Pygame：如何将分离轴定理 (SAT) 应用于旋转正方形？
Pygame: How do I apply Separating Axis Theorem (SAT) to Rotating Squares?
我不想要代码（我真的想要代码），但是有人可以向我解释如何创建对角线以查看是否有间隙吗？我知道我们必须使用矢量，但我不知道如何使用 python
所以，使用分离轴定理的逻辑，如果你不能在 2 个正方形之间画一条线，那么它们就会重叠和碰撞。我做了一些接近的东西，它不完美但很接近，我也没有考虑正方形的旋转但是如果你找到一种方法来找到正方形的 vertices/corners ，那么这很容易工作。我的做法是把方块变成线，然后直接在方块的中间和方块之间的线的法线处画一条线，有点乱，但是一看就明白了。然后我使用 line intersecting maths 来查找它们是否相交。
import pygame
from pygame.locals import *
from pygame import Vector2
pygame.init()
screen = pygame.display.set_mode((500,500))
#check if 2 lines are intersecting
def LineIntersect(line1, line2):
#the math is from wikipedia
x1 = line1[0].x
y1 = line1[0].y
x2 = line1[1].x
y2 = line1[1].y
x3 = line2[0].x
y3 = line2[0].y
x4 = line2[1].x
y4 = line2[1].y
den = (x1 - x2) * (y3 - y4) - (y1 - y2) * (x3 - x4)
if den == 0:
return
t = ((x1 - x3) * (y3 - y4) - (y1 - y3) * (x3 - x4)) / den
u = -((x1 - x2) * (y1 - y3) - (y1 - y2) * (x1 - x3)) / den
if t > 0 and t < 1 and u > 0 and u < 1:
pt = Vector2()
pt.x = x1 + t * (x2 - x1)
pt.y = y1 + t * (y2 - y1)
return pt
return
#class for sqaure
class square:
def __init__(self,x,y,w):
self.x = x
self.y = y
self.w = w
self.centerx = self.x + w//2
self.centery = self.y + w//2
self.col = (255,0,0)
def Draw(self, outline = False):
if outline:
self.Outline()
else:
pygame.draw.rect(screen,self.col,(self.x,self.y,self.w,self.w))
def Outline(self):
for point1, point2 in self.Lines():
pygame.draw.line(screen,sqr2.col,point1,point2,1)
#get the lines that make up the square, the outline/perameter
def Lines(self):
lines = []
lines.append((Vector2(self.x,self.y),Vector2(self.x+self.w,self.y)))
lines.append((Vector2(self.x,self.y),Vector2(self.x,self.y + self.w)))
lines.append((Vector2(self.x + self.w,self.y + self.w),Vector2(self.x+self.w,self.y)))
lines.append((Vector2(self.x + self.w,self.y + self.w),Vector2(self.x,self.y + self.w)))
return lines
#draw a line inbetween the 2 squares
def DrawLineInBetween():
#draw a line between the 2 squares, get gradient
#to avoid divide by zero
if abs(sqr1.x - sqr2.x) == 0:
gradient = "infinity"
else:
#rise over run
#left - right = run
left = sqr1 if sqr1.x < sqr2.x else sqr2
right = sqr1 if left == sqr2 else sqr2
gradient = ((left.y - right.y)/abs(sqr1.x - sqr2.x))
#print("gradient:",gradient)
#get the middle point between the centers of the squares
middle = (max(sqr1.x + sqr1.w//2, sqr2.x + sqr2.w//2) - abs(sqr1.x - sqr2.x)//2,
max(sqr1.y + sqr1.w//2, sqr2.y + sqr2.w//2) - abs(sqr1.y - sqr2.y)//2)
#to avoid divide by 0
if gradient == 0:
point1 = Vector2(middle[0], middle[1] + 100)
point2 = Vector2(middle[0], middle[1] - 100)
elif gradient == "infinity":
point1 = Vector2(middle[0] - 100, middle[1])
point2 = Vector2(middle[0] + 100, middle[1])
else:
#get normal of line
gradient = -1/gradient
#print("normal:",gradient)
point1 = Vector2(middle[0] + 100, middle[1] + int(-100 * gradient))
