Adding simple perspective to a 3D renderer in pygame - python

I have created a 3D renderer in pyGame however I would now like to add perspective. I have been trying for a while now and can't seem to figure it out.
I have read that the most simplest form of perspective is to multiply the x and y coordinates by the inverse of the z coordinate so that the x and y are dependant on the z value. This means that the x and y distances should decrease with the z coordinate increasing and x and y should increase with z decreasing. I have managed to get this to work slightly however it seems to accumulate so when I spin the box left and right the back of the box gets very small and seems to accumulate a negative scale instead of remaining at a constant size with being at the set z distance.
Here is my code:
wireframe.py:
class Wireframe:
def __init__(self):
self.nodes = np.zeros((0,4))
self.edges = []
def addNodes(self, node_array):
ones_column = np.ones((len(node_array), 1))
ones_added = np.hstack((node_array, ones_column))
self.nodes = np.vstack((self.nodes, ones_added))
def addEdges(self, edgeList):
self.edges += edgeList
def outputNodes(self):
print("\n --- Nodes ---")
for i, (x, y, z, _) in enumerate(self.nodes):
print(" %d: (%.2f, %.2f, %.2f)" % (i, node.x, node.y, node.z))
def outputEdges(self):
print("\n --- Edges ---")
for i, (node1, node2) in enumerate(self.edges):
print(" %d: %d -> %d" % (i, node1, node2))
def translate(self, axis, d):
if axis in ['x', 'y', 'z']:
for node in self.nodes:
setattr(node, axis, getattr(node, axis) + d)
def scale(self, centre_x, centre_y, scale):
for node in self.nodes:
node.x = centre_x + scale * (node.x - centre_x)
node.y = centre_y + scale * (node.y - centre_y)
node.z *= scale
def findCentre(self):
num_nodes = len(self.nodes)
meanX = sum([node.x for node in self.nodes]) / num_nodes
meanY = sum([node.y for node in self.nodes]) / num_nodes
meanZ = sum([node.z for node in self.nodes]) / num_nodes
return (meanX, meanY, meanZ)
def rotateZ(self, centre, radians):
cx, cy, cz = centre
for node in self.nodes:
x = node.x - cx
y = node.y - cy
d = math.hypot(y,x)
theta = math.atan2(y,x) + radians
node.x = cx + d * math.cos(theta)
node.y = cy + d * math.sin(theta)
def rotateX(self, centre, radians):
cx, cy, cz = centre
for node in self.nodes:
y = node.y - cy
z = node.z - cz
d = math.hypot(y,z)
theta = math.atan2(y, z) + radians
node.z = cz + d * math.cos(theta)
node.y = cy + d * math.sin(theta)
def rotateY(self, centre, radians):
cx, cy, cz = centre
for node in self.nodes:
x = node.x - cx
z = node.z - cz
d = math.hypot(x, z)
theta = math.atan2(x, z) + radians
node.z = cz + d * math.cos(theta)
node.x = cx + d * math.sin(theta)
def transform(self, matrix):
self.nodes = np.dot(self.nodes, matrix)
def transform_for_perspective(self):
for node in self.nodes:
print(node[0], node[1], node[2])
if node[2] != 0:
node[0] = node[0]*(1/(1-(node[2]*0.00005)))
node[1] = node[1]*(1/(1-(node[2]*0.00005)))
node[2] = node[2]*1
def translationMatrix(self, dx=0, dy=0, dz=0):
return np.array([[1,0,0,0],
[0,1,0,0],
[0,0,1,0],
[dx,dy,dz,1]])
def scaleMatrix(self, sx=0, sy=0, sz=0):
return np.array([[sx, 0, 0, 0],
[0, sy, 0, 0],
[0, 0, sz, 0],
[0, 0, 0, 1]])
def rotateXMatrix(self, radians):
c = np.cos(radians)
s = np.sin(radians)
return np.array([[1,0,0,0],
[0,c,-s,0],
[0,s,c,0],
[0,0,0,1]])
def rotateYMatrix(self, radians):
c = np.cos(radians)
s = np.sin(radians)
return np.array([[c,0,s,0],
[0,1,0,0],
[-s,0,c,0],
[0,0,0,1]])
def rotateZMatrix(self, radians):
c = np.cos(radians)
s = np.sin(radians)
return np.array([[c,-s, 0, 0],
[s,c,0,0],
[0,0,1,0],
[0,0,0,1]])
def movCamera(self, tilt, pan):
return np.array([[1,0,0,200],
[0,1,0,0],
[pan,tilt,1,0],
[0,0,0,0]])
projectionViewer.py
from wireframe import *
import pygame
import numpy as np
class ProjectionViewer:
''' Displays 3D Objects on a Pygame Screen '''
def __init__(self, width, height):
self.width = width
self.height = height
self.screen = pygame.display.set_mode((width, height))
pygame.display.set_caption('Wireframe Display')
self.background = (10,10,50)
self.wireframes = {}
self.displayNodes = True
self.displayEdges = True
self.nodeColour = (255,255,255)
self.edgeColour = (200,200,200)
self.nodeRadius = 4
def run(self):
key_to_function = {
pygame.K_LEFT: (lambda x: x.translateAll([-10, 0, 0])),
pygame.K_RIGHT:(lambda x: x.translateAll([ 10, 0, 0])),
pygame.K_DOWN: (lambda x: x.translateAll([0, 10, 0])),
pygame.K_UP: (lambda x: x.translateAll([0, -10, 0])),
pygame.K_a: (lambda x: x.rotate_about_Center('Y', -0.08)),
pygame.K_d: (lambda x: x.rotate_about_Center('Y', 0.08)),
pygame.K_w: (lambda x: x.rotate_about_Center('X', -0.08)),
pygame.K_s: (lambda x: x.rotate_about_Center('X', 0.08)),
pygame.K_EQUALS: (lambda x: x.scale_centre([1.25,1.25,1.25])),
pygame.K_MINUS: (lambda x: x.scale_centre([0.8,0.8,0.8])),
pygame.K_q: (lambda x: x.rotateAll('X', 0.1)),
pygame.K_z: (lambda x: x.rotateAll('Z', 0.1)),
pygame.K_x: (lambda x: x.rotateAll('Z', -0.1)),
pygame.K_p: (lambda x: x.perspectiveMode()),
pygame.K_t: (lambda x: x.translate_Camera())
}
running = True
flag = False
while running:
keys = pygame.key.get_pressed()
for event in pygame.event.get():
if event.type == pygame.QUIT:
running = False
if keys[pygame.K_LEFT]:
key_to_function[pygame.K_LEFT](self)
if keys[pygame.K_RIGHT]:
key_to_function[pygame.K_RIGHT](self)
if keys[pygame.K_DOWN]:
key_to_function[pygame.K_DOWN](self)
if keys[pygame.K_UP]:
key_to_function[pygame.K_UP](self)
if keys[pygame.K_EQUALS]:
key_to_function[pygame.K_EQUALS](self)
