Pygame中Marching Squares可视化无输出问题求助

我尝试在Pygame中使用Marching Squares算法绘制心形的隐式方程，已实现该算法但未绘制出任何图形，希望排查原因。

代码实现如下：

import pygame

w = 500
h = 500


grid = []
for i in range(-h//2, h//2):
    tempo = []
    for j in range(-w//2, w//2):
        tempo.append((i**2 + j**2 - 1)**3 - i**2 * j**3)
    grid.append(tempo)
    print(i)


def Bisection_Method(a, b, t, state, thresh = 0.001):
    if state:
        a -= w/2
        b -= w/2
    else:
        a -= h/2
        b -= h/2

    mid = (a + b)/2
    while abs(b - a) >= thresh:
        a1 = 0
        k1 = 0
        if state:
            i = a
            r = mid
            j = t

            a1 = (i**2 + j**2 - 1)**3 - i**2 * j**3
            k1 = (r**2 + j**2 - 1)**3 - r**2 * j**3
        else:
            i = t
            r = mid
            j = a
            a1 = (i**2 + j**2 - 1)**3 - i**2 * j**3
            k1 = (i**2 + r**2 - 1)**3 - i**2 * r**3)


        if(k1 == 0):
            return mid
        
        mid = (a + b)/2

        if(a1 * k1 < 0):
            b = mid
        else:
            a = mid
    if state:
        mid += w/2
    else:
        mid += h/2

    return mid


def MarchingSquares(i1, j1, i2, j2, i3, j3, i4, j4, plane):
    finalP1 = pygame.math.Vector2(float('inf'), float('inf'))
    finalP2 = pygame.math.Vector2(float('inf'), float('inf'))
    finalP3 = pygame.math.Vector2(float('inf'), float('inf'))
    finalP4 = pygame.math.Vector2(float('inf'), float('inf'))

    if((plane[i1][j1] < 0 and plane[i2][j2] > 0 and plane[i3][j3] > 0 and plane[i4][j4] > 0) or (plane[i1][j1] > 0 and plane[i2][j2] < 0 and plane[i3][j3] < 0 and plane[i4][j4] < 0)):
        finalP1 = pygame.math.Vector2(Bisection_Method(j1, j2, i1, True), i1)
        finalP2 = pygame.math.Vector2(j1, Bisection_Method(i1, i3, j1, False))
    elif((plane[i1][j1] > 0 and plane[i2][j2] < 0 and plane[i3][j3] > 0 and plane[i4][j4] > 0) or (plane[i1][j1] < 0 and plane[i2][j2] > 0 and plane[i3][j3] < 0 and plane[i4][j4] < 0)):
        finalP1 = pygame.math.Vector2(Bisection_Method(j1, j2, i1, True), i1)
        finalP2 = pygame.math.Vector2(j2, Bisection_Method(i4, i2, j2, False))
    elif((plane[i1][j1] > 0 and plane[i2][j2] > 0 and plane[i3][j3] < 0 and plane[i4][j4] > 0) or (plane[i1][j1] < 0 and plane[i2][j2] < 0 and plane[i3][j3] > 0 and plane[i4][j4] < 0)):
        finalP1 = pygame.math.Vector2(Bisection_Method(j3, j4, i3, True), i3)
        finalP2 = pygame.math.Vector2(j3, Bisection_Method(i1, i3, j3, False))  
    elif((plane[i1][j1] > 0 and plane[i2][j2] > 0 and plane[i3][j3] > 0 and plane[i4][j4] < 0) or (plane[i1][j1] < 0 and plane[i2][j2] < 0 and plane[i3][j3] < 0 and plane[i4][j4] > 0)):
        finalP1 = pygame.math.Vector2(Bisection_Method(j3, j4, i4, True), i4)
        finalP2 = pygame.math.Vector2(j4, Bisection_Method(i4, i2, j4, False))  
    elif((plane[i1][j1] > 0 and plane[i2][j2] > 0 and plane[i3][j3] < 0 and plane[i4][j4] < 0) or (plane[i1][j1] < 0 and plane[i2][j2] < 0 and plane[i3][j3] > 0 and plane[i4][j4] > 0)):
        finalP1 = pygame.math.Vector2(j1, Bisection_Method(i1, i3, j1, False))
        finalP2 = pygame.math.Vector2(j2, Bisection_Method(i4, i2, j2, False))
    elif((plane[i1][j1] > 0 and plane[i2][j2] > 0 and plane[i3][j3] > 0 and plane[i4][j4] < 0) or (plane[i1][j1] < 0 and plane[i2][j2] > 0 and plane[i3][j3] < 0 and plane[i4][j4] > 0)):
        finalP1 = pygame.math.Vector2(Bisection_Method(j1, j2, i1, True), i1)
        finalP2 = pygame.math.Vector2(Bisection_Method(j3, j4, i3, True), i3)
    elif((plane[i1][j1] < 0 and plane[i2][j2] > 0 and plane[i3][j3] > 0 and plane[i4][j4] < 0) or (plane[i1][j1] > 0 and plane[i2][j2] < 0 and plane[i3][j3] < 0 and plane[i4][j4] > 0)):
        i = (i1 + i3 - h)/2
        j = (j1 + j3 - w)/2

