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I need help to make an optimization graph in 3 dimensions with manim. I am having difficulty understanding how to use the projection methods and to represent the axes and data in three-dimensional space. If anyone has experience with manim and can help me understand how to do it, I would greatly appreciate it. Thank you
Note: I am trying to graph the schewefel function below I attach part of the code that I have been working on
%%manim -qm -v WARNING AckleyAnimation
class Schewefel(ThreeDScene):
def func(self,u,v):
return x * np.sin(np.sqrt(np.abs(x))) + y * np.sin(np.sqrt(np.abs(y)))
def construct(self):
cielo = '#C4DDFF'
azul = '#001D6E'
rojo = "#B20600"
axes = ThreeDAxes()
self.set_camera_orientation(phi=65*DEGREES,theta=60*DEGREES)
# self.add(axes,x,y)
name_function = Tex(r"Schwefel function." ,font_size=38).to_corner(UL)
self.add_fixed_in_frame_mobjects(name_function)
funcion = MathTex(r"f(x) = 418.9829d - \sum_{i=1}^{d} x_i \sin \sqrt{|x_i|}", font_size=30).to_corner(UL)
self.play(Write(name_function))
self.play(FadeOut(name_function))
self.add_fixed_in_frame_mobjects(funcion)
self.play(Write(funcion))
surface_plane = Surface(
lambda u, v: np.array([u, v, self.func(u, v)]),
u_range=[-100,100],
v_range=[-100,100],
resolution=(50, 50))
self.play(Write(surface_plane))
Graphics
function Schewefel
Correction:
So far I modified the script and I have the following
%%manim -qm -v WARNING PlotSurfaceExample
class PlotSurfaceExample(ThreeDScene):
def construct(self):
resolution_fa = 16
self.set_camera_orientation(phi=75 * DEGREES, theta=-60 * DEGREES)
axes = ThreeDAxes(x_range=(-500, 500, 1800), y_range=(-500, 500, 1800), z_range=(-500, 500, 1800))
def param_trig(u, v):
x = u
y = v
z = x * np.sin(np.sqrt(np.abs(x))) + y * np.sin(np.sqrt(np.abs(y)))
return z
trig_plane = axes.plot_surface(
param_trig,
resolution=(resolution_fa, resolution_fa),
u_range = (-500, 500),
v_range = (-500, 500),
colorscale = [BLUE, GREEN, YELLOW, ORANGE, RED],
)
self.add(axes)
self.play(Write(trig_plane))
but it gives me this result
but nevertheless I hope this
I am trying to draw a rectangle which would have an edge next to each of its sides (it should represent a building with a fence) for one building it goes quite well, but when I am trying to add a new building it messes itself up completely.
I have this code to create buildings:
class Building():
def __init__(self, Box_2_World,shape, position, sensor= None):
self.Box_2_World = Box_2_World
self.shape = shape
self.position = position
if sensor == None:
sensor = False
self.sensor = sensor
self.footprint = self.Box_2_World.CreateStaticBody(position = position,
angle = 0.0,
fixtures = b2FixtureDef(
shape = b2PolygonShape(box=(self.shape)),
density = 1000,
friction = 1000))
self.Lower_Fence = self.Box_2_World.CreateStaticBody(position=(self.footprint.position[0],self.footprint.position[1] -1.75*self.shape[1]))
self.Lower_Fence.CreateEdgeChain([(self.Lower_Fence.position[0]-4.25*self.shape[0],self.Lower_Fence.position[1]),
(self.Lower_Fence.position[0]-2.25*self.shape[0],self.Lower_Fence.position[1]),
])
self.Right_Fence = self.Box_2_World.CreateStaticBody(position=(self.footprint.position[0]-1*self.shape[0],self.footprint.position[1]))
self.Right_Fence.CreateEdgeChain([(self.Right_Fence.position[0],self.Right_Fence.position[1] - 1.25*self.shape[1]),
(self.Right_Fence.position[0],self.Right_Fence.position[1]-3.25*self.shape[1]),