if keys[pygame.K_MINUS]:
key_to_function[pygame.K_MINUS](self)
if keys[pygame.K_LEFT]:
key_to_function[pygame.K_LEFT](self)
if keys[pygame.K_q]:
key_to_function[pygame.K_q](self)
if keys[pygame.K_w]:
key_to_function[pygame.K_w](self)
if keys[pygame.K_a]:
key_to_function[pygame.K_a](self)
if keys[pygame.K_s]:
key_to_function[pygame.K_s](self)
if keys[pygame.K_z]:
key_to_function[pygame.K_z](self)
if keys[pygame.K_x]:
key_to_function[pygame.K_x](self)
if keys[pygame.K_p]:
key_to_function[pygame.K_p](self)
if keys[pygame.K_t]:
key_to_function[pygame.K_t](self)
if keys[pygame.K_d]:
key_to_function[pygame.K_d](self)
self.display()
pygame.display.flip()
def addWireframe(self, name, wireframe):
self.wireframes[name] = wireframe
#translate to center
wf = Wireframe()
matrix = wf.translationMatrix(-self.width/2,-self.height/2,0)
for wireframe in self.wireframes.values():
wireframe.transform(matrix)
wf = Wireframe()
matrix = wf.translationMatrix(self.width,self.height,0)
for wireframe in self.wireframes.values():
wireframe.transform(matrix)
def display(self):
self.screen.fill(self.background)
for wireframe in self.wireframes.values():
if self.displayEdges:
for n1, n2 in wireframe.edges:
pygame.draw.aaline(self.screen, self.edgeColour, wireframe.nodes[n1][:2], wireframe.nodes[n2][:2],1)
wireframe.transform_for_perspective()
if self.displayNodes:
for node in wireframe.nodes:
pygame.draw.circle(self.screen, self.nodeColour, (int(node[0]), int(node[1])), self.nodeRadius, 0)
def translateAll(self, vector):
''' Translate all wireframes along a given axis by d units '''
wf = Wireframe()
matrix = wf.translationMatrix(*vector)
for wireframe in self.wireframes.values():
wireframe.transform(matrix)
def scaleAll(self, vector):
wf = Wireframe()
matrix = wf.scaleMatrix(*vector)
for wireframe in self.wireframes.values():
wireframe.transform(matrix)
def rotateAll(self, axis, theta):
wf = Wireframe()
if axis == 'X':
matrix = wf.rotateXMatrix(theta)
elif axis == 'Y':
matrix = wf.rotateYMatrix(theta)
elif axis == 'Z':
matrix = wf.rotateZMatrix(theta)
for wireframe in self.wireframes.values():
wireframe.transform(matrix)
#wireframe.transform_for_perspective()
def moveCameraX(self,x,y):
wf = Wireframe()
matrix = wf.movCamera(x,y)
print("test")
for wireframe in self.wireframes.values():
wireframe.transform(matrix)
def moveCameraZ(self,x,y):
wf = Wireframe()
matrix = wf.testMat((0,0,val))
for wireframe in self.wireframes.values():
wireframe.transform(matrix)
def perspectiveMode(self):
#First translate the centre of screen to 0,0
wf = Wireframe()
matrix = wf.translationMatrix(-self.width/2,-self.height/2,0)
for wireframe in self.wireframes.values():
wireframe.transform(matrix)
#perform the perspectivecorrection
wf = Wireframe()
matrix = wf.translationMatrix(-self.width/2,-self.height/2,0)
for wireframe in self.wireframes.values():
matrix = wf.perspectiveCorrection(1.2)
wireframe.transform(matrix)
wf = Wireframe()
matrix = wf.translationMatrix(self.width/2,self.height/2,0)
for wireframe in self.wireframes.values():
wireframe.transform(matrix)
def rotate_about_Center(self, Axis, theta):
#First translate Centre of screen to 0,0
wf = Wireframe()
matrix = wf.translationMatrix(-self.width/2,-self.height/2,0)
for wireframe in self.wireframes.values():
wireframe.transform(matrix)
#Do Rotation
wf = Wireframe()
if Axis == 'X':
matrix = wf.rotateXMatrix(theta)
elif Axis == 'Y':
matrix = wf.rotateYMatrix(theta)
elif Axis == 'Z':
matrix = wf.rotateZMatrix(theta)
for wireframe in self.wireframes.values():
wireframe.transform(matrix)
#Translate back to centre of screen
wf = Wireframe()
matrix = wf.translationMatrix(self.width/2,self.height/2,0)
for wireframe in self.wireframes.values():
wireframe.transform(matrix)
#Do perspective if needed
def scale_centre(self, vector):
#Transform center of screen to origin
wf = Wireframe()
matrix = wf.translationMatrix(-self.width/2,-self.height/2,0)
for wireframe in self.wireframes.values():
wireframe.transform(matrix)
#Scale the origin by vector
wf = Wireframe()
matrix = wf.scaleMatrix(*vector)
for wireframe in self.wireframes.values():
wireframe.transform(matrix)
wf = Wireframe()
matrix = wf.translationMatrix(self.width/2,self.height/2,0)
for wireframe in self.wireframes.values():
wireframe.transform(matrix)
def add_perspective(self):
for wireframe in self.wireframes.values():
for node in wireframe.nodes:
if node[2] != 0:
print("Point ----------")
print("x node", node[0])
print("y node", node[1])
print("z node", node[2])
node[0] = node[0] + (10/node[2])
node[1] = node[1] + (10/node[2])
main.py
from projectionViewer import ProjectionViewer
import wireframe
import numpy as np
cube = wireframe.Wireframe()
cube_nodes = [(x, y, z) for x in (-100, 100) for y in (-100, 100) for z in (-100, 100)]
print(cube_nodes)
cube.addNodes(np.array(cube_nodes))
cube.addEdges([(n, n + 4) for n in range(0, 4)])
cube.addEdges([(n, n + 1) for n in range(0, 8, 2)])
cube.addEdges([(n, n + 2) for n in (0, 1, 4, 5)])
pv = ProjectionViewer(1200, 1000)
pv.addWireframe('cube', cube)
pv.run()
The code that does the multiplying is in the wireframe file and the transform_for_perspective() function.
def transform_for_perspective(self):
for node in self.nodes:
print(node[0], node[1], node[2])
if node[2] != 0:
node[0] = node[0]*(1/(1-(node[2]*0.00005)))
node[1] = node[1]*(1/(1-(node[2]*0.00005)))
node[2] = node[2]*1
If anyone could tell me where I am going wrong and explain in which order I need to call the perspective matrix, i.e rotation then perspective or perspective and then rotation.
