多边形的孔

我需要创建一个立方体的3D模型,在一个面的中心打出一个圆形孔,完全穿过立方体到达另一侧.我能够为面孔和孔生成顶点.

四个面(不受孔影响)可以建模为单个三角形条.孔的内部也可以建模为单个三角形条.

如何为有孔的面生成索引缓冲区？是否有标准算法来执行此操作？

我正在使用Direct3D,但欢迎来自其他地方的想法.

要生成所需的索引缓冲区,您可以这样做.在2D中将所讨论的面思考为具有顶点(±1,±1)的正方形,并将孔作为圆形在中间.

您沿着圆的边缘行走,将其划分为若干段.

对于每个顶点,将其投影到周围的正方形上(x/M,y/M),其中M是max(abs(x),abs(y)).M是最大坐标的绝对值,因此这将缩放(x,y),使最大坐标为±1.

这一行你也分成了一些段.

成对连接的两个后续行的段作为面.

这是一个示例,将圆圈细分为64个段,每个射线划分为8个段.您可以选择符合要求的数字.

alt text http://pici.se/pictures/AVhcssRRz.gif

这是一些Python代码,用于演示:

from math import sin, cos, pi
from itertools import izip

def pairs(iterable):
    """Yields the previous and the current item on each iteration.
    """
    last = None
    for item in iterable:
        if last is not None:
            yield last, item
        last = item

def circle(radius, subdiv):
    """Yields coordinates of a circle.
    """
    for angle in xrange(0,subdiv+1):
        x = radius * cos(angle * 2 * pi / subdiv)
        y = radius * sin(angle * 2 * pi / subdiv)
        yield x, y

def line(x0,y0,x1,y1,subdiv):
    """Yields coordinates of a line.
    """
    for t in xrange(subdiv+1):
        x = (subdiv - t)*x0 + t*x1
        y = (subdiv - t)*y0 + t*y1
        yield x/subdiv, y/subdiv

def tesselate_square_with_hole((x,y),(w,h), radius=0.5, subdiv_circle=64, subdiv_ray=8):
    """Yields quads of a tesselated square with a circluar hole.
    """
    for (x0,y0),(x1,y1) in pairs(circle(radius,subdiv_circle)):
        M0 = max(abs(x0),abs(y0))
        xM0, yM0 = x0/M0, y0/M0

        M1 = max(abs(x1),abs(y1))
        xM1, yM1 = x1/M1, y1/M1

        L1 = line(x0,y0,xM0,yM0,subdiv_ray)
        L2 = line(x1,y1,xM1,yM1,subdiv_ray)
        for ((xa,ya),(xb,yb)),((xc,yc),(xd,yd)) in pairs(izip(L1,L2)):
            yield ((x+xa*w/2,y+ya*h/2),
                   (x+xb*w/2,y+yb*h/2),
                   (x+xc*w/2,y+yc*h/2),
                   (x+xd*w/2,y+yd*h/2))


import pygame
def main():
    """Simple pygame program that displays the tesselated figure.
    """
    print('Calculating faces...')
    faces = list(tesselate_square_with_hole((150,150),(200,200),0.5,64,8))
    print('done')

    pygame.init()
    pygame.display.set_mode((300,300))
    surf = pygame.display.get_surface()
    running = True

    while running:
        need_repaint = False
        for event in pygame.event.get() or [pygame.event.wait()]:
            if event.type == pygame.QUIT:
                running = False
            elif event.type in (pygame.VIDEOEXPOSE, pygame.VIDEORESIZE):
                need_repaint = True
        if need_repaint:
            print('Repaint')
            surf.fill((255,255,255))
            for pa,pb,pc,pd in faces:
                # draw a single quad with corners (pa,pb,pd,pc)
                pygame.draw.aalines(surf,(0,0,0),True,(pa,pb,pd,pc),1)
            pygame.display.flip()

try:
    main()
finally:
    pygame.quit()