])
self.Upper_Fence = self.Box_2_World.CreateStaticBody(position=(self.footprint.position[0],self.footprint.position[1] -0.45* self.shape[1]))
self.Upper_Fence.CreateEdgeChain([(self.Upper_Fence.position[0] - 4.25* self.shape[0],self.Upper_Fence.position[1]),
(self.Upper_Fence.position[0]- 3.25* self.shape[0]+ self.shape[0],self.Upper_Fence.position[1]),
])
self.Left_Fence = self.Box_2_World.CreateStaticBody(position=(self.footprint.position[0]-2.25*self.shape[0],self.footprint.position[1]))
self.Left_Fence.CreateEdgeChain([(self.Left_Fence.position[0],self.Left_Fence.position[1] - 1.25*self.shape[1]),
(self.Left_Fence.position[0],self.Left_Fence.position[1]-3*self.shape[1]),
])
Skyscrapers = []
Rectangles = [(pos_X-5, pos_Y-5),(pos_X+15, pos_Y -5),(pos_X - 5,pos_Y + 15),(pos_X+15, pos_Y + 15)]
for i in range(4):
Skyscrapers.append(Building(Box_2_World,shape = (5,5), position = Rectangles[i]))
and these functions to draw it using PyGame:
SCREEN_OFFSETX, SCREEN_OFFSETY = SCREEN_WIDTH/16, SCREEN_HEIGHT
def fix_vertices(vertices):
return [(int(SCREEN_OFFSETX + v[0]), int(SCREEN_OFFSETY - v[1])) for v in vertices]
def _draw_polygon(polygon, screen, body, fixture):
transform = body.transform
vertices = fix_vertices([transform * v * PPM for v in polygon.vertices])
pygame.draw.polygon(
screen, [c / 2.0 for c in colors[body.type]], vertices, 0)
pygame.draw.polygon(screen, colors[body.type], vertices, 1)
polygonShape.draw = _draw_polygon
def _draw_edge(edge, screen, body, fixture):
vertices = fix_vertices(
[body.transform * edge.vertex1 * PPM, body.transform * edge.vertex2 * PPM])
pygame.draw.line(screen, colors[body.type], vertices[0], vertices[1])
edgeShape.draw = _draw_edge
And the output is this: Blue rectangles represent buildings, blue lines are fences, first building fits quite nice, but the others are for some reason out of desired positions
Also, if you find out a way how to create the fences using for loop, it would be great (that's the reason why I put for-loop tag into this question)
Any help appreciated
The coordinates which are passed to CreateEdgeChain have to be relative to the body.
The position of the body is set when the object is constructed e.g:
self.Lower_Fence = self.Box_2_World.CreateStaticBody(
position=(self.footprint.position[0], self.footprint.position[1] -1.75*self.shape[1]))
And the edges have to be relative to this position rather than an absolute position.e.g:
self.Lower_Fence.CreateEdgeChain([(-4.25*self.shape[0], 0), (-2.25*self.shape[0], 0)])
To create the fences in a for-loop, you've to define a list of the edges. With the list of the edges you can create a list of fences:
fence_edges = [
[(-4.25, -1.75), (-2.25, -1.75)],
[(-1.00, -1.25), (-1.00, -3.25)],
[(-4.25, -0.45), (-2.25, -0.45)],
[(-2.25, -1.25), (-2.25, -3.25)]
]
self.Fences = []
for edge in fence_edges:
p1, p2 = edge
fence = self.Box_2_World.CreateStaticBody(position=self.footprint.position[:])
fence.CreateEdgeChain(
[(p1[0] * self.shape[0], p1[1] * self.shape[1]),
(p2[0] * self.shape[0], p2[1] * self.shape[1])])
self.Fences.append(fence)
self.Lower_Fence, self.Right_Fence, self.Upper_Fence, self.Left_Fence = self.Fences
I am trying to draw a rectangle which would have an edge next to each of its sides (it should represent a building with a fence) for one building it goes quite well, but when I am trying to add a new building it messes itself up completely.
