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Coulombs Law: Protons atract each other

I'am working on a simulation of the Coulomb's Law with pygame, but I have a problem. When I start the Simulation an set two Protons, they attract each other. But there is more!
When I set an electron and a proton, they both start to "travel" with a constant distance to each other in the same direction.
Here is my code:
import pygame
import numpy as np
import math
pygame.init()
# window-settings
WIDTH, HEIGHT = 800, 800
WIN = pygame.display.set_mode((WIDTH, HEIGHT))
pygame.display.set_caption("Electric field simulation")
# constants
Pi = np.pi
epsilon0 = 8.85 * (10**(-12))
q = 1.6 * (10**-19)
# colors
WHITE = (255,255,255)
BLACK = (0,0,0)
BLUE = (100, 149, 237)
RED = (188, 39, 50)
class Charge:
TIMESTEP = 50000
def __init__(self, x, y, radius, color, q):
self.x = x
self.y = y
self.radius = radius
self.color = color
self.q = q
self.x_vel = 0
self.y_vel = 0
def draw(self, win):
pygame.draw.circle(win, self.color, (self.x, self.y), self.radius)
def attraction(self, other):
other_x, other_y = other.x, other.y
distance_x = other_x - self.x
distance_y = other_y - self.y
distance = math.sqrt(distance_x ** 2 + distance_y ** 2)
force = (1 / (4 * Pi * epsilon0)) * self.q * other.q / (distance ** 2)
theta = math.atan2(distance_y, distance_x)
force_x = math.cos(theta) * force
force_y = math.sin(theta) * force
return force_x, force_y
def update_position(self, charges):
total_fx = total_fy = 0
for charge in charges:
if self == charge:
continue
fx, fy = self.attraction(charge)
total_fx += fx
total_fy += fy
self.x_vel += total_fx / self.q * self.TIMESTEP
self.y_vel += total_fy / self.q * self.TIMESTEP
self.x += self.x_vel * self.TIMESTEP
self.y += self.y_vel * self.TIMESTEP
def main():
run = True
clock = pygame.time.Clock()
proton = Charge(200, 200, 10, RED, q)
electron = Charge(300, 200, 10, BLUE, -q)
charges = [electron, proton]
while run:
clock.tick(60)
WIN.fill(WHITE)
for event in pygame.event.get():
if event.type == pygame.QUIT:
run = False
if event.type == pygame.MOUSEBUTTONDOWN: # To set charges
if event.button == 1: # Sets positive charge
charges.append(Charge(pygame.mouse.get_pos()[0], pygame.mouse.get_pos()[1], 10, RED, q))
if event.button == 3: # Sets negitive charge
charges.append(Charge(pygame.mouse.get_pos()[0], pygame.mouse.get_pos()[1], 10, BLUE, -q))
for charge in charges:
charge.update_position(charges)
charge.draw(WIN)
pygame.display.update()
pygame.quit()
if __name__ == "__main__":
main()
I think the problem is the attraction-function, but I don't know how to solve it.

At the moment I have not the possibility to run your code but have you mixed up the direction of your force?
At least Wikipedia calculates r1-r2
Annother source of error might be the sin, cos etc. functions have you checked for your example that the calculated values are correct?
If I understand your code correct you update all positions one after eachother and apply the changes right away. Dependend on your application you might want to
Calculate all forces
Update all Values
Otherwise you have a multiple states of your system in just one time step.