Also, Because Pygame starts at (0,0) in the top left corner this means that if I want to rotate about the centre of the screen I have to translate the centre of the screen, perform the rotation matrix and then translate it back to the centre. What does this mean for perspective? do I have to translate the centre of the screen to the top left and then perform the perspective matrix and then translate it back again?
Any help would be much appreciated.

The transformation that you are applying in transform_for_perspective should only be applied once. However, it seems that you are calling it on every frame, and as it stores the output in the same variable (self.nodes) it is applied many times.
Consider saving the output of that transformation in a new field (such as self.perspective_nodes).
Also, the transformation was not working for me, I tried to do some variations and came up with this:
class Wireframe:
def __init__(self):
self.nodes = np.zeros((0, 4))
self.perspective_nodes = None
self.edges = []
....
def transform_for_perspective(self, center):
self.perspective_nodes = self.nodes.copy()
for i in range(len(self.nodes)):
node = self.nodes[i]
p_node = self.perspective_nodes[i]
print(node[0], node[1], node[2])
if node[2] != 0:
p_node[0] = center[0] + (node[0]-center[0])*250/(200-(node[2]))
p_node[1] = center[1] + (node[1]-center[1])*250/(200-(node[2]))
p_node[2] = node[2] * 1
You also need to modify display in projectionViewer:
def display(self):
self.screen.fill(self.background)
for wireframe in self.wireframes.values():
wireframe.transform_for_perspective((self.width/2, self.height/2))
if self.displayNodes:
for node in wireframe.perspective_nodes:
pygame.draw.circle(self.screen, self.nodeColour, (int(
node[0]), int(node[1])), self.nodeRadius, 0)
if self.displayEdges:
for n1, n2 in wireframe.edges:
pygame.draw.aaline(
self.screen, self.edgeColour, wireframe.perspective_nodes[n1][:2], wireframe.perspective_nodes[n2][:2], 1)

Related

How to obtain the precise values of the streets of a city with OSMnx?

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m.fill(GRAY)
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m.draw_road(data['geometry'], inc, BLUE)
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m.update()
Other functions and objects I use for plotting. This is the code of map.py
from typing import List, Tuple
from window import Window
from pygame import gfxdraw
from shapely.geometry import LineString
def build_rect(
start: Tuple[float,float],
end: Tuple[float,float],
width: float = 3
) -> List[Tuple[float,float]]:
x0, y0 = start
x1, y1 = end
if x0**2 + y0**2 > x1**2 + y1**2:
x0, y0 = end
x1, y1 = start
# vector from start to end
vX, vY = x1 - x0, y1 - y0
# normal vector
nX, nY = -vY, vX
# normalize
n = (nX**2 + nY**2)**0.5
nX, nY = width/n * nX, width/n * nY
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x2, y2 = x1 + nX, y1 + nY
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x3, y3 = x0 + nX, y0 + nY
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class Map(Window):
def __init__(self, width, height, **kwargs):
super().__init__(width, height, **kwargs)
def draw_road(self, st: LineString, inc: float, color: Tuple[float,float,float]):
last = None
for c in st.__geo_interface__['coordinates']:
c = (inc*c[0], inc*c[1])
if last == None:
last = (c[0] - self.lat,c[1] - self.lng)
continue
lat = c[0] - self.lat
lng = c[1] - self.lng
pts = build_rect(last, (lat, lng))
gfxdraw.filled_polygon(self.screen, [
(self.x + lat * self.zoom, self.y + lng * self.zoom)
for lat, lng in pts
], color)
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import pygame
from pygame import gfxdraw
from pygame.locals import *
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def __init__(self, width, height, **kwargs):
self.width = width
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self.zoom -= self.i_zoom
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(self.x + pt[0] * self.zoom, self.y + pt[1] * self.zoom)
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pygame.display.update()

Attribute Error while using PyQtgraph libraries in my python code

I'm running a code from github site and it has this error ( last lines) :
File "D:\Anaconda3\lib\site-packages\pyqtgraph\opengl\GLViewWidget.py", line 152, in viewMatrix
tr.translate(-center.x(), -center.y(), -center.z())
AttributeError: 'int' object has no attribute 'x'
I found that the error is related to pyqtgraph libraries and i didn't change their files
just install the last versions of PyOpenGl and PyQtGraph in spyder
can you please help me in this error?
We need more information,
The problem seems to be related to the fact that center is an int but you use it as an object with attributs
Can we see center's initialization ?
the GlViewWidget.py file :
from ..Qt import QtCore, QtGui, QtOpenGL, QT_LIB
from OpenGL.GL import *
import OpenGL.GL.framebufferobjects as glfbo
import numpy as np
from .. import Vector
from .. import functions as fn
##Vector = QtGui.QVector3D
ShareWidget = None
class GLViewWidget(QtOpenGL.QGLWidget):
"""
Basic widget for displaying 3D data
- Rotation/scale controls
- Axis/grid display
- Export options
High-DPI displays: Qt5 should automatically detect the correct resolution.
For Qt4, specify the ``devicePixelRatio`` argument when initializing the
widget (usually this value is 1-2).
