种情况。

如果您跳过所有面，其中至少一个 z 坐标为负(在眼睛后面)，您可以轻松测试该行为:

while True:
    # [...]

    for obj in objects:
        # [...]

        for f in range(len(obj.faces)):
            face = obj.faces[f]

            #on_screen = False
            #for i in face:
            #    x,y = screen_coords[i]
            #    if vert_list[i][2]>0 and x>0 and x<w and y>0 and y<h: on_screen = True; break

            # draw a face if any projected coordinate (x, y) is in the viewing volume 
            on_screen = False
            for i in face:
                x,y = screen_coords[i]
                if x>0 and x<w and y>0 and y<h: on_screen = True; break
            # skip a face if NOT ALL z coordinates are positive
            if on_screen:
                on_screen = all([vert_list[i][2]>0 for i in face])

            if on_screen:
                # [...]

<小时/>

可以通过在假设的近平面处裁剪几何体来解决该问题。请参阅Viewing frustum :

while True:
    # [...]

    for obj in objects:
        # [...]

        for f in range(len(obj.faces)):
            face = obj.faces[f]

            on_screen = False
            for i in face:
                x,y = screen_coords[i]
                if vert_list[i][2]>0 and x>0 and x<w and y>0 and y<h: on_screen = True; break

            # clip geometry at near plane
            if on_screen:
                near = 0.01
                for i in face:
                    if vert_list[i][2]<0:
                        x, y, z = vert_list[i]
                        nearscale = 200/near
                        x,y = x*nearscale,y*nearscale
                        screen_coords[i] = (cx+int(x),cy+int(y))

            if on_screen:
                coords = [screen_coords[i] for i in face]
                face_list += [coords]
                face_color += [obj.colors[f]]
                depth += [sum(sum(vert_list[j][i]**2 for i in range(3)) for j in face) / len(face)]