Okay I solved the problem by calculating the direction of the force. With this I calculate at first the the force but return the absolute and then calculate the direction and speed.
Here is the code of my changes (I just changed something in the updating and attracting function):
def attraction(self, other):
other_x, other_y = other.x, other.y
distance_x = self.x - other_x
distance_y = self.y - other_y
distance = math.sqrt(distance_x ** 2 + distance_y ** 2)
if self.q != other.q and distance < 5:
return 0,0
force = (1 / (4 * Pi * epsilon0)) * self.q * other.q / (distance ** 2)
force_x = distance_x / distance*np.abs(force)
force_y = distance_y / distance*np.abs(force)
return force_x, force_y
def update_position(self, charges):
total_fx = total_fy = 0
for charge in charges:
if self == charge:
continue
fx, fy = self.attraction(charge)
total_fx += fx
total_fy += fy
self.x_vel += total_fx / self.q * self.TIMESTEP
self.y_vel += total_fy / self.q * self.TIMESTEP
if self != charge and self.q < 0 and self.q != charge.q:
x = abs(self.x - charge.x)
y = abs(self.y - charge.y)
self.direction = [x / np.sqrt((x ** 2) + (y ** 2)),y / np.sqrt((x ** 2) + (y ** 2))]
elif self != charge and self.q > 0 and self.q != charge.q:
x = abs(self.x - charge.x)
y = abs(self.y - charge.y)
self.direction = [-x / np.sqrt((x ** 2) + (y ** 2)), -y / np.sqrt((x ** 2) + (y ** 2))]
elif self != charge and self.q < 0 and self.q == charge.q:
x = abs(self.x - charge.x)
y = abs(self.y - charge.y)
self.direction = [-x / np.sqrt((x ** 2) + (y ** 2)), -y / np.sqrt((x ** 2) + (y ** 2))]
elif self != charge and self.q > 0 and self.q == charge.q:
x = abs(self.x - charge.x)
y = abs(self.y - charge.y)
self.direction = [x / np.sqrt((x ** 2) + (y ** 2)), y / np.sqrt((x ** 2) + (y ** 2))]
self.x += self.x_vel * self.TIMESTEP * self.direction[0]
self.y += self.y_vel * self.TIMESTEP * self.direction[1]
I know this code isn't that beautiful, but at first it works.

How to draw a dashed curved line with pygame?

I need to draw sine and cosine waves on a coordinate system exactly like in this picture. I did all the work well except I failed to represent dashed and curved line with pygame. I have smth similar to what I need, but how can I make it curved? Or how can I improve this to make it like pygame.draw.lines, not pygame.draw.line?
import pygame
import math
class Point:
# constructed using a normal tupple
def __init__(self, point_t = (0,0)):
self.x = float(point_t[0])
self.y = float(point_t[1])
# define all useful operators
def __add__(self, other):
return Point((self.x + other.x, self.y + other.y))
def __sub__(self, other):
return Point((self.x - other.x, self.y - other.y))
def __mul__(self, scalar):
return Point((self.x*scalar, self.y*scalar))
def __div__(self, scalar):
return Point((self.x/scalar, self.y/scalar))
def __len__(self):
return int(math.sqrt(self.x**2 + self.y**2))
# get back values in original tuple format
def get(self):
return (self.x, self.y)
def draw_dashed_line(surf, color, start_pos, end_pos, width=1, dash_length=4):
origin = Point(start_pos)
target = Point(end_pos)
displacement = target - origin
length = len(displacement)
slope = displacement.__div__(length)
for index in range(0, int(length/dash_length), 2):
start = origin + (slope * index * dash_length)
end = origin + (slope * (index + 1) * dash_length)
pygame.draw.line(surf, color, start.get(), end.get(), width)
pygame.init()
screen = pygame.display.set_mode((400, 300))
done = False
while not done:
draw_dashed_line(screen,(0,255,0),(0,0),(110,110))
for event in pygame.event.get():
if event.type == pygame.QUIT:
done = True
pygame.display.flip()