I have this code to create buildings:
class Building():
def __init__(self, Box_2_World,shape, position, sensor= None):
self.Box_2_World = Box_2_World
self.shape = shape
self.position = position
if sensor == None:
sensor = False
self.sensor = sensor
self.footprint = self.Box_2_World.CreateStaticBody(position = position,
angle = 0.0,
fixtures = b2FixtureDef(
shape = b2PolygonShape(box=(self.shape)),
density = 1000,
friction = 1000))
self.Lower_Fence = self.Box_2_World.CreateStaticBody(position=(self.footprint.position[0],self.footprint.position[1] -1.75*self.shape[1]))
self.Lower_Fence.CreateEdgeChain([(self.Lower_Fence.position[0]-4.25*self.shape[0],self.Lower_Fence.position[1]),
(self.Lower_Fence.position[0]-2.25*self.shape[0],self.Lower_Fence.position[1]),
])
self.Right_Fence = self.Box_2_World.CreateStaticBody(position=(self.footprint.position[0]-1*self.shape[0],self.footprint.position[1]))
self.Right_Fence.CreateEdgeChain([(self.Right_Fence.position[0],self.Right_Fence.position[1] - 1.25*self.shape[1]),
(self.Right_Fence.position[0],self.Right_Fence.position[1]-3.25*self.shape[1]),
])
self.Upper_Fence = self.Box_2_World.CreateStaticBody(position=(self.footprint.position[0],self.footprint.position[1] -0.45* self.shape[1]))
self.Upper_Fence.CreateEdgeChain([(self.Upper_Fence.position[0] - 4.25* self.shape[0],self.Upper_Fence.position[1]),
(self.Upper_Fence.position[0]- 3.25* self.shape[0]+ self.shape[0],self.Upper_Fence.position[1]),
])
self.Left_Fence = self.Box_2_World.CreateStaticBody(position=(self.footprint.position[0]-2.25*self.shape[0],self.footprint.position[1]))
self.Left_Fence.CreateEdgeChain([(self.Left_Fence.position[0],self.Left_Fence.position[1] - 1.25*self.shape[1]),
(self.Left_Fence.position[0],self.Left_Fence.position[1]-3*self.shape[1]),
])
Skyscrapers = []
Rectangles = [(pos_X-5, pos_Y-5),(pos_X+15, pos_Y -5),(pos_X - 5,pos_Y + 15),(pos_X+15, pos_Y + 15)]
for i in range(4):
Skyscrapers.append(Building(Box_2_World,shape = (5,5), position = Rectangles[i]))
and these functions to draw it using PyGame:
SCREEN_OFFSETX, SCREEN_OFFSETY = SCREEN_WIDTH/16, SCREEN_HEIGHT
def fix_vertices(vertices):
return [(int(SCREEN_OFFSETX + v[0]), int(SCREEN_OFFSETY - v[1])) for v in vertices]
def _draw_polygon(polygon, screen, body, fixture):
transform = body.transform
vertices = fix_vertices([transform * v * PPM for v in polygon.vertices])
pygame.draw.polygon(
screen, [c / 2.0 for c in colors[body.type]], vertices, 0)
pygame.draw.polygon(screen, colors[body.type], vertices, 1)
polygonShape.draw = _draw_polygon
def _draw_edge(edge, screen, body, fixture):
vertices = fix_vertices(
[body.transform * edge.vertex1 * PPM, body.transform * edge.vertex2 * PPM])
pygame.draw.line(screen, colors[body.type], vertices[0], vertices[1])
edgeShape.draw = _draw_edge
And the output is this: Blue rectangles represent buildings, blue lines are fences, first building fits quite nice, but the others are for some reason out of desired positions
Also, if you find out a way how to create the fences using for loop, it would be great (that's the reason why I put for-loop tag into this question)
Any help appreciated
The coordinates which are passed to CreateEdgeChain have to be relative to the body.