"""
def __init__(self, parent=None, devicePixelRatio=None):
global ShareWidget
if ShareWidget is None:
## create a dummy widget to allow sharing objects (textures, shaders, etc) between views
ShareWidget = QtOpenGL.QGLWidget()
QtOpenGL.QGLWidget.__init__(self, parent, ShareWidget)
self.setFocusPolicy(QtCore.Qt.ClickFocus)
self.opts = {
'center': Vector(0,0,0), ## will always appear at the center of the widget
'distance': 10.0, ## distance of camera from center
'fov': 60, ## horizontal field of view in degrees
'elevation': 30, ## camera's angle of elevation in degrees
'azimuth': 45, ## camera's azimuthal angle in degrees
## (rotation around z-axis 0 points along x-axis)
'viewport': None, ## glViewport params; None == whole widget
'devicePixelRatio': devicePixelRatio,
}
self.setBackgroundColor('k')
self.items = []
self.noRepeatKeys = [QtCore.Qt.Key_Right, QtCore.Qt.Key_Left, QtCore.Qt.Key_Up, QtCore.Qt.Key_Down, QtCore.Qt.Key_PageUp, QtCore.Qt.Key_PageDown]
self.keysPressed = {}
self.keyTimer = QtCore.QTimer()
self.keyTimer.timeout.connect(self.evalKeyState)
self.makeCurrent()
def addItem(self, item):
self.items.append(item)
if hasattr(item, 'initializeGL'):
self.makeCurrent()
try:
item.initializeGL()
except:
self.checkOpenGLVersion('Error while adding item %s to GLViewWidget.' % str(item))
item._setView(self)
#print "set view", item, self, item.view()
self.update()
def removeItem(self, item):
self.items.remove(item)
item._setView(None)
self.update()
def initializeGL(self):
self.resizeGL(self.width(), self.height())
def setBackgroundColor(self, *args, **kwds):
"""
Set the background color of the widget. Accepts the same arguments as
pg.mkColor() and pg.glColor().
"""
self.opts['bgcolor'] = fn.glColor(*args, **kwds)
self.update()
def getViewport(self):
vp = self.opts['viewport']
dpr = self.devicePixelRatio()
if vp is None:
return (0, 0, int(self.width() * dpr), int(self.height() * dpr))
else:
return tuple([int(x * dpr) for x in vp])
def devicePixelRatio(self):
dpr = self.opts['devicePixelRatio']
if dpr is not None:
return dpr
if hasattr(QtOpenGL.QGLWidget, 'devicePixelRatio'):
return QtOpenGL.QGLWidget.devicePixelRatio(self)
else:
return 1.0
def resizeGL(self, w, h):
pass
#glViewport(*self.getViewport())
#self.update()
def setProjection(self, region=None):
m = self.projectionMatrix(region)
glMatrixMode(GL_PROJECTION)
glLoadIdentity()
a = np.array(m.copyDataTo()).reshape((4,4))
glMultMatrixf(a.transpose())
def projectionMatrix(self, region=None):
if region is None:
dpr = self.devicePixelRatio()
region = (0, 0, self.width() * dpr, self.height() * dpr)
x0, y0, w, h = self.getViewport()
dist = self.opts['distance']
fov = self.opts['fov']
nearClip = dist * 0.001
farClip = dist * 1000.
r = nearClip * np.tan(fov * 0.5 * np.pi / 180.)
t = r * h / w
## Note that X0 and width in these equations must be the values used in viewport
left = r * ((region[0]-x0) * (2.0/w) - 1)
right = r * ((region[0]+region[2]-x0) * (2.0/w) - 1)
bottom = t * ((region[1]-y0) * (2.0/h) - 1)
top = t * ((region[1]+region[3]-y0) * (2.0/h) - 1)
tr = QtGui.QMatrix4x4()
tr.frustum(left, right, bottom, top, nearClip, farClip)
return tr
def setModelview(self):
glMatrixMode(GL_MODELVIEW)
glLoadIdentity()
m = self.viewMatrix()
a = np.array(m.copyDataTo()).reshape((4,4))
glMultMatrixf(a.transpose())
def viewMatrix(self):
tr = QtGui.QMatrix4x4()
tr.translate( 0.0, 0.0, -self.opts['distance'])
tr.rotate(self.opts['elevation']-90, 1, 0, 0)
tr.rotate(self.opts['azimuth']+90, 0, 0, -1)
center = self.opts['center']
tr.translate(-center.x(), -center.y(), -center.z())
return tr
def itemsAt(self, region=None):
"""
Return a list of the items displayed in the region (x, y, w, h)
relative to the widget.
"""
region = (region[0], self.height()-(region[1]+region[3]), region[2], region[3])
#buf = np.zeros(100000, dtype=np.uint)
buf = glSelectBuffer(100000)
try:
glRenderMode(GL_SELECT)
glInitNames()
glPushName(0)
self._itemNames = {}
self.paintGL(region=region, useItemNames=True)
finally:
hits = glRenderMode(GL_RENDER)
items = [(h.near, h.names[0]) for h in hits]
items.sort(key=lambda i: i[0])
return [self._itemNames[i[1]] for i in items]
def paintGL(self, region=None, viewport=None, useItemNames=False):
"""
viewport specifies the arguments to glViewport. If None, then we use self.opts['viewport']
region specifies the sub-region of self.opts['viewport'] that should be rendered.
Note that we may use viewport != self.opts['viewport'] when exporting.
"""
if viewport is None:
glViewport(*self.getViewport())
else:
glViewport(*viewport)
self.setProjection(region=region)
self.setModelview()
bgcolor = self.opts['bgcolor']
glClearColor(*bgcolor)
glClear( GL_DEPTH_BUFFER_BIT | GL_COLOR_BUFFER_BIT )
self.drawItemTree(useItemNames=useItemNames)
def drawItemTree(self, item=None, useItemNames=False):
if item is None:
items = [x for x in self.items if x.parentItem() is None]
else:
items = item.childItems()
items.append(item)
items.sort(key=lambda a: a.depthValue())
for i in items:
if not i.visible():
continue
if i is item:
try:
glPushAttrib(GL_ALL_ATTRIB_BITS)
if useItemNames:
glLoadName(i._id)
self._itemNames[i._id] = i
i.paint()
except:
from .. import debug
debug.printExc()
msg = "Error while drawing item %s." % str(item)
ver = glGetString(GL_VERSION)
if ver is not None:
ver = ver.split()[0]
if int(ver.split(b'.')[0]) < 2:
print(msg + " The original exception is printed above; however, pyqtgraph requires OpenGL version 2.0 or greater for many of its 3D features and your OpenGL version is %s. Installing updated display drivers may resolve this issue." % ver)
else:
print(msg)
finally:
glPopAttrib()
else:
glMatrixMode(GL_MODELVIEW)
glPushMatrix()
try:
tr = i.transform()
a = np.array(tr.copyDataTo()).reshape((4,4))
glMultMatrixf(a.transpose())
self.drawItemTree(i, useItemNames=useItemNames)
finally:
glMatrixMode(GL_MODELVIEW)
glPopMatrix()
def setCameraPosition(self, pos=None, distance=None, elevation=None, azimuth=None):
if pos is not None:
self.opts['center'] = pos
if distance is not None:
self.opts['distance'] = distance
if elevation is not None:
self.opts['elevation'] = elevation
if azimuth is not None:
self.opts['azimuth'] = azimuth
self.update()
def cameraPosition(self):
"""Return current position of camera based on center, dist, elevation, and azimuth"""
center = self.opts['center']
dist = self.opts['distance']
elev = self.opts['elevation'] * np.pi/180.