Write a function that operates similar as pygame.draw.line() but draws a dashed straight line. The function has an additional argument prev_line_len which indicates where the line segment is within a consecutive curve. Compute the Euclidean distance between the points and the Unit vector that points from the beginning of the line segment to its end. Distribute the strokes along the line:
def draw_dashed_line(surf, color, p1, p2, prev_line_len, dash_length=8):
dx, dy = p2[0]-p1[0], p2[1]-p1[1]
if dx == 0 and dy == 0:
return
dist = math.hypot(dx, dy)
dx /= dist
dy /= dist
step = dash_length*2
start = (int(prev_line_len) // step) * step
end = (int(prev_line_len + dist) // step + 1) * step
for i in range(start, end, dash_length*2):
s = max(0, start - prev_line_len)
e = min(start - prev_line_len + dash_length, dist)
if s < e:
ps = p1[0] + dx * s, p1[1] + dy * s
pe = p1[0] + dx * e, p1[1] + dy * e
pygame.draw.line(surf, color, pe, ps
Write another function that behaves similarly to pygame.draw.lines(), but uses the former function (draw_dashed_line) to draw the dashed curve. Calculate the length from the beginning of the curve to the beginning of each line segment and pass it to the function:
def draw_dashed_lines(surf, color, points, dash_length=8):
line_len = 0
for i in range(1, len(points)):
p1, p2 = points[i-1], points[i]
dist = math.hypot(p2[0]-p1[0], p2[1]-p1[1])
draw_dashed_line(surf, color, p1, p2, line_len, dash_length)
line_len += dist
Minimal example:
repl.it/#Rabbid76/DashedLine
import pygame
import math
def draw_dashed_line(surf, color, p1, p2, prev_line_len, dash_length=8):
dx, dy = p2[0]-p1[0], p2[1]-p1[1]
if dx == 0 and dy == 0:
return
dist = math.hypot(dx, dy)
dx /= dist
dy /= dist
step = dash_length*2
start = (int(prev_line_len) // step) * step
end = (int(prev_line_len + dist) // step + 1) * step
for i in range(start, end, dash_length*2):
s = max(0, start - prev_line_len)
e = min(start - prev_line_len + dash_length, dist)
if s < e:
ps = p1[0] + dx * s, p1[1] + dy * s
pe = p1[0] + dx * e, p1[1] + dy * e
pygame.draw.line(surf, color, pe, ps)
def draw_dashed_lines(surf, color, points, dash_length=8):
line_len = 0
for i in range(1, len(points)):
p1, p2 = points[i-1], points[i]
dist = math.hypot(p2[0]-p1[0], p2[1]-p1[1])
draw_dashed_line(surf, color, p1, p2, line_len, dash_length)
line_len += dist
pygame.init()
screen = pygame.display.set_mode((400, 300))
done = False
line = [(i, 150 + math.sin(math.radians(i*2)) * 100) for i in range(400)]
while not done:
for event in pygame.event.get():
if event.type == pygame.QUIT:
done = True
draw_dashed_lines(screen, (255, 255, 255), line)
pygame.display.flip()

Pygame: How do I apply Separating Axis Theorem (SAT) to Rotating Squares?

I don't want the code (I really do want the code), but can someone explain to me how I can create the diagonal line to see if there's a gap? I know we have to use vectors, but I don't know how to do that using python

So, using the logic of Separating Axis Theorem that if you cant draw a line in between 2 squares then they are overlapping and colliding. I made something close, its not perfect but its close, I also haven't accounted for rotation of squares but if you find a way to find the vertices/corners of the square, then this could easily work. The way i did it was that i turned the squares into lines and drew a line directly in the middle of the squares and at the normal of the line in between the squares, its a bit confusing but it makes sense once you see it. I then used line intersecting maths to find if they intersect.
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 = ""
doing rotating squares:
added rotation variable in square class, i used this answer to find the corners of the square, then once i have the corners, used the line intersetion.
Here is new 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