The position of the body is set when the object is constructed e.g:
self.Lower_Fence = self.Box_2_World.CreateStaticBody(
position=(self.footprint.position[0], self.footprint.position[1] -1.75*self.shape[1]))
And the edges have to be relative to this position rather than an absolute position.e.g:
self.Lower_Fence.CreateEdgeChain([(-4.25*self.shape[0], 0), (-2.25*self.shape[0], 0)])
To create the fences in a for-loop, you've to define a list of the edges. With the list of the edges you can create a list of fences:
fence_edges = [
[(-4.25, -1.75), (-2.25, -1.75)],
[(-1.00, -1.25), (-1.00, -3.25)],
[(-4.25, -0.45), (-2.25, -0.45)],
[(-2.25, -1.25), (-2.25, -3.25)]
]
self.Fences = []
for edge in fence_edges:
p1, p2 = edge
fence = self.Box_2_World.CreateStaticBody(position=self.footprint.position[:])
fence.CreateEdgeChain(
[(p1[0] * self.shape[0], p1[1] * self.shape[1]),
(p2[0] * self.shape[0], p2[1] * self.shape[1])])
self.Fences.append(fence)
self.Lower_Fence, self.Right_Fence, self.Upper_Fence, self.Left_Fence = self.Fences
I'm trying visualise the sine waves addition in python using tkinter, and I'm trying to build lines between each circles center, but what I've tried so far didnt work as I thought it would. is there a way to fix what I've tried (see code), or a way to move only one coordinates point of a line independantly from the other?
As you'll see in the code if you run it, I've tried a method where each iteration the previous line is erased and a new one is created. When I run the code there is actually a line between each center of the circles just like I want, but facts are those lines persist and won't erase themselves; for some reason it seems like the canvas.delete(line) doesnt work as I expected it to.
here's the full code. The interesting part is in the 'updateline' fonction, into 'act()' func.
import math
import tkinter as tk
##important to know! -- the way I'm creating the circles is by setting an object, the bounds of the circle, depending on amplitude asked by user.
##then the programs calculates the path of these bounds, depending on circles, amplitude, phase and frequency of the sine waves asked by the user from the tkinter GUI.
##finally, the program creates and moves along this path a circle, representing visually the sine wave.
top = tk.Tk()
top.title('Superposition')
choice = tk.Tk()
choice.title('Parametres')
f = tk.Frame(choice,bd=3)
f.pack(side='top')
g = tk.Frame(choice,bd=3)
g.pack(side='bottom')
tk.Label(f,text="nbre ondes:",width = 10).grid(row=0,column=0)
sines = tk.Spinbox(f,from_=1,to=50,width=10,textvariable=tk.DoubleVar(value=2))
sines.grid(row=0,column=1)
sines.delete(0,5)
sines.insert(0,2)
delai = tk.Scale(g, orient='vertical', from_=100, to=1,resolution=1, length=100,label='delai')
delai.grid(row=0,column=0)
hauteur = tk.Scale(g, orient='vertical', from_=1100, to=100,resolution=100, length=100,label='fenetre')
hauteur.grid(row=0,column=1)
taillec1 = tk.Scale(g, orient='vertical', from_=3.5, to=0.1,resolution=0.1, length=100,label='taille')
taillec1.grid(row=0,column=2)
delai.set(20)
hauteur.set(600)
taillec1.set(1.5)
def grilledechoix():
numberofsines = int(sines.get())
for i in f.grid_slaves():
if int(i.grid_info()["row"]) > numberofsines+2:
i.grid_forget()
for i in range(1,numberofsines+1):
tk.Label(f,text="phase n."+str(i),width = 10).grid(row=i+2,column=4)
phase = tk.Spinbox(f,from_=-180,to=180,width=10)
phase.grid(row=i+2,column=5)
phase.delete(0,5)
phase.insert(0, 0)
for i in range(1,numberofsines+1):
tk.Label(f,text="amp. n."+str(i),width = 10).grid(row=i+2,column=0)
ampli = tk.Spinbox(f,from_=1,to=10000000,width=10)
ampli.grid(row=i+2,column=1)
ampli.delete(0,5)
ampli.insert(0,10)
for i in range(1,numberofsines+1):
tk.Label(f,text="freq n."+str(i),width = 10).grid(row=i+2,column=2)
freq = tk.Spinbox(f,from_=-1000,to=1000,width=10)
freq.grid(row=i+2,column=3)
freq.delete(0,5)
freq.insert(0,5)
def act():
h = g.grid_slaves()[1].get()
delai = g.grid_slaves()[2].get()
taillec1 = g.grid_slaves()[0].get()
w = h
ampdict = {'box1':100 * ((h/700)*taillec1)}
frqdict = {}
aaadict = {}
fffdict = {}
phadict = {}
numberofsines = int(sines.get())
sin = lambda degs: math.sin(math.radians(degs))
cos = lambda degs: math.cos(math.radians(degs))
for i in range(1,numberofsines+1):
fffdict['box'+str(numberofsines-i+1)] = f.grid_slaves()[(2*i)-2].get()
aaadict['box'+str(numberofsines-i+1)] = f.grid_slaves()[(2*i)-2+2*numberofsines].get()
phadict['box'+str(numberofsines-i+1)] = f.grid_slaves()[(2*i)-2+4*numberofsines].get()
for i in range(1,numberofsines+1):
ampdict['box'+str(i)] = (float(ampdict['box1'])/float(aaadict['box1'])) * float(aaadict['box'+str(i)])
frqdict['box'+str(i)] = float(fffdict['box'+str(i)])/float(fffdict['box1'])
class obj(object):
cos0, cos180 = cos(0), cos(180)
sin90, sin270 = sin(90), sin(270)
def __init__(i, x, y, rayon):
i.x, i.y = x, y
i.rayon = rayon
def bounds(i):
return (i.x + i.rayon*i.cos0, i.y + i.rayon*i.sin270,
i.x + i.rayon*i.cos180, i.y + i.rayon*i.sin90)
def updateposition(canvas, id, cent, obj, path):
obj.x, obj.y = next(path)
x0, y0, x1, y1 = canvas.coords(id)
oldx, oldy = (x0+x1) // 2, (y0+y1) // 2
dx, dy = obj.x - oldx, obj.y - oldy
canvas.move(id, dx, dy)
canvas.move(cent, dx, dy)
canvas.after(delai, updateposition, canvas, id, cent, obj, path)
def updateline(canvas, line, robj0, cent0, robj1, cent1):
x00, y00, x01, y01 = canvas.coords(cent0) ##defining coords of the two ovals asked, representing centers of circles
x10, y10, x11, y11 = canvas.coords(cent1)
oldx0, oldy0 = (x00+x01) // 2, (y00+y01) // 2 ##defining center coords of the two ovals
oldx1, oldy1 = (x10+x11) // 2, (y10+y11) // 2
dx0, dy0 = robj0.x - oldx0, robj0.y - oldy0 ##defining the deltax and deltay, difference of movements between frames, of the two ovals
dx1, dy1 = robj1.x - oldx1, robj1.y - oldy1
canvas.after(delai, canvas.delete, line) ##deleting previous line, does not work and I don't know why. I've also tried 'canvas.delete(line)', giving same results
canvas.create_line(oldx0+dx0, oldy0+dy0, oldx1+dx1, oldy1+dy1) ##creating new line
canvas.after(delai, updateline, canvas, line, robj0, cent0, robj1, cent1) ##function invoking itself after delay 'delai'
def posobj(pt,ang,deltang):
while True:
yield pt.x + pt.rayon*cos(ang), pt.y + pt.rayon*sin(ang)
ang = (ang+deltang)%360
try:
top.pack_slaves()[0].destroy()
except:
pass
canvas = tk.Canvas(top, bg='white', height=h, width=w)
canvas.pack(side='right')