azim = self.opts['azimuth'] * np.pi/180.
pos = Vector(
center.x() + dist * np.cos(elev) * np.cos(azim),
center.y() + dist * np.cos(elev) * np.sin(azim),
center.z() + dist * np.sin(elev)
)
return pos
def orbit(self, azim, elev):
"""Orbits the camera around the center position. *azim* and *elev* are given in degrees."""
self.opts['azimuth'] += azim
self.opts['elevation'] = np.clip(self.opts['elevation'] + elev, -90, 90)
self.update()
def pan(self, dx, dy, dz, relative='global'):
"""
Moves the center (look-at) position while holding the camera in place.
============== =======================================================
**Arguments:**
*dx* Distance to pan in x direction
*dy* Distance to pan in y direction
*dx* Distance to pan in z direction
*relative* String that determines the direction of dx,dy,dz.
If "global", then the global coordinate system is used.
If "view", then the z axis is aligned with the view
direction, and x and y axes are inthe plane of the
view: +x points right, +y points up.
If "view-upright", then x is in the global xy plane and
points to the right side of the view, y is in the
global xy plane and orthogonal to x, and z points in
the global z direction.
============== =======================================================
Distances are scaled roughly such that a value of 1.0 moves
by one pixel on screen.
Prior to version 0.11, *relative* was expected to be either True (x-aligned) or
False (global). These values are deprecated but still recognized.
"""
# for backward compatibility:
relative = {True: "view-upright", False: "global"}.get(relative, relative)
if relative == 'global':
self.opts['center'] += QtGui.QVector3D(dx, dy, dz)
elif relative == 'view-upright':
cPos = self.cameraPosition()
cVec = self.opts['center'] - cPos
dist = cVec.length() ## distance from camera to center
xDist = dist * 2. * np.tan(0.5 * self.opts['fov'] * np.pi / 180.) ## approx. width of view at distance of center point
xScale = xDist / self.width()
zVec = QtGui.QVector3D(0,0,1)
xVec = QtGui.QVector3D.crossProduct(zVec, cVec).normalized()
yVec = QtGui.QVector3D.crossProduct(xVec, zVec).normalized()
self.opts['center'] = self.opts['center'] + xVec * xScale * dx + yVec * xScale * dy + zVec * xScale * dz
elif relative == 'view':
# pan in plane of camera
elev = np.radians(self.opts['elevation'])
azim = np.radians(self.opts['azimuth'])
fov = np.radians(self.opts['fov'])
dist = (self.opts['center'] - self.cameraPosition()).length()
fov_factor = np.tan(fov / 2) * 2
scale_factor = dist * fov_factor / self.width()
z = scale_factor * np.cos(elev) * dy
x = scale_factor * (np.sin(azim) * dx - np.sin(elev) * np.cos(azim) * dy)
y = scale_factor * (np.cos(azim) * dx + np.sin(elev) * np.sin(azim) * dy)
self.opts['center'] += QtGui.QVector3D(x, -y, z)
else:
raise ValueError("relative argument must be global, view, or view-upright")
self.update()
def pixelSize(self, pos):
"""
Return the approximate size of a screen pixel at the location pos
Pos may be a Vector or an (N,3) array of locations
"""
cam = self.cameraPosition()
if isinstance(pos, np.ndarray):
cam = np.array(cam).reshape((1,)*(pos.ndim-1)+(3,))
dist = ((pos-cam)**2).sum(axis=-1)**0.5
else:
dist = (pos-cam).length()
xDist = dist * 2. * np.tan(0.5 * self.opts['fov'] * np.pi / 180.)
return xDist / self.width()
def mousePressEvent(self, ev):
self.mousePos = ev.pos()
def mouseMoveEvent(self, ev):
diff = ev.pos() - self.mousePos
self.mousePos = ev.pos()
if ev.buttons() == QtCore.Qt.LeftButton:
if (ev.modifiers() & QtCore.Qt.ControlModifier):
self.pan(diff.x(), diff.y(), 0, relative='view')
else:
self.orbit(-diff.x(), diff.y())
elif ev.buttons() == QtCore.Qt.MidButton:
if (ev.modifiers() & QtCore.Qt.ControlModifier):
self.pan(diff.x(), 0, diff.y(), relative='view-upright')
else:
self.pan(diff.x(), diff.y(), 0, relative='view-upright')
def mouseReleaseEvent(self, ev):
pass
# Example item selection code:
#region = (ev.pos().x()-5, ev.pos().y()-5, 10, 10)
#print(self.itemsAt(region))
## debugging code: draw the picking region
#glViewport(*self.getViewport())
#glClear( GL_DEPTH_BUFFER_BIT | GL_COLOR_BUFFER_BIT )
#region = (region[0], self.height()-(region[1]+region[3]), region[2], region[3])
#self.paintGL(region=region)
#self.swapBuffers()
def wheelEvent(self, ev):
delta = 0
if QT_LIB in ['PyQt4', 'PySide']:
delta = ev.delta()
else:
delta = ev.angleDelta().x()
if delta == 0:
delta = ev.angleDelta().y()
if (ev.modifiers() & QtCore.Qt.ControlModifier):
self.opts['fov'] *= 0.999**delta
else:
self.opts['distance'] *= 0.999**delta
self.update()
def keyPressEvent(self, ev):
if ev.key() in self.noRepeatKeys:
ev.accept()
if ev.isAutoRepeat():
return
self.keysPressed[ev.key()] = 1
self.evalKeyState()
def keyReleaseEvent(self, ev):
if ev.key() in self.noRepeatKeys:
ev.accept()
if ev.isAutoRepeat():
return
try:
del self.keysPressed[ev.key()]
except:
self.keysPressed = {}
self.evalKeyState()
def evalKeyState(self):
speed = 2.0
if len(self.keysPressed) > 0:
for key in self.keysPressed:
if key == QtCore.Qt.Key_Right:
self.orbit(azim=-speed, elev=0)
elif key == QtCore.Qt.Key_Left:
self.orbit(azim=speed, elev=0)
elif key == QtCore.Qt.Key_Up:
self.orbit(azim=0, elev=-speed)
elif key == QtCore.Qt.Key_Down:
self.orbit(azim=0, elev=speed)
elif key == QtCore.Qt.Key_PageUp:
pass
elif key == QtCore.Qt.Key_PageDown:
pass
self.keyTimer.start(16)
else:
self.keyTimer.stop()
def checkOpenGLVersion(self, msg):