Problem with calculating line intersections

I am trying to display the points of intersecting lines, but the calculated points are between the actual intersectings.
(https://en.wikipedia.org/wiki/Line%E2%80%93line_intersection)
I have checked the formulars multiple times and used another formula for calculating the intersecting points x, y [x3+u*(x4-x3), y3+u*(y4-y3)] instead of [x1+t*(x2-x1), y1+t*(y2-y1)], but that just made the points somewhere really wrong
("d" is not referenced on the wikipedia page and is just the divisor for the formulars of t and u)
Function for calculating the intersection
def checkcol(self, startObs, endObs):
x1, y1 = startObs
x2, y2 = endObs
x3, y3 = run.lamp
x4, y4 = self.endpoint
d = (x1-x2)*(y3-y4)-(y1-y2)*(x3-x4)
t = ((x1-x3)*(y3-y4)-(y1-y3)*(x3-x4))/d
u = ((x1-x2)*(y1-y3)-(y1-y2)*(x1-x3))/d
if 0 < t < 1 and 1 > u > 0:
pygame.draw.circle(run.screen, pygame.Color('green'), (round(x1+t*(x2-x1)), round(y1+t*(y2-y1))), 3)
The whole code
import pygame
import sys
import math
import random as rd
class Obs(object):
def __init__(self, startp, endp):
self.startp = startp
self.endp = endp
def drawww(self):
pygame.draw.line(run.screen, pygame.Color('red'), (self.startp), (self.endp))
for ray in run.lines:
ray.checkcol(self.startp, self.endp)
class rays(object):
def __init__(self, endpoint):
self.width = 2
self.endpoint = endpoint
def draww(self):
pygame.draw.line(run.screen, pygame.Color('white'), run.lamp, self.endpoint, 2)
def moveEnd(self, xoff, yoff):
self.endpoint[0] += xoff
self.endpoint[1] += yoff
def checkcol(self, startObs, endObs):
x1, y1 = startObs
x2, y2 = endObs
x3, y3 = run.lamp
x4, y4 = self.endpoint
d = (x1-x2)*(y3-y4)-(y1-y2)*(x3-x4)
t = ((x1-x3)*(y3-y4)-(y1-y3)*(x3-x4))/d
u = ((x1-x2)*(y1-y3)-(y1-y2)*(x1-x3))/d
if 0 < t < 1 and 1 > u > 0:
pygame.draw.circle(run.screen, pygame.Color('green'), (round(x1+t*(x2-x1)), round(y1+t*(y2-y1))), 3)
class Control(object):
def __init__(self):
self.winw = 800
self.winh = 800
self.screen = pygame.display.set_mode((self.winw, self.winh))
self.fps = 60
self.clock = pygame.time.Clock()
self.lamp = [400, 400]
self.lampr = 13
self.lines = []
self.r = 10
self.Obs = [Obs((rd.randint(0, self.winw), rd.randint(0, self.winh)),
(rd.randint(0, self.winw), rd.randint(0, self.winh))) for i in range(5)]
self.done = False
def event_loop(self):
for event in pygame.event.get():
if event.type == pygame.QUIT:
self.done = True
elif event.type == pygame.KEYDOWN:
if event.key == pygame.K_F5:
self.__init__()
if pygame.mouse.get_pressed() == (1, 0, 0):
self.lamp = (pygame.mouse.get_pos())
for line in self.lines:
line.moveEnd(pygame.mouse.get_rel()[0], pygame.mouse.get_rel()[1])
def draw(self):
self.screen.fill((pygame.Color('black')))
pygame.draw.circle(self.screen, pygame.Color('white'), self.lamp, self.lampr)
for line in self.lines:
line.draww()
for obs in self.Obs:
obs.drawww()
def createlines(self):
self.lines.clear()
for angle in range(0, 361, 9):
self.lines.append(rays([self.lamp[0] + 1200 * math.cos(angle), self.lamp[1] + 1200 * math.sin(angle)]))
def main_loop(self):
while not self.done:
self.event_loop()
self.createlines()
self.draw()
pygame.display.update()
self.clock.tick(self.fps)
pygame.display.set_caption(f"Draw FPS: {self.clock.get_fps()}")
if __name__ == '__main__':
run = Control()
run.main_loop()
pygame.quit()
sys.exit()
Expected the points of intersecting to be at the actual points of intersection.