robj = {}
r = {}
posobjet = {}
line = {}
cent = {}
## the following 'for' loop creates a number of circles corresponding to sine waves, as much as the user asked.
for i in range(1,int(sines.get())+2):
if i != int(sines.get())+1:
if i == 1:
robj[str(i)] = obj(h/2,h/2,float(ampdict['box'+str(i)]))
r[str(i)] = canvas.create_oval(robj[str(i)].bounds(),fill='',outline='black')
cent[str(i)] = canvas.create_oval(h/2+h/200,h/2+h/200.,h/2-h/200,h/2-h/200, fill='white', outline='red')
posobjet[str(i)] = posobj(robj[str(i)],float(phadict['box'+str(i)]),float(frqdict['box'+str(i)]))
else:
robj[str(i)] = obj(robj[str(i-1)].x,robj[str(i-1)].y,float(ampdict['box'+str(i)]))
r[str(i)] = canvas.create_oval(robj[str(i)].bounds(),fill='',outline='black')
cent[str(i)] = canvas.create_oval(robj[str(i)].x+h/200,robj[str(i)].y+h/200,robj[str(i)].x-h/200,robj[str(i)].y-h/200, fill='white', outline='blue')
line[str(i)] = canvas.create_line(0,0,0,0)
posobjet[str(i)] = posobj(robj[str(i)],float(phadict['box'+str(i)]),float(frqdict['box'+str(i)]))
top.after(delai, updateposition, canvas, r[str(i)], cent[str(i)], robj[str(i)], posobjet[str(i-1)])
##here I'm invoking the updateline function using the constant 'delai', the line i, and objects defining the bounds of the center objects, the little blue/red dots appearing as the center of each circles(run the code, it'll be easier to understand)
top.after(delai, updateline, canvas, line[str(i)], robj[str(i-1)], cent[str(i-1)], robj[str(i)], cent[str(i)])
else:
robj[str(i)] = obj(robj[str(i-1)].x,robj[str(i-1)].y,h/200)
r[str(i)] = canvas.create_oval(robj[str(i)].bounds(),fill='white',outline='red')
cent[str(i)] = canvas.create_oval(robj[str(i)].x+h/200,robj[str(i)].y+h/200,robj[str(i)].x-h/200,robj[str(i)].y-h/200, fill='white', outline='red')
line[str(i)] = canvas.create_line(0,0,0,0)
top.after(delai, updateposition, canvas, r[str(i)], cent[str(i)], robj[str(i)], posobjet[str(i-1)])
##2nd and last time invoking the updateline function, for the line between the last circle's point and the final red point.
top.after(delai, updateline, canvas, line[str(i)], robj[str(i-1)], cent[str(i-1)], robj[str(i)], cent[str(i)])
top.mainloop()
ok = tk.Button(f,text='NBRE',command=grilledechoix)
ok.grid(row=0,column=2)
ac = tk.Button(f,text='APPLY',command=act)
ac.grid(row=0,column=3)
grilledechoix()
act()
I expected the lines to disappear once the updateline function called itself again, because of that 'canvas.delete(line)' line into updateline, and I can't really understand why it does that.
anyway if you have a solution to make the lines move, without creating and deleting them each time the function is called, feel free to tell me.
Thanks!