## Only to be called from within exception handler.
ver = glGetString(GL_VERSION).split()[0]
if int(ver.split(b'.')[0]) < 2:
from .. import debug
debug.printExc()
raise Exception(msg + " The original exception is printed above; however, pyqtgraph requires OpenGL version 2.0 or greater for many of its 3D features and your OpenGL version is %s. Installing updated display drivers may resolve this issue." % ver)
else:
raise
def readQImage(self):
"""
Read the current buffer pixels out as a QImage.
"""
w = self.width()
h = self.height()
self.repaint()
pixels = np.empty((h, w, 4), dtype=np.ubyte)
pixels[:] = 128
pixels[...,0] = 50
pixels[...,3] = 255
glReadPixels(0, 0, w, h, GL_RGBA, GL_UNSIGNED_BYTE, pixels)
# swap B,R channels for Qt
tmp = pixels[...,0].copy()
pixels[...,0] = pixels[...,2]
pixels[...,2] = tmp
pixels = pixels[::-1] # flip vertical
img = fn.makeQImage(pixels, transpose=False)
return img
def renderToArray(self, size, format=GL_BGRA, type=GL_UNSIGNED_BYTE, textureSize=1024, padding=256):
w,h = map(int, size)
self.makeCurrent()
tex = None
fb = None
try:
output = np.empty((w, h, 4), dtype=np.ubyte)
fb = glfbo.glGenFramebuffers(1)
glfbo.glBindFramebuffer(glfbo.GL_FRAMEBUFFER, fb )
glEnable(GL_TEXTURE_2D)
tex = glGenTextures(1)
glBindTexture(GL_TEXTURE_2D, tex)
texwidth = textureSize
data = np.zeros((texwidth,texwidth,4), dtype=np.ubyte)
## Test texture dimensions first
glTexImage2D(GL_PROXY_TEXTURE_2D, 0, GL_RGBA, texwidth, texwidth, 0, GL_RGBA, GL_UNSIGNED_BYTE, None)
if glGetTexLevelParameteriv(GL_PROXY_TEXTURE_2D, 0, GL_TEXTURE_WIDTH) == 0:
raise Exception("OpenGL failed to create 2D texture (%dx%d); too large for this hardware." % shape[:2])
## create teture
glTexImage2D(GL_TEXTURE_2D, 0, GL_RGBA, texwidth, texwidth, 0, GL_RGBA, GL_UNSIGNED_BYTE, data.transpose((1,0,2)))
self.opts['viewport'] = (0, 0, w, h) # viewport is the complete image; this ensures that paintGL(region=...)
# is interpreted correctly.
p2 = 2 * padding
for x in range(-padding, w-padding, texwidth-p2):
for y in range(-padding, h-padding, texwidth-p2):
x2 = min(x+texwidth, w+padding)
y2 = min(y+texwidth, h+padding)
w2 = x2-x
h2 = y2-y
## render to texture
glfbo.glFramebufferTexture2D(glfbo.GL_FRAMEBUFFER, glfbo.GL_COLOR_ATTACHMENT0, GL_TEXTURE_2D, tex, 0)
self.paintGL(region=(x, h-y-h2, w2, h2), viewport=(0, 0, w2, h2)) # only render sub-region
glBindTexture(GL_TEXTURE_2D, tex) # fixes issue #366
## read texture back to array
data = glGetTexImage(GL_TEXTURE_2D, 0, format, type)
data = np.fromstring(data, dtype=np.ubyte).reshape(texwidth,texwidth,4).transpose(1,0,2)[:, ::-1]
output[x+padding:x2-padding, y+padding:y2-padding] = data[padding:w2-padding, -(h2-padding):-padding]
finally:
self.opts['viewport'] = None
glfbo.glBindFramebuffer(glfbo.GL_FRAMEBUFFER, 0)
glBindTexture(GL_TEXTURE_2D, 0)
if tex is not None:
glDeleteTextures([tex])
if fb is not None:
glfbo.glDeleteFramebuffers([fb])
return output
Somewhere in your code you are setting the center to be an int. setCameraPosition, maybe? It needs to be a Vector object, instead.

My parabola is working fine alone, but it's wrong in Pygame

So I created this parabola class which can be instantiated with 3 parameters (a, b and c) or with 3 points belonging to the parabola. The punti() function returns all the points belonging to the parabola in a range defined by n and m. Here's the code (Most of this is in Italian, sorry):
class Parabola:
def __init__(self, tipo=0, *params):
'''
Il tipo è 0 per costruire la parabola con a, b, c; 1 per costruire la parabola con
tre punti per la quale passa
'''
if tipo == 0:
self.__a = params[0]
self.__b = params[1]
self.__c = params[2]
self.__delta = self.__b ** 2 - (4 * self.__a * self.__c)
elif tipo == 1:
matrix_a = np.array([
[params[0][0]**2, params[0][0], 1],
[params[1][0]**2, params[1][0], 1],
[params[2][0]**2, params[2][0], 1]
])
matrix_b = np.array([params[0][1], params[1][1], params[2][1]])
matrix_c = np.linalg.solve(matrix_a, matrix_b)
self.__a = round(matrix_c[0], 2)
self.__b = round(matrix_c[1], 2)
self.__c = round(matrix_c[2], 2)
self.__delta = self.__b ** 2 - (4 * self.__a * self.__c)
def trovaY(self, x):
y = self.__a * x ** 2 + self.__b * x + self.__c
return y
def punti(self, n, m, step=1):
output = []
for x in range(int(min(n, m)), int(max(n, m)) + 1, step):
output.append((x, self.trovaY(x)))
return output
Now my little game is about shooting targets with a bow and i have to use the parabola for the trajectory and it passes by 3 points:
The player center
A point with the cursor's x and player's y
A point in the middle with the cursors's y
The trajectory is represented by a black line but it clearly doesn't work and I can't understand why. Here's the code of the game (Don't mind about the bow's rotation, I still have to make it function properly):
import os
import sys
import pygame
from random import randint
sys.path.insert(
1, __file__.replace("pygame-prototype\\" + os.path.basename(__file__), "coniche\\")
)
import parabola
# Initialization
pygame.init()
WIDTH, HEIGHT = 1024, 576
screen = pygame.display.set_mode((WIDTH, HEIGHT))
# Function to rotate without losing quality
def rot_from_zero(surface, angle):
rotated_surface = pygame.transform.rotozoom(surface, angle, 1)
rotated_rect = rotated_surface.get_rect()
return rotated_surface, rotated_rect
# Function to map a range of values to another
def map_range(value, leftMin, leftMax, rightMin, rightMax):
# Figure out how 'wide' each range is
leftSpan = leftMax - leftMin
rightSpan = rightMax - rightMin
# Convert the left range into a 0-1 range (float)
valueScaled = float(value - leftMin) / float(leftSpan)