To find the intersection points of 2 rays or line segments in two-dimensional space, I use vector arithmetic and the following algorithm:
P ... point on the 1. line
R ... direction of the 1. line
Q ... point on the 2. line
S ... 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
See also Line–line intersection
If t == 1, then X = P + R. This can be used to assess whether the intersection is on a line segment.
If a line is defined through the 2 points L1 and L2, it can be defined that P = L1 and R = L2-L1. Therefore the point of intersection (X) lies on the line segment from L1 to L2 if 0 <= t <= 1.
The same relation applies to u and S.
The following function implements the above algorithm using pygame.math.Vector2 objects of the pygame.math module:
def intersect_line_line_vec2(startObs, endObs, origin, endpoint):
P = pygame.Vector2(startObs)
R = (endObs - P)
Q = pygame.Vector2(origin)
S = (endpoint - Q)
d = R.dot((S.y, -S.x))
if d == 0:
return None
t = (Q-P).dot((S.y, -S.x)) / d
u = (Q-P).dot((R.y, -R.x)) / d
if 0 <= t <= 1 and 0 <= u <= 1:
X = P + R * t
return (X.x, X.y)
return None
The same algorithm without the use of the pygame.math module, less readable but more or less the same:
def intersect_line_line(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 P1[0] * t + P0[0] * (1-t), P1[1] * t + P0[1] * (1-t)
return None
Applied to your code, this means:
class rays(object):
# [...]
def checkcol(self, startObs, endObs):
P = pygame.Vector2(startObs)
R = (endObs - P).normalize()
Q = pygame.Vector2(run.lamp)
S = (self.endpoint - Q).normalize()
d = R.dot((S.y, -S.x))
if R.dot((S.y, -S.x)) == 0:
return
t = (Q-P).dot((S.y, -S.x)) / d
u = (Q-P).dot((R.y, -R.x)) / d
if 0 <= t <= 1 and 0 <= u <= 1:
X = P + R * t
pygame.draw.circle(run.screen, pygame.Color('green'), (round(X.x), round(X.y)), 3)
Minimal example: repl.it/#Rabbid76/PyGame-IntersectLines
import pygame
import math
import random
def intersect_line_line_vec2(startObs, endObs, origin, endpoint):
P = pygame.Vector2(startObs)
R = (endObs - P)
Q = pygame.Vector2(origin)
S = (endpoint - Q)
d = R.dot((S.y, -S.x))
if d == 0:
return None
t = (Q-P).dot((S.y, -S.x)) / d
u = (Q-P).dot((R.y, -R.x)) / d
if 0 <= t <= 1 and 0 <= u <= 1:
X = P + R * t
return (X.x, X.y)
return None
def intersect_line_line(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 P1[0] * t + P0[0] * (1-t), P1[1] * t + P0[1] * (1-t)
return None
def createRays(center):
return [(center[0] + 1200 * math.cos(angle), center[1] + 1200 * math.sin(angle)) for angle in range(0, 360, 10)]
def createObstacles(surface):
w, h = surface.get_size()
return [((random.randrange(w), random.randrange(h)), (random.randrange(w), random.randrange(h))) for _ in range(5)]
window = pygame.display.set_mode((800, 800))
clock = pygame.time.Clock()
origin = window.get_rect().center
rays = createRays(origin)
obstacles = createObstacles(window)
move_center = True
run = True
while run:
clock.tick(60)
for event in pygame.event.get():
if event.type == pygame.QUIT:
run = False
if event.type == pygame.MOUSEBUTTONDOWN:
obstacles = createObstacles(window)
if event.type == pygame.KEYDOWN:
move_center = not move_center
if move_center:
origin = pygame.mouse.get_pos()
rays = createRays(origin)
window.fill(0)
for endpoint in rays:
pygame.draw.line(window, (128, 128, 128), origin, endpoint)
pygame.draw.circle(window, (255, 255, 255), origin, 10)
for start, end in obstacles:
pygame.draw.line(window, (255, 0, 0), start, end)
for endpoint in rays:
pos = intersect_line_line(start, end, origin, endpoint)
if pos:
pygame.draw.circle(window, (0, 255, 0), (round(pos[0]), round(pos[1])), 3)
pygame.display.flip()
pygame.quit()
exit()

Trying to code the Recaman Sequence, but issue with the parameters I pass for drawing an arc