If I understand the problem correctly, I believe the issue is with this code:
canvas.after(delai, canvas.delete, line)
canvas.create_line(oldx0+dx0, oldy0+dy0, oldx1+dx1, oldy1+dy1)
canvas.after(delai, updateline, canvas, line, robj0, cent0, robj1, cent1)
It fails to reassign the new line to the line variable for the next call. Instead try:
canvas.after(delai, canvas.delete, line)
line = canvas.create_line(oldx0+dx0, oldy0+dy0, oldx1+dx1, oldy1+dy1)
canvas.after(delai, updateline, canvas, line, robj0, cent0, robj1, cent1)
Which gets rid of the extra lines when I run it. Let me know if I've missed the point.
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Edit the question to include desired behavior, a specific problem or error, and the shortest code necessary to reproduce the problem. This will help others answer the question.
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I want to draw a triangle like this:
I have tried different ways of solving it, but I have not done it correctly. How to add median lines in the triangle? Could someone please help and explain this to me?
from turtle import *
import random
def allTriMedian (w=300):
speed (0)
vertices = []
point = turtle.Point(x,y)
for i in range (3):
x = random.randint(0,300)
y = random.randint(0,300)
vertices.append(trutle.Point(x,y))
point = turtle.Point(x,y)
triangle = turtle.Polygon(vertices)
a = triangle.side()
b = triangle.side()
c = triangle.side()
m1 = tirangle.median
m2 = triangle.median
m3 = triangle.median
I tried to put the equation directly
def Median (a, b, c):
m1 = sqrt((((2b^2)+(2c^2)-(a^2))))
m2 = sqrt((((2a^2)+(2c^2)-(b^2))))
m3 = sqrt((((2a^2)+(2b^2)-(c^2))))
triangle.setFill("yellow")
triangle.draw(allTriMedian)
Or I thought to find a midpoint and draw a line segment to connect the vertices and midpoints.
def getMid(p1,p2):
return ( (p1[0]+p2[0]) / 2, (p1[1] + p2[1]))
mid1 = Line((point(p1[0]+p2[0]) / 2),point(x))
mid2 = Line((point(p2[1]+p3[1]) / 2),point(y))
I hate doing math. Let's see if we can solve this by throwing turtles at the problem. Lots of turtles.
We'll randomly generate the verticies of the triangle. Taking pairs of verticies in turn, we'll start a turtle at each heading toward the other. When the turtles collide (at the midpoint), we'll eliminate one turtle and send the other toward the vertex not in the pair. Once we've done this three times (with six turtles), we should have the drawing in question. Well, mostly (no fill in my solution):
from turtle import Turtle, Screen
from random import seed, randint
WIDTH, HEIGHT = 640, 480
def meet_in_the_middle(turtle_1, turtle_2):
position_2 = turtle_2.position()
while True:
turtle_1.setheading(turtle_1.towards(turtle_2))
turtle_1.forward(1)
position_1 = turtle_1.position()
if int(position_1[0]) == int(position_2[0]) and int(position_1[1]) == int(position_2[1]):
break
turtle_2.setheading(turtle_2.towards(turtle_1))
turtle_2.forward(1)
position_2 = turtle_2.position()
if int(position_2[0]) == int(position_1[0]) and int(position_2[1]) == int(position_1[1]):
break
seed()
screen = Screen()
screen.setup(WIDTH * 1.25, HEIGHT * 1.25)
vertices = []
for _ in range(3):
x = randint(-WIDTH//2, WIDTH//2)
y = randint(-HEIGHT//2, HEIGHT//2)
vertices.append((x, y))
A, B, C = vertices
turtle_AtoB = Turtle(shape='turtle')