        state = (i**2 + j**2 - 1)**3 - i**2 * j**3
        if((state < 0 and plane[i1][j1] < 0) or (state > 0 and plane[i1][j1] > 0)):
            finalP1 = pygame.math.Vector2(j1, Bisection_Method(i1, i3, j1, False))
            finalP2 = pygame.math.Vector2(Bisection_Method(j3, j4, i3, True), i3)
            finalP3 = pygame.math.Vector2(Bisection_Method(j1, j2, i1, True), i1)
            finalP4 = pygame.math.Vector2(j4, Bisection_Method(i2, i4, j4, False))
        else:
            finalP2 = pygame.math.Vector2(j1, Bisection_Method(i1, i3, j1, False))
            finalP3 = pygame.math.Vector2(Bisection_Method(j3, j4, i3, True), i3)
            finalP1 = pygame.math.Vector2(Bisection_Method(j1, j2, i1, True), i1)
            finalP4 = pygame.math.Vector2(j4, Bisection_Method(i2, i4, j4, False))
    
    return finalP1, finalP2, finalP3, finalP4


t = []
for i in range(h - 1):
    for j in range(w - 1):
        P1, P2, P3, P4 = MarchingSquares(i, j, i, j + 1, i + 1, j, i + 1, j + 1, grid)

        t.append([P1, P2, P3, P4])
    print("marching {i}")
# pygame setup
pygame.init()
screen = pygame.display.set_mode((w, h))
clock = pygame.time.Clock()
running = True
dt = 0

while running:
    # poll for events
    # pygame.QUIT event means the user clicked X to close your window
    for event in pygame.event.get():
        if event.type == pygame.QUIT:
            running = False

    # fill the screen with a color to wipe away anything from last frame
    screen.fill("white")

    for x in t:
        pygame.draw.line(screen, "purple", x[0], x[1])

        if(x[2].x != float('inf')):
            pygame.draw.line(screen, "purple", x[2], x[3])

    # flip() the display to put your work on screen
    pygame.display.flip()

    # limits FPS to 60
    # dt is delta time in seconds since last frame, used for framerate-
    # independent physics.
    dt = clock.tick(60) / 1000


pygame.quit()

代码说明 #

• 先生成全屏幕网格，存储心形隐式方程在每个网格点的计算值
• 通过if-else判断Marching Squares的16种情况（部分合并判断）
• 使用二分法（Bisection_Method）作为根查找算法，state参数区分X轴/Y轴的插值计算
• 当前运行结果为空白窗口

内容的提问来源于stack exchange，提问作者NikoMolecule