python - 如何对凹面多边形进行三角剖分？

Question

我刚刚开始图形编程，并尝试使用实现Delaunay算法的opencv的Subdiv2D类对凹面进行三角剖分。

我的代码进一步在下面产生以下输出，其中红线标记生成的三角形。到现在为止还挺好。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。

我可以想到的一种方法是计算每个三角形的质心，然后测试其是否在多边形内。但是...这真的是该算法的方法吗？

# -*- 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()

Answer 1

第27行的triangles = subdiv.getTriangleList()将生成4个三角形，其中包括不需要的三角形。

尽管不理想，但将第32行上的for t in triangles:更改为for t in triangles[:3]: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()

尽管这解决了问题，但不是理想的。此解决方案不考虑更多的三角形，仅解决了症状，而不是问题的根源。