turtle_AtoB.penup()
turtle_AtoB.goto(A)
turtle_AtoB.pendown()
turtle_BtoA = Turtle(shape='turtle')
turtle_BtoA.penup()
turtle_BtoA.goto(B)
turtle_BtoA.pendown()
meet_in_the_middle(turtle_AtoB, turtle_BtoA)
turtle_BtoA.hideturtle()
turtle_AtoB.setheading(turtle_AtoB.towards(C))
turtle_AtoB.goto(C)
turtle_AtoB.hideturtle()
turtle_BtoC = Turtle(shape='turtle')
turtle_BtoC.penup()
turtle_BtoC.goto(B)
turtle_BtoC.pendown()
turtle_CtoB = Turtle(shape='turtle')
turtle_CtoB.penup()
turtle_CtoB.goto(C)
turtle_CtoB.pendown()
meet_in_the_middle(turtle_BtoC, turtle_CtoB)
turtle_CtoB.hideturtle()
turtle_BtoC.setheading(turtle_BtoC.towards(A))
turtle_BtoC.goto(A)
turtle_BtoC.hideturtle()
turtle_CtoA = Turtle(shape='turtle')
turtle_CtoA.penup()
turtle_CtoA.goto(C)
turtle_CtoA.pendown()
turtle_AtoC = Turtle(shape='turtle')
turtle_AtoC.penup()
turtle_AtoC.goto(A)
turtle_AtoC.pendown()
meet_in_the_middle(turtle_CtoA, turtle_AtoC)
turtle_AtoC.hideturtle()
turtle_CtoA.setheading(turtle_CtoA.towards(B))
turtle_CtoA.goto(B)
turtle_CtoA.hideturtle()
screen.exitonclick()
Turtles at work:
Finished drawing:
thanks to cdlane, I took his code and put some functionality into functions to make it a Little clearer (at least for me)
# -*- coding: cp1252 -*-
import turtle
from turtle import Turtle, Screen
from random import seed, randint
WIDTH, HEIGHT = 640, 480
def create_screen(width, height):
screen = Screen()
screen.setup(width * 1.25, height * 1.25)
return screen
def create_points(count,width = WIDTH, height = HEIGHT):
vertices = []
for _ in range(count):
x = randint(-width//2, width//2)
y = randint(-height//2, height//2)
vertices.append((x, y))
return vertices
def create_turtle_at_position(position):
turtle = Turtle(shape='turtle')
turtle.hideturtle()
turtle.penup()
turtle.goto(position)
turtle.showturtle()
turtle.pendown()
return turtle
def meet_in_the_middle(turtle_1, turtle_2):
position_2 = turtle_2.position()
while True:
turtle_1.setheading(turtle_1.towards(turtle_2))
turtle_1.forward(1)
position_1 = turtle_1.position()
if int(position_1[0]) == int(position_2[0]) and int(position_1[1]) == int(position_2[1]):
break
turtle_2.setheading(turtle_2.towards(turtle_1))
turtle_2.forward(1)
position_2 = turtle_2.position()
if int(position_2[0]) == int(position_1[0]) and int(position_2[1]) == int(position_1[1]):
break
turtle_1.hideturtle()
turtle_2.hideturtle()
return create_turtle_at_position(position_2)
def draw_median(P1st, P2nd, POpposite):
turtle_AtoB = create_turtle_at_position(P1st)
turtle_BtoA = create_turtle_at_position(P2nd)
turtle_AandBmiddle = meet_in_the_middle(turtle_AtoB, turtle_BtoA)
turtle_AandBmiddle.setheading(turtle_AandBmiddle.towards(POpposite))
turtle_AandBmiddle.goto(POpposite)
return turtle_AandBmiddle
seed()
sc = create_screen(WIDTH, HEIGHT)
for _ in range(5):
sc = create_screen(WIDTH, HEIGHT)
A, B, C = create_points(3)
draw_median(A,B,C)
draw_median(B,C,A)
draw_median(C,A,B)
sc.exitonclick()
mathematical it is the easiest way to calculate this by vector. Let me say you have a triangle ABC and want to draw a line from A to the middle of BC so your vector starts at A and ends on A + AB + 1/2 BC or A + AC + 1/2 CB (vectorial)
(ax) + (bx - ax) + 0.5 (cx - bx)
(ay) (by - ay) (cy - by)
that results in the coordinates for the opposite Point of
x = 0.5(cx + bx)
y = 0.5(cy + by)