point2 = Vector2(middle[0] - 100, middle[1] + int(100 * gradient))
#print(point1)
#print(point2)
#print(middle)
pygame.draw.line(screen,(0,255,0),point1,point2,1)
line = (point1, point2)
return line
sqr1 = square(100,100,50)
sqr2 = square(200,100,50)
Clock = pygame.time.Clock()
running = True
key = ""
while running:
screen.fill((0,0,0))
sqr1.Draw(outline=True)
sqr2.Draw()
line = DrawLineInBetween()
for sqr_line in sqr1.Lines():
pt = LineIntersect(line,sqr_line)
if pt:
pygame.draw.circle(screen,(0,255,255),(int(pt.x),int(pt.y)),5)
if key == "s":
sqr1.y += 1
elif key == "w":
sqr1.y -= 1
if key == "d":
sqr1.x += 1
if key == "a":
sqr1.x -= 1
pygame.display.update()
Clock.tick(60)
for e in pygame.event.get():
if e.type == pygame.QUIT:
pygame.quit()
running = False
if e.type == MOUSEBUTTONDOWN:
print(e.pos)
if e.type == KEYDOWN:
key = e.unicode
if e.type == KEYUP:
key = ""
旋转正方形：
在正方形 class 中添加了旋转变量，我使用 this answer 找到正方形的角，然后一旦我有了角，就使用线交叉。
这是新的 class:
#class for sqaure
class square:
def __init__(self,x,y,w):
self.x = x
self.y = y
self.w = w
self.centerx = self.x + w//2
self.centery = self.y + w//2
self.col = (255,0,0)
self.rotation_angle = 0
def Draw(self, outline = False):
if outline:
self.Outline()
else:
pygame.draw.rect(screen,self.col,(self.x,self.y,self.w,self.w))
#this used the normal coordinate of an unrotated square to find new coordinates of rotated sqaure
def GetCorner(self,tempX,tempY):
angle = math.radians(self.rotation_angle)
rotatedX = tempX*math.cos(angle) - tempY*math.sin(angle);
rotatedY = tempX*math.sin(angle) + tempY*math.cos(angle);
x = rotatedX + self.centerx;
y = rotatedY + self.centery;
return Vector2(x,y)
def Outline(self):
for point1, point2 in self.Lines():
pygame.draw.line(screen,sqr2.col,point1,point2,1)
#new lines method, only changed to GetCorner()
def Lines(self):
lines = []
top_left = self.GetCorner(self.x - self.centerx, self.y - self.centery)
top_right = self.GetCorner(self.x + self.w - self.centerx, self.y - self.centery)
bottom_left = self.GetCorner(self.x - self.centerx, self.y + self.w - self.centery)
bottom_right = self.GetCorner(self.x + self.w - self.centerx, self.y + self.w - self.centery)
lines.append((top_left,top_right))
lines.append((top_left,bottom_left))
lines.append((bottom_right,top_right))
lines.append((bottom_right,bottom_left))
return lines
#chnaged to this as rotation rotates around center, so need to update both x and centerx
def Move(self,x =None, y = None):
if x:
self.x += x
self.centerx += x
if y:
self.y += y
self.centery += y
#get the lines that make up the square, the outline/perameter
#def Lines(self):
#lines = []
#lines.append((Vector2(self.x,self.y),Vector2(self.x+self.w,self.y)))
#lines.append((Vector2(self.x,self.y),Vector2(self.x,self.y + self.w)))
#lines.append((Vector2(self.x + self.w,self.y + self.w),Vector2(self.x+self.w,self.y)))
#lines.append((Vector2(self.x + self.w,self.y + self.w),Vector2(self.x,self.y + self.w)))