This question has two parts to it:
The logic - to construct the cool pattern of semi circles of the Recaman Sequence, does my logic/code work?
Pygame specific issue.
I get the following error when I run my code:
pg.draw.arc(screen, black, [xi,yi,dx,dy], 180,0,1)
ValueError: width greater than ellipse radius
I don't see how the width ends up being > radius of the ellipse... and I've looked into this for about two hours now, and I really need some outside help. Thanks!
My Code:
def recaman():
sequence = [0]
limit = 10
def genNums(n):
index = 0
for i in range(1,n):
if index-i>0 and index-i not in sequence:
index-=i
sequence.append(index)
else:
index+=i
sequence.append(index)
screen = pg.display.set_mode((display_width,display_height),pg.FULLSCREEN)
tick = 0
genNums(limit)
while tick < 1000000:
zx = display_width//limit
zy = (display_height/2)//limit
xi = 0
yi = 0
xf = 0
yf = 0
curX = 0
curY = 540
dx = xf - xi
dy = yf - yi
for event in pg.event.get():
if event.type == pg.QUIT:
tick = 1000
screen.fill(white)
direction = 'down'
for n in range(0,len(sequence)-1):
yi = 540
if n % 2 == 0:
direction = 'down'
else:
direction = 'up'
if sequence[n+1] > sequence[n]:
curX += n * zx
xf = curX
xi = curX - (n * zx)
else:
curX -= n * zx
xf = curX
xi = curX + (n*zx)
if direction == 'up':
yf = curY - (n*zy)
if direction == 'down':
yf = curY + (n*zy)
p1 = (xi,yi)
p2 = (xf,yf)
pg.draw.arc(screen, black, [xi,yi,dx,dy], 180,0,1)
pg.display.update()
tick += 1
recaman()

The angle to pygame.draw.arc() has to be set in radian. Further the width and the height of the rectangular area have to be grater 0.
The parts of a Recaman Sequence are semi-circles. Calculate the diameter of a part and calculate the lower left origin of the square which surrounds the circle with the corresponding diameter of the part. Draw either the upper semi-circle (from 0 to math.pi) or lower semi-circle (from math.pi to 2*math.pi).
import math
line_width = 5
diameter = abs(dx) + line_width
px = xi if dx > 0 else xi + dx
py = display_height/2 - diameter/2.0
if diameter > line_width*2:
start_ang = 0 if dy < 0 else math.pi
end_ang = start_ang + math.pi + 0.01
pg.draw.arc(screen, black, [px, py, diameter, diameter], start_ang, end_ang, line_width)
e.g. curve with limit = 40:
Full code:
import pygame as pg
import math
pg.init()
white = (255,255,255)
black = ( 0, 0, 0)
display_width, display_height = (800,600)
def recaman():
sequence = [0]
limit = 40
def genNums(n):
index = 0
for i in range(1,n):
if index-i>0 and index-i not in sequence:
index-=i
sequence.append(index)
else:
index+=i
sequence.append(index)
#screen = pg.display.set_mode((display_width,display_height),pg.FULLSCREEN)
screen = pg.display.set_mode((display_width,display_height))
tick = 0
genNums(limit)
done = False
while tick < 1000000 and not done:
for event in pg.event.get():
if event.type == pg.QUIT:
done = True
zx = display_width/limit
zy = (display_height/2)/limit
xi = 0
yi = 0
xf = 0
yf = 0
curX = 0
curY = 500
screen.fill(white)
direction = 'down'
for n in range(0,len(sequence)-1):
yi = 500
if n % 2 == 0:
direction = 'down'
else:
direction = 'up'
if sequence[n+1] > sequence[n]:
curX += n * zx
xf = curX
xi = curX - (n * zx)
else:
curX -= n * zx
xf = curX
xi = curX + (n*zx)
if direction == 'up':
yf = curY - (n*zy)
if direction == 'down':
yf = curY + (n*zy)
p1 = (xi,yi)
p2 = (xf,yf)
dx = xf - xi
dy = yf - yi
line_width = 5
diameter = abs(dx) + line_width
px = xi if dx > 0 else xi + dx
py = display_height/2 - diameter/2.0
if diameter > line_width*2:
start_ang = 0 if dy < 0 else math.pi
end_ang = start_ang + math.pi + 0.01
pg.draw.arc(screen, black, [px, py, diameter, diameter], start_ang, end_ang, line_width)
pg.display.update()
tick += 1
recaman()