使用 python 中的 pygame 找到多条线的每个交点以创建游戏板
Finding every point of intersection of multiple lines using pygame in python for creation of game board
我需要在我的代码中找到每条线的交点。在这些点上，我想把我的棋子放进去。游戏的逻辑就像井字游戏，如果一个玩家将 3 个相同颜色的弹珠排成一排 he/she 可以抢到另一个玩家没有按顺序排列的棋子。
到目前为止我的代码：
import pygame
# Define some colors
BLACK = (0, 0, 0)
WHITE = (255, 255, 255)
GREEN = (0, 255, 0)
RED = (255, 0, 0)
# This sets the WIDTH and HEIGHT of each grid location
WIDTH = 20
HEIGHT = 20
# This sets the margin between each cell
MARGIN = 5
# Create a 2 dimensional array. A two dimensional
# array is simply a list of lists.
grid = []
for row in range(19):
# Add an empty array that will hold each cell
# in this row
grid.append([])
for column in range(19):
grid[row].append(0) # Append a cell
# Set row 1, cell 5 to one. (Remember rows and
# column numbers start at zero.)
grid[1][5] = 1
pygame.init()
WINDOW_SIZE = [800, 600]
screen = pygame.display.set_mode(WINDOW_SIZE)
pygame.display.set_caption("Array Backed Grid")
done = False
clock = pygame.time.Clock()
while not done:
# Set the screen background
screen.fill(BLACK)
# Draw the grid
for row in range(19):
for column in range(19):
color = WHITE
if grid[row][column] == 1:
color = GREEN
board_lines = [
( 13,15,462,15 ), ( 13,469,462,469 ), #lin1 and line2,outer rect
( 62,86,409,86 ), ( 62,389,409,389 ), #line3 and l4,mid reect
( 114,186,360,186 ), ( 114,318,360,318 ), #line5,l6,internl rect
( 13,15,13,469 ), ( 462,12,462,469 ), #line9,l10,left and right sides
( 62,86,62,389 ), ( 409,85,409,389 ), #l7,l8left and right sides
( 114,186,114,316), ( 360,187,360,318 ), #l11,lin12left and right sides
( 237,15,237,186 ), ( 237,469,237,320 ), #upper V.line,lowerV
( 13,242,113,242 ), ( 360,242,462,242 ) #rIGHT LEFT hoRIZONTAL LINE
]
for line in board_lines:
line_from = ( line[0], line[1] )
line_to = ( line[2], line[3] )
pygame.draw.line( screen, RED, line_from, line_to, 3)
# Limit to 60 frames per second
clock.tick(60)
pygame.display.flip()
pygame.quit()
以下函数计算由点 (P0、P1) 和 (Q0、Q1) 给出的 2 条线的交点：
def lineLineIntersect(P0, P1, Q0, Q1):
d = (P1[0]-P0[0]) * (Q1[1]-Q0[1]) + (P1[1]-P0[1]) * (Q0[0]-Q1[0])
if d == 0:
return None
t = ((Q0[0]-P0[0]) * (Q1[1]-Q0[1]) + (Q0[1]-P0[1]) * (Q0[0]-Q1[0])) / d
u = ((Q0[0]-P0[0]) * (P1[1]-P0[1]) + (Q0[1]-P0[1]) * (P0[0]-P1[0])) / d
if 0 <= t <= 1 and 0 <= u <= 1:
return round(P1[0] * t + P0[0] * (1-t)), round(P1[1] * t + P0[1] * (1-t))
return None
算法有详细解释，在的回答中：
P ... point on the 1. line
R ... normalized direction of the 1. line
