3D图形的深度问题 [英] Depth issue with 3D graphics
问题描述
我最近在YouTube上复制了一段代码，其中涉及Python中的3d图形，而未使用OpenGL等3D模块.该视频仅适用于多维数据集，因此我尝试在形状中添加四面体，然后事情突然出现在原本不应该出现的地方.代码如下:
导入pygame，sys，数学，随机def rotation2d(pos，rad):x，y = pos;s，c = math.sin(rad)，math.cos(rad);返回x * c-y * s，y * c + x * s凸轮类:def __init __(self，pos = {0,0,0)，rot = {0,0)):self.pos =列表(pos)self.rot =列表(腐烂)def事件(自身，事件):如果event.type == pygame.MOUSEMOTION:x，y = event.rel;x/= 200；y/= 200self.rot [0] + = y;self.rot [1] + = xdef更新(self，dt，key):s = dt * 10如果key [pygame.K_q]:self.pos [1] + = s如果key [pygame.K_e]:self.pos [1]-= sx，y = s * math.sin(self.rot [1])，s * math.cos(self.rot [1])如果key [pygame.K_w]:self.pos [0] + = x;self.pos [2] + = y如果key [pygame.K_s]:self.pos [0]-= x;self.pos [2]-= y如果key [pygame.K_a]:self.pos [0]-= y;self.pos [2] + = x如果key [pygame.K_d]:self.pos [0] + = y;self.pos [2]-= x如果key [pygame.K_r]:self.pos [0] = 0;self.pos [1] = 0; \self.pos [2] =-5;self.rot [0] = 0;self.rot [1] = 0多维数据集类:面=(0,1,2,3)，(4,5,6,7)，(0,1,5,4)，(2,3,7,6)，(0,3,7,4)，(1,2,6,5)颜色=(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)，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)):self.vertices =(v0，v1，v2，v3，v4，v5，v6，v7)x，y，z = posself.verts = [self.vertices中的X，Y，Z的((x + X/2，y + Y/2，z + Z/2)]四面体类:面=(1,2,3)，(0,1,2)，(0,1,3)，(0,2,3)颜色=(255,0,0)，(255,128,0)，(255,255,0)，(255,255,255)def __init __(self，pos =(0,0,0)，v0 =(0,0，.866)，v1 =(-.866，-1，-1)，v2 =(-.866,1，-1)，v3 =(.866,0，-1)):self.vertices =(v0，v1，v2，v3)x，y，z = posself.verts = [self.vertices中的X，Y，Z的((x + X/2，y + Y/2，z + Z/2)]pygame.init()w，h = 400,400；cx，cy = w//2，h//2屏幕= pygame.display.set_mode((w，h))时钟= pygame.time.Clock()cam =凸轮((0,0，-5))pygame.event.get();pygame.mouse.get_rel()pygame.mouse.set_visible(0);pygame.event.set_grab(1)对象= [立方体((0,0,0))，立方体((0,0,2))，四面体((0,0,1))]而True:dt = clock.tick()/1000对于pygame.event.get()中的事件:如果event.type == pygame.QUIT:pygame.quit();sys.exit()如果event.type == pygame.KEYDOWN:如果event.key == pygame.K_ESCAPE:pygame.quit();sys.exit()cam.events(事件)screen.fill((0,0,0))face_list = [];face_color = [];深度= []对于对象中的obj:vert_list = [];screen_coords = []对于obj.verts中的x，y，z:x- = cam.pos [0];y- = cam.pos [1]; z- = cam.pos [2]x，z = rotate2d((x，z)，cam.rot [1])y，z = rotation2d((y，z)，cam.rot [0])vert_list + = [(x，y，z)]f = 200/zx，y = x * f，y * fscreen_coords + = [(cx + int(x)，cy + int(y))]对于范围内的f(len(obj.faces)):脸= obj.faces [f]on_screen = False对于我的脸:x，y = screen_coords [i]如果vert_list [i] [2]＞ 0且x＞ 0且x ＜w且y＞ 0且y ＜h:on_screen = True；休息如果在屏幕上:coords = [screen_coords [i] for i in face]face_list + = [坐标]face_color + = [obj.colors [f]]深度+ = [sum(sum(sum(vert_list [j] [i] for face in j))** 2 for i in range(3))]]顺序=已排序(范围(len(face_list))，key = lambda i:depth [i]，reverse = 1)对我来说:尝试:pygame.draw.polygon(screen，face_color [i]，face_list [i])除了:通过键= pygame.key.get_pressed()pygame.display.flip()cam.update(dt，key) 我的问题是，当 cam.pos 距离对象至少7.5时，四面体部分会通过两侧的立方体显示出来:
如您所见，四面体本应埋在立方体下，但仍在显示.有人可以建议对代码进行编辑，以阻止四面体通过任何对象显示吗?
您实际尝试做的是按照
但是请注意，如果面彼此靠近，则仍然可能会出现问题(例如，将面覆盖在同一平面中).那不是一个精确的算法.它不是为触摸"对象而设计的.
I copied a code off YouTube recently, about 3d graphics in Python without the use of 3D modules, like OpenGL. The video worked with only cubes, so I tried adding a tetrahedron to the shapes, and things started popping up where they weren't supposed to. The code is as follows:
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),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)):
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]
class Tetrahedron:
faces = (1,2,3),(0,1,2),(0,1,3),(0,2,3)
colors = (255,0,0),(255,128,0),(255,255,0),(255,255,255)
def __init__(self,pos=(0,0,0),v0=(0,0,.866),v1=(-.866,-1,-1),v2=(-.866,1,-1),v3=(.866,0,-1)):
self.vertices = (v0,v1,v2,v3)
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)
objects = [Cube((0,0,0)),Cube((0,0,2)),Tetrahedron((0,0,1))]
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] for j in face)**2 for i in range(3))]
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)
My problem is that the tetrahedron part is showing up through the cubes on either side, when the cam.pos is at least 7.5 away from the object:
As you can see, the tetrahedron is supposed to be buried under the cube, but it's still showing up. Can someone please suggest an edit to the code which will stop the tetrahedron from showing up through any objects?
What you actually try to do is to sort the faces by the square of the Euclidean distance to the vertices of the face.
But sum(vert_list[j][i] for j in face)**2 does not compute the square of the euclidean distance. It computes the square of the sum of the components of a coordinate. The square of the euclidean distance is
vert_list[j][0]**2 + vert_list[j][1]**2 + vert_list[j][2]**2
That is not the same as
(vert_list[j][0] + vert_list[j][1] + vert_list[j][2])**2
Furthermore you do not take into account the number of vertices of a face, because the squared distances are summed.
Note, the faces of the cube are quads and have 4 vertices, but the faces of the tetrahedron are triangles and have 3 vertices.
Correct the computation of the squared distance and divide by the number of vertices, to solve the issue:
depth += [sum(sum(vert_list[j][i] for j in face)**2 for i in range(3))]
depth += [sum(sum(vert_list[j][i]**2 for i in range(3)) for j in face) / len(face)]
But note, if faces are close to another there still may occur an issue (e.g. covering faces in the same plane). That is not an exact algorithm. It is not designed for "touching" objects.
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