# Convert the 0-1 range into a value in the right range.
return rightMin + (valueScaled * rightSpan)
# Player class
class Player:
def __init__(self, x, y, width=64, height=64):
self.rect = pygame.Rect(x, y, width, height)
self.dirx = 0
self.diry = 0
def draw(self):
rectangle = pygame.draw.rect(screen, (255, 0, 0), self.rect)
# Target class
class Target:
def __init__(self, x, y, acceleration=0.25):
self.x, self.y = x, y
self.image = pygame.image.load(
__file__.replace(os.path.basename(__file__), "target.png")
)
self.speed = 0
self.acceleration = acceleration
def draw(self):
screen.blit(self.image, (self.x, self.y))
def update(self):
self.speed -= self.acceleration
self.x += int(self.speed)
if self.speed < -1:
self.speed = 0
player = Player(64, HEIGHT - 128)
# Targets init
targets = []
targets_spawn_time = 3000
previous_ticks = pygame.time.get_ticks()
# Ground animation init
ground_frames = []
for i in os.listdir(__file__.replace(os.path.basename(__file__), "ground_frames")):
ground_frames.append(
pygame.image.load(
__file__.replace(os.path.basename(__file__), "ground_frames\\" + i)
)
) # Load all ground frames
ground_frame_counter = 0 # Keep track of the current ground frame
frame_counter = 0
# Bow
bow = pygame.image.load(__file__.replace(os.path.basename(__file__), "bow.png"))
angle = 0
while 1:
for event in pygame.event.get():
if event.type == pygame.QUIT:
sys.exit()
# Spawning the targets
current_ticks = pygame.time.get_ticks()
if current_ticks - previous_ticks >= targets_spawn_time:
targets.append(Target(WIDTH, randint(0, HEIGHT - 110)))
previous_ticks = current_ticks
screen.fill((101, 203, 214))
player.draw()
for i, e in list(enumerate(targets))[::-1]:
e.draw()
e.update()
if e.x <= -e.image.get_rect().width:
del targets[i]
# Calculating the angle of the bow
mouse_pos = pygame.Vector2(pygame.mouse.get_pos())
angle = map_range(mouse_pos.x, 0, WIDTH, 90, 0)
# Rotate the bow
rotated_bow, rotated_bow_rect = rot_from_zero(bow, angle)
rotated_bow_rect.center = player.rect.center
screen.blit(rotated_bow, rotated_bow_rect)
# Animate the ground
if frame_counter % 24 == 0:
ground_frame_counter += 1
if ground_frame_counter >= len(ground_frames):
ground_frame_counter = 0
for i in range(round(WIDTH / ground_frames[ground_frame_counter].get_rect().width)):
screen.blit(
ground_frames[ground_frame_counter],
(
ground_frames[ground_frame_counter].get_rect().width * i,
HEIGHT - ground_frames[ground_frame_counter].get_rect().height,
),
)
# Calculating the trajectory
mouse_pos.x = (
mouse_pos.x if mouse_pos.x != rotated_bow_rect.centerx else mouse_pos.x + 1
)
# print(mouse_pos, rotated_bow_rect.center)
v_x = rotated_bow_rect.centerx + ((mouse_pos.x - rotated_bow_rect.centerx) / 2)
trajectory_parabola = parabola.Parabola(
1,
rotated_bow_rect.center,
(mouse_pos.x, rotated_bow_rect.centery),
(v_x, mouse_pos.y),
)
trajectory = [(i[0], int(i[1])) for i in trajectory_parabola.punti(0, WIDTH)]
pygame.draw.lines(screen, (0, 0, 0), False, trajectory)
pygame.draw.ellipse(
screen, (128, 128, 128), pygame.Rect(v_x - 15, mouse_pos.y - 15, 30, 30)
)
pygame.draw.ellipse(
screen,
(128, 128, 128),
pygame.Rect(mouse_pos.x - 15, rotated_bow_rect.centery - 15, 30, 30),
)
pygame.display.update()
if frame_counter == 120:
for i in trajectory:
print(i)
frame_counter += 1
You can run all of this and understand what's wrong with it, help?
You round the values of a, b and c to 2 decimal places. This is too inaccurate for this application:
self.__a = round(matrix_c[0], 2)
self.__b = round(matrix_c[1], 2)
self.__c = round(matrix_c[2], 2)
self.__a = matrix_c[0]
self.__b = matrix_c[1]
self.__c = matrix_c[2]
Similar to answer above... rounding is the issue here. This is magnified when the scale of the coordinates gets bigger.
However, disagree with other solution: It does not matter what order you pass the coordinates into your parabola construction. Any order works fine. points are points.