Q ... point on the 2. line
S ... normalized direction of the 2. line
alpha ... angle between Q-P and R
beta ... angle between R and S
gamma = 180° - alpha - beta
h = | Q - P | * sin(alpha)
u = h / sin(beta)
t = | Q - P | * sin(gamma) / sin(beta)
t = dot(Q-P, (S.y, -S.x)) / dot(R, (S.y, -S.x)) = determinant(mat2(Q-P, S)) / determinant(mat2(R, S))
u = dot(Q-P, (R.y, -R.x)) / dot(R, (S.y, -S.x)) = determinant(mat2(Q-P, R)) / determinant(mat2(R, S))
X = P + R * t = Q + S * u
您必须评估一条线段是否与任何其他线段相交。通过使用函数 lineLineIntersect:
遍历嵌套循环中的线并找到线与除自身以外的任何其他线的交集
intersectionPoints = []
for i, line1 in enumerate(board_lines):
for line2 in board_lines[i:]:
isectP = lineLineIntersect(line1[:2], line1[2:], line2[:2], line2[2:])
if isectP:
intersectionPoints.append(isectP)
在交点画圆：
for isectP in intersectionPoints:
pygame.draw.circle(screen, GREEN, isectP, 5)
看例子：
import pygame
import math
def lineLineIntersect(P0, P1, Q0, Q1):
d = (P1[0]-P0[0]) * (Q1[1]-Q0[1]) + (P1[1]-P0[1]) * (Q0[0]-Q1[0])
if d == 0:
return None
t = ((Q0[0]-P0[0]) * (Q1[1]-Q0[1]) + (Q0[1]-P0[1]) * (Q0[0]-Q1[0])) / d
u = ((Q0[0]-P0[0]) * (P1[1]-P0[1]) + (Q0[1]-P0[1]) * (P0[0]-P1[0])) / d
if 0 <= t <= 1 and 0 <= u <= 1:
return round(P1[0] * t + P0[0] * (1-t)), round(P1[1] * t + P0[1] * (1-t))
return None
board_lines = [
( 13,15,462,15 ), ( 13,469,462,469 ), #lin1 and line2,outer rect
( 62,86,409,86 ), ( 62,389,409,389 ), #line3 and l4,mid reect
( 114,186,360,186 ), ( 114,318,360,318 ), #line5,l6,internl rect
( 13,15,13,469 ), ( 462,12,462,469 ), #line9,l10,left and right sides
( 62,86,62,389 ), ( 409,85,409,389 ), #l7,l8left and right sides
( 114,186,114,316), ( 360,187,360,318 ), #l11,lin12left and right sides
( 237,15,237,186 ), ( 237,469,237,320 ), #upper V.line,lowerV
( 13,242,113,242 ), ( 360,242,462,242 ) #rIGHT LEFT hoRIZONTAL LINE
]
pygame.init()
intersectionPoints = []
for i, line1 in enumerate(board_lines):
for line2 in board_lines[i:]:
isectP = lineLineIntersect(line1[:2], line1[2:], line2[:2], line2[2:])
if isectP:
intersectionPoints.append(isectP)
# Define some colors
BLACK = (0, 0, 0)
WHITE = (255, 255, 255)
GREEN = (0, 255, 0)
RED = (255, 0, 0)
# This sets the WIDTH and HEIGHT of each grid location
WIDTH = 20
HEIGHT = 20
# This sets the margin between each cell
MARGIN = 5
# Create a 2 dimensional array. A two dimensional
# array is simply a list of lists.
grid = []
for row in range(19):
# Add an empty array that will hold each cell
# in this row
grid.append([])
for column in range(19):