#return lines
我不想要代码（我真的想要代码），但是有人可以向我解释如何创建对角线以查看是否有间隙吗？我知道我们必须使用矢量，但我不知道如何使用 python
所以，使用分离轴定理的逻辑，如果你不能在 2 个正方形之间画一条线，那么它们就会重叠和碰撞。我做了一些接近的东西，它不完美但很接近，我也没有考虑正方形的旋转但是如果你找到一种方法来找到正方形的 vertices/corners ，那么这很容易工作。我的做法是把方块变成线，然后直接在方块的中间和方块之间的线的法线处画一条线，有点乱，但是一看就明白了。然后我使用 line intersecting maths 来查找它们是否相交。
import pygame
from pygame.locals import *
from pygame import Vector2
pygame.init()
screen = pygame.display.set_mode((500,500))
#check if 2 lines are intersecting
def LineIntersect(line1, line2):
#the math is from wikipedia
x1 = line1[0].x
y1 = line1[0].y
x2 = line1[1].x
y2 = line1[1].y
x3 = line2[0].x
y3 = line2[0].y
x4 = line2[1].x
y4 = line2[1].y
den = (x1 - x2) * (y3 - y4) - (y1 - y2) * (x3 - x4)
if den == 0:
return
t = ((x1 - x3) * (y3 - y4) - (y1 - y3) * (x3 - x4)) / den
u = -((x1 - x2) * (y1 - y3) - (y1 - y2) * (x1 - x3)) / den
if t > 0 and t < 1 and u > 0 and u < 1:
pt = Vector2()
pt.x = x1 + t * (x2 - x1)
pt.y = y1 + t * (y2 - y1)
return pt
return
#class for sqaure
class square:
def __init__(self,x,y,w):
self.x = x
self.y = y
self.w = w
self.centerx = self.x + w//2
self.centery = self.y + w//2
self.col = (255,0,0)
def Draw(self, outline = False):
if outline:
self.Outline()
else:
pygame.draw.rect(screen,self.col,(self.x,self.y,self.w,self.w))
def Outline(self):
for point1, point2 in self.Lines():
pygame.draw.line(screen,sqr2.col,point1,point2,1)
#get the lines that make up the square, the outline/perameter
def Lines(self):
lines = []
lines.append((Vector2(self.x,self.y),Vector2(self.x+self.w,self.y)))
lines.append((Vector2(self.x,self.y),Vector2(self.x,self.y + self.w)))
lines.append((Vector2(self.x + self.w,self.y + self.w),Vector2(self.x+self.w,self.y)))
lines.append((Vector2(self.x + self.w,self.y + self.w),Vector2(self.x,self.y + self.w)))
return lines
#draw a line inbetween the 2 squares
def DrawLineInBetween():
#draw a line between the 2 squares, get gradient
#to avoid divide by zero
if abs(sqr1.x - sqr2.x) == 0:
gradient = "infinity"
else:
#rise over run
#left - right = run
left = sqr1 if sqr1.x < sqr2.x else sqr2
right = sqr1 if left == sqr2 else sqr2
gradient = ((left.y - right.y)/abs(sqr1.x - sqr2.x))
#print("gradient:",gradient)
#get the middle point between the centers of the squares
middle = (max(sqr1.x + sqr1.w//2, sqr2.x + sqr2.w//2) - abs(sqr1.x - sqr2.x)//2,
max(sqr1.y + sqr1.w//2, sqr2.y + sqr2.w//2) - abs(sqr1.y - sqr2.y)//2)
#to avoid divide by 0
if gradient == 0:
point1 = Vector2(middle[0], middle[1] + 100)
point2 = Vector2(middle[0], middle[1] - 100)
elif gradient == "infinity":
point1 = Vector2(middle[0] - 100, middle[1])
point2 = Vector2(middle[0] + 100, middle[1])
else:
#get normal of line
gradient = -1/gradient
#print("normal:",gradient)
point1 = Vector2(middle[0] + 100, middle[1] + int(-100 * gradient))
point2 = Vector2(middle[0] - 100, middle[1] + int(100 * gradient))