Here is a pic of your original parabola function "drooping" because of rounding error:
p1 = (0, 10) # left
p2 = (100, 10) # right
p3 = (50, 100) # apex
p = Parabola(1, p3, p2, p1)
traj = p.punti(0, 100)
xs, ys = zip(*traj)
plt.scatter(xs, ys)
plt.plot([0, 100], [10, 10], color='r')
plt.show()

Incorrect Rotation of Shape in Python

I'm trying to create a rotating plane in pygame. I'm converting 3d (x, y, z) coordinates to screen coordinates (x, y), and then rotating the screen coordinates. This seems to work when its rotating on both the x and y axis, but when it's rotating on only one axis (I commented out the y axis rotation) it is slanted. I can't seem to figure out why?
import pygame
import math
red = (255, 0, 0)
class Vector3:
def __init__(self, _x, _y, _z):
self.x = _x
self.y = _y
self.z = _z
class Vector2:
def __init__(self, _x, _y):
self.x = _x
self.y = _y
class Plane:
def draw(self, screen, value):
scale = 25
points = []
vertices = [Vector3(0, 1, 0),
Vector3(1, 1, 0),
Vector3(1, 0, 0),
Vector3(0, 0, 0)]
for vert in vertices:
x, y = vec3to2(vert)
points.append(Vector2(x * scale + 40, y * scale + 100))
print((x, y))
centerx = (points[0].x + points[1].x + points[2].x + points[3].x) / 4
centery = (points[0].y + points[1].y + points[2].y + points[3].y) / 4
for point in points:
rotx, roty = vec3rot(point, math.radians(value), centerx, centery)
point.x = rotx
#point.y = roty
pygame.draw.line(screen, red, (points[0].x, points[0].y), (points[1].x, points[1].y))
pygame.draw.line(screen, red, (points[1].x, points[1].y), (points[2].x, points[2].y))
pygame.draw.line(screen, red, (points[0].x, points[0].y), (points[3].x, points[3].y))
pygame.draw.line(screen, red, (points[3].x, points[3].y), (points[2].x, points[2].y))
pygame.draw.circle(screen, red, (int(centerx), int(centery)), 1)
def vec3to2(vect3):
try:
_x = vect3.x / vect3.z
except ZeroDivisionError:
_x = vect3.x
try:
_y = vect3.y / vect3.z
except ZeroDivisionError:
_y = vect3.y
return(_x, _y)
def vec3rot(vect3, theta, centerx, centery):
_x = centerx + (vect3.x - centerx) * math.cos(theta) - (vect3.y - centery) * math.sin(theta)
_y = centery + (vect3.x - centerx) * math.sin(theta) + (vect3.y - centery) * math.cos(theta)
return(_x, _y)
def main():
pygame.init()
screen = pygame.display.set_mode((640, 480))
v = 0
plane = Plane()
running = True
while running:
screen.fill((0, 0, 0))
plane.draw(screen, v)
pygame.display.flip()
v += 0.1
for event in pygame.event.get():
if event.type == pygame.QUIT:
running = False
main()

How to draw a Spiral & Arc Shape Curves using pygame? [duplicate]

I am trying to make realistic water in pygame:
This is till now my code:
from random import randint
import pygame
WIDTH = 700
HEIGHT = 500
win = pygame.display.set_mode((WIDTH, HEIGHT))
WHITE = (255, 255, 255)
BLACK = (0, 0, 0)
AQUA = 'aqua'
RADIUS = 1
x, y = 0, HEIGHT//2
K = 1
FORCE = 100
VELOCITY = 0.5
run = True
class Molecule:
def __init__(self, x, y, radius, force, k):
self.x = x
self.y = y
self.radius = radius
self.force = force
self.k = k
self.max_amplitude = y + force/k
self.min_amplitude = y - force/k
self.up = False
self.down = True
self.restore = False
def draw(self, win):
pygame.draw.circle(win, BLACK, (self.x, self.y), self.radius)
def oscillate(self):
if self.y <= self.max_amplitude and self.down == True:
self.y += VELOCITY
if self.y == self.max_amplitude or self.up:
self.up = True
self.down = False
self.y -= VELOCITY
if self.y == self.min_amplitude:
self.up = False
self.down = True
molecules = []
for i in range(100):
FORCE = randint(10, 20)
molecules.append(Molecule(x, y, RADIUS, FORCE, K))
x += 10
while run:
for event in pygame.event.get():
if event.type == pygame.QUIT:
run = False
win.fill(WHITE)
for molecule in molecules:
molecule.draw(win)
molecule.oscillate()
for i in range(len(molecules)):
try:
pygame.draw.line(win, BLACK, (molecules[i].x, molecules[i].y), (molecules[i+1].x, molecules[i+1].y))
pygame.draw.line(win, AQUA, (molecules[i].x, molecules[i].y), (molecules[i+1].x, HEIGHT))
except:
pass
pygame.display.flip()
pygame.quit()
But as may expected the water curve is not smooth:
Look at it:
Sample Img1
I want to connect the two randomly added wave points using a set of circles not line like in this one so that a smooth curve could occur.
And in this way i could add the water color to it such that it will draw aqua lines or my desired color line from the point to the end of screen and all this will end up with smooth water flowing simulation.
Now the question is how could i make the points connect together smoothly into a smooth curve by drawing point circles at relative points?
I suggest sticking the segments with a Bézier curves. Bézier curves can be drawn with pygame.gfxdraw.bezier
Calculate the slopes of the tangents to the points along the wavy waterline:
ts = []
for i in range(len(molecules)):
pa = molecules[max(0, i-1)]
pb = molecules[min(len(molecules)-1, i+1)]
ts.append((pb.y-pa.y) / (pb.x-pa.x))
Use the the tangents to define 4 control points for each segment and draw the curve with pygame.gfxdraw.bezier:
for i in range(len(molecules)-1):
p0 = molecules[i].x, molecules[i].y
p3 = molecules[i+1].x, molecules[i+1].y
p1 = p0[0] + 10, p0[1] + 10 * ts[i]
p2 = p3[0] - 10, p3[1] - 10 * ts[i+1]
pygame.gfxdraw.bezier(win, [p0, p1, p2, p3], 4, BLACK)
Complete example:
from random import randint
import pygame
import pygame.gfxdraw
WIDTH = 700
HEIGHT = 500
win = pygame.display.set_mode((WIDTH, HEIGHT))
WHITE = (255, 255, 255)
BLACK = (0, 0, 0)
AQUA = 'aqua'
RADIUS = 1
x, y = 0, HEIGHT//2
K = 1
FORCE = 100
VELOCITY = 0.5
class Molecule:
def __init__(self, x, y, radius, force, k):
self.x = x
self.y = y
self.radius = radius
self.force = force
self.k = k
self.max_amplitude = y + force/k
self.min_amplitude = y - force/k
self.up = False
self.down = True
self.restore = False
def draw(self, win):
pygame.draw.circle(win, BLACK, (self.x, self.y), self.radius)
def oscillate(self):
if self.y <= self.max_amplitude and self.down == True:
self.y += VELOCITY
if