grid[row].append(0) # Append a cell
# Set row 1, cell 5 to one. (Remember rows and
# column numbers start at zero.)
grid[1][5] = 1
WINDOW_SIZE = [800, 600]
screen = pygame.display.set_mode(WINDOW_SIZE)
pygame.display.set_caption("Array Backed Grid")
done = False
clock = pygame.time.Clock()
while not done:
for event in pygame.event.get():
if event.type == pygame.QUIT:
done = True
# Set the screen background
screen.fill(BLACK)
# Draw the grid
for row in range(19):
for column in range(19):
color = WHITE
if grid[row][column] == 1:
color = GREEN
for line in board_lines:
pygame.draw.line(screen, RED, line[:2], line[2:], 3)
for isectP in intersectionPoints:
pygame.draw.circle(screen, GREEN, isectP, 5)
# Limit to 60 frames per second
clock.tick(60)
pygame.display.flip()
pygame.quit()
我需要在我的代码中找到每条线的交点。在这些点上，我想把我的棋子放进去。游戏的逻辑就像井字游戏，如果一个玩家将 3 个相同颜色的弹珠排成一排 he/she 可以抢到另一个玩家没有按顺序排列的棋子。
到目前为止我的代码：
import pygame
# Define some colors
BLACK = (0, 0, 0)
WHITE = (255, 255, 255)
GREEN = (0, 255, 0)
RED = (255, 0, 0)
# This sets the WIDTH and HEIGHT of each grid location
WIDTH = 20
HEIGHT = 20
# This sets the margin between each cell
MARGIN = 5
# Create a 2 dimensional array. A two dimensional
# array is simply a list of lists.
grid = []
for row in range(19):
# Add an empty array that will hold each cell
# in this row
grid.append([])
for column in range(19):
grid[row].append(0) # Append a cell
# Set row 1, cell 5 to one. (Remember rows and
# column numbers start at zero.)
grid[1][5] = 1
pygame.init()
WINDOW_SIZE = [800, 600]
screen = pygame.display.set_mode(WINDOW_SIZE)
pygame.display.set_caption("Array Backed Grid")
done = False
clock = pygame.time.Clock()
while not done:
# Set the screen background
screen.fill(BLACK)
# Draw the grid
for row in range(19):
for column in range(19):
color = WHITE
if grid[row][column] == 1:
color = GREEN
board_lines = [
( 13,15,462,15 ), ( 13,469,462,469 ), #lin1 and line2,outer rect
( 62,86,409,86 ), ( 62,389,409,389 ), #line3 and l4,mid reect
( 114,186,360,186 ), ( 114,318,360,318 ), #line5,l6,internl rect
( 13,15,13,469 ), ( 462,12,462,469 ), #line9,l10,left and right sides
( 62,86,62,389 ), ( 409,85,409,389 ), #l7,l8left and right sides
( 114,186,114,316), ( 360,187,360,318 ), #l11,lin12left and right sides
( 237,15,237,186 ), ( 237,469,237,320 ), #upper V.line,lowerV
( 13,242,113,242 ), ( 360,242,462,242 ) #rIGHT LEFT hoRIZONTAL LINE
]
for line in board_lines:
line_from = ( line[0], line[1] )
line_to = ( line[2], line[3] )
pygame.draw.line( screen, RED, line_from, line_to, 3)
# Limit to 60 frames per second
clock.tick(60)
pygame.display.flip()
pygame.quit()
以下函数计算由点 (P0、P1) 和 (Q0、Q1) 给出的 2 条线的交点：
def lineLineIntersect(P0, P1, Q0, Q1):
d = (P1[0]-P0[0]) * (Q1[1]-Q0[1]) + (P1[1]-P0[1]) * (Q0[0]-Q1[0])
if d == 0:
return None
t = ((Q0[0]-P0[0]) * (Q1[1]-Q0[1]) + (Q0[1]-P0[1]) * (Q0[0]-Q1[0])) / d
u = ((Q0[0]-P0[0]) * (P1[1]-P0[1]) + (Q0[1]-P0[1]) * (P0[0]-P1[0])) / d
if 0 <= t <= 1 and 0 <= u <= 1:
return round(P1[0] * t + P0[0] * (1-t)), round(P1[1] * t + P0[1] * (1-t))
return None
算法有详细解释，在
P ... point on the 1. line
R ... normalized direction of the 1. line
Q ... point on the 2. line
S ... normalized direction of the 2. line
