python - 如何对凹多边形进行三角剖分?
问题描述
我刚刚开始使用图形编程并尝试使用Subdiv2D
实现 Delaunay 算法的 opencv 类对凹多边形进行三角剖分。
我的代码在下面进一步生成以下输出,其中红线标记了生成的三角形。到目前为止,一切都很好。然而,该算法还为多边形的凹面部分计算了一个三角形。
我在这里做错了什么,如何防止这种行为?我没有找到可以传递给Subdiv2D
函数的任何形式的约束。
我能想到的一种方法是计算每个三角形的质心,然后测试它是否在多边形内。但是......这真的是这个算法的方法吗?
# -*- coding: utf-8 -*-
import numpy as np
import cv2
width = 800
height = 600
img = np.zeros((height,width,3), np.uint8)
pts = np.array([[100,50],[200,300],[700,200],[500,100],[400,150]], np.int32)
rect = (0, 0, width, height)
def rect_contains(rect, point) :
if point[0] <rect[0] :
return False
elif point[1] < rect[1] :
return False
elif point[0] > rect[2] :
return False
elif point[1] > rect[3] :
return False
return True
def draw_triangeles(rect, points, img) :
subdiv = cv2.Subdiv2D()
subdiv.initDelaunay(rect)
for p in points:
subdiv.insert((p[0], p[1]))
triangles = subdiv.getTriangleList()
for t in triangles:
pt1 = (t[0], t[1])
pt2 = (t[2], t[3])
pt3 = (t[4], t[5])
if rect_contains(rect, pt1) and rect_contains(rect, pt2) and rect_contains(rect, pt3) :
cv2.line(img, pt1, pt2, (0,0,255), 2)
cv2.line(img, pt2, pt3, (0,0,255), 2)
cv2.line(img, pt3, pt1, (0,0,255), 2)
def draw_points(points, img):
for p in points:
cv2.circle(img, (p[0], p[1]), 2, (255,255,255), 2)
# Draw polygon
cv2.fillPoly(img, [pts], (0, 255, 0))
# Draw result of triangulation
draw_triangeles(rect, pts, img)
# Draw vertices on top
draw_points(pts, img)
#hull = cv2.convexHull(pts)
#cv2.polylines(img, [hull], True, (0, 255, 0))
cv2.imshow("image", img)
cv2.waitKey()
cv2.destroyAllWindows()
解决方案
triangles = subdiv.getTriangleList()
第 27 行将生成 4 个三角形,包括不需要的三角形。
虽然不理想,但更改for t in triangles:
为for t in triangles[:3]:
第 32 行将绘制除最后一个(不需要的)三角形之外的所有三角形。
完整代码:
# -*- coding: utf-8 -*-
import numpy as np
import cv2
width = 800
height = 600
img = np.zeros((height,width,3), np.uint8)
pts = np.array([[100,50],[200,300],[700,200],[500,100],[400,150]], np.int32)
rect = (0, 0, width, height)
def rect_contains(rect, point) :
if point[0] <rect[0] :
return False
elif point[1] < rect[1] :
return False
elif point[0] > rect[2] :
return False
elif point[1] > rect[3] :
return False
return True
def draw_triangeles(rect, points, img) :
subdiv = cv2.Subdiv2D()
subdiv.initDelaunay(rect)
for p in points:
subdiv.insert((p[0], p[1]))
triangles = subdiv.getTriangleList()
for t in triangles[:3]:
pt1 = (t[0], t[1])
pt2 = (t[2], t[3])
pt3 = (t[4], t[5])
if rect_contains(rect, pt1) and rect_contains(rect, pt2) and rect_contains(rect, pt3) :
cv2.line(img, pt1, pt2, (0,0,255), 2)
cv2.line(img, pt2, pt3, (0,0,255), 2)
cv2.line(img, pt3, pt1, (0,0,255), 2)
def draw_points(points, img):
for p in points:
cv2.circle(img, (p[0], p[1]), 2, (255,255,255), 2)
# Draw polygon
cv2.fillPoly(img, [pts], (0, 255, 0))
# Draw result of triangulation
draw_triangeles(rect, pts, img)
# Draw vertices on top
draw_points(pts, img)
#hull = cv2.convexHull(pts)
#cv2.polylines(img, [hull], True, (0, 255, 0))
cv2.imshow("image", img)
cv2.waitKey()
cv2.destroyAllWindows()
虽然这样解决了问题,但并不理想。这种解决方案没有考虑更多的三角形,只解决了症状,而不是问题的根源。