#print(point1)
#print(point2)
#print(middle)
pygame.draw.line(screen,(0,255,0),point1,point2,1)
line = (point1, point2)
return line
sqr1 = square(100,100,50)
sqr2 = square(200,100,50)
Clock = pygame.time.Clock()
running = True
key = ""
while running:
screen.fill((0,0,0))
sqr1.Draw(outline=True)
sqr2.Draw()
line = DrawLineInBetween()
for sqr_line in sqr1.Lines():
pt = LineIntersect(line,sqr_line)
if pt:
pygame.draw.circle(screen,(0,255,255),(int(pt.x),int(pt.y)),5)
if key == "s":
sqr1.y += 1
elif key == "w":
sqr1.y -= 1
if key == "d":
sqr1.x += 1
if key == "a":
sqr1.x -= 1
pygame.display.update()
Clock.tick(60)
for e in pygame.event.get():
if e.type == pygame.QUIT:
pygame.quit()
running = False
if e.type == MOUSEBUTTONDOWN:
print(e.pos)
if e.type == KEYDOWN:
key = e.unicode
if e.type == KEYUP:
key = ""
旋转正方形： 在正方形 class 中添加了旋转变量，我使用 this answer 找到正方形的角，然后一旦我有了角，就使用线交叉。
这是新的 class:
#class for sqaure
class square:
def __init__(self,x,y,w):
self.x = x
self.y = y
self.w = w
self.centerx = self.x + w//2
self.centery = self.y + w//2
self.col = (255,0,0)
self.rotation_angle = 0
def Draw(self, outline = False):
if outline:
self.Outline()
else:
pygame.draw.rect(screen,self.col,(self.x,self.y,self.w,self.w))
#this used the normal coordinate of an unrotated square to find new coordinates of rotated sqaure
def GetCorner(self,tempX,tempY):
angle = math.radians(self.rotation_angle)
rotatedX = tempX*math.cos(angle) - tempY*math.sin(angle);
rotatedY = tempX*math.sin(angle) + tempY*math.cos(angle);
x = rotatedX + self.centerx;
y = rotatedY + self.centery;
return Vector2(x,y)
def Outline(self):
for point1, point2 in self.Lines():
pygame.draw.line(screen,sqr2.col,point1,point2,1)
#new lines method, only changed to GetCorner()
def Lines(self):
lines = []
top_left = self.GetCorner(self.x - self.centerx, self.y - self.centery)
top_right = self.GetCorner(self.x + self.w - self.centerx, self.y - self.centery)
bottom_left = self.GetCorner(self.x - self.centerx, self.y + self.w - self.centery)
bottom_right = self.GetCorner(self.x + self.w - self.centerx, self.y + self.w - self.centery)
lines.append((top_left,top_right))
lines.append((top_left,bottom_left))
lines.append((bottom_right,top_right))
lines.append((bottom_right,bottom_left))
return lines
#chnaged to this as rotation rotates around center, so need to update both x and centerx
def Move(self,x =None, y = None):
if x:
self.x += x
self.centerx += x
if y:
self.y += y
self.centery += y
#get the lines that make up the square, the outline/perameter
#def Lines(self):
#lines = []
#lines.append((Vector2(self.x,self.y),Vector2(self.x+self.w,self.y)))
#lines.append((Vector2(self.x,self.y),Vector2(self.x,self.y + self.w)))
#lines.append((Vector2(self.x + self.w,self.y + self.w),Vector2(self.x+self.w,self.y)))
#lines.append((Vector2(self.x + self.w,self.y + self.w),Vector2(self.x,self.y + self.w)))
#return lines