alpha ... angle between Q-P and R
beta ... angle between R and S
gamma = 180° - alpha - beta
h = | Q - P | * sin(alpha)
u = h / sin(beta)
t = | Q - P | * sin(gamma) / sin(beta)
t = dot(Q-P, (S.y, -S.x)) / dot(R, (S.y, -S.x)) = determinant(mat2(Q-P, S)) / determinant(mat2(R, S))
u = dot(Q-P, (R.y, -R.x)) / dot(R, (S.y, -S.x)) = determinant(mat2(Q-P, R)) / determinant(mat2(R, S))
X = P + R * t = Q + S * u
您必须评估一条线段是否与任何其他线段相交。通过使用函数 lineLineIntersect:
intersectionPoints = []
for i, line1 in enumerate(board_lines):
for line2 in board_lines[i:]:
isectP = lineLineIntersect(line1[:2], line1[2:], line2[:2], line2[2:])
if isectP:
intersectionPoints.append(isectP)
在交点画圆：
for isectP in intersectionPoints:
pygame.draw.circle(screen, GREEN, isectP, 5)
看例子：
import pygame
import math
def lineLineIntersect(P0, P1, Q0, Q1):
d = (P1[0]-P0[0]) * (Q1[1]-Q0[1]) + (P1[1]-P0[1]) * (Q0[0]-Q1[0])
if d == 0:
return None
t = ((Q0[0]-P0[0]) * (Q1[1]-Q0[1]) + (Q0[1]-P0[1]) * (Q0[0]-Q1[0])) / d
u = ((Q0[0]-P0[0]) * (P1[1]-P0[1]) + (Q0[1]-P0[1]) * (P0[0]-P1[0])) / d
if 0 <= t <= 1 and 0 <= u <= 1:
return round(P1[0] * t + P0[0] * (1-t)), round(P1[1] * t + P0[1] * (1-t))
return None
board_lines = [
( 13,15,462,15 ), ( 13,469,462,469 ), #lin1 and line2,outer rect
( 62,86,409,86 ), ( 62,389,409,389 ), #line3 and l4,mid reect
( 114,186,360,186 ), ( 114,318,360,318 ), #line5,l6,internl rect
( 13,15,13,469 ), ( 462,12,462,469 ), #line9,l10,left and right sides
( 62,86,62,389 ), ( 409,85,409,389 ), #l7,l8left and right sides
( 114,186,114,316), ( 360,187,360,318 ), #l11,lin12left and right sides
( 237,15,237,186 ), ( 237,469,237,320 ), #upper V.line,lowerV
( 13,242,113,242 ), ( 360,242,462,242 ) #rIGHT LEFT hoRIZONTAL LINE
]
pygame.init()
intersectionPoints = []
for i, line1 in enumerate(board_lines):
for line2 in board_lines[i:]:
isectP = lineLineIntersect(line1[:2], line1[2:], line2[:2], line2[2:])
if isectP:
intersectionPoints.append(isectP)
# Define some colors
BLACK = (0, 0, 0)
WHITE = (255, 255, 255)
GREEN = (0, 255, 0)
RED = (255, 0, 0)
# This sets the WIDTH and HEIGHT of each grid location
WIDTH = 20
HEIGHT = 20
# This sets the margin between each cell
MARGIN = 5
# Create a 2 dimensional array. A two dimensional
# array is simply a list of lists.
grid = []
for row in range(19):
# Add an empty array that will hold each cell
# in this row
grid.append([])
for column in range(19):
grid[row].append(0) # Append a cell
# Set row 1, cell 5 to one. (Remember rows and
# column numbers start at zero.)
grid[1][5] = 1
WINDOW_SIZE = [800, 600]
screen = pygame.display.set_mode(WINDOW_SIZE)
pygame.display.set_caption("Array Backed Grid")
done = False
clock = pygame.time.Clock()
while not done:
for event in pygame.event.get():
if event.type == pygame.QUIT:
done = True
# Set the screen background
screen.fill(BLACK)
# Draw the grid
for row in range(19):
for column in range(19):
color = WHITE
if grid[row][column] == 1:
color = GREEN
for line in board_lines:
pygame.draw.line(screen, RED, line[:2], line[2:], 3)
for isectP in intersectionPoints:
pygame.draw.circle(screen, GREEN, isectP, 5)
# Limit to 60 frames per second
clock.tick(60)
pygame.display.flip()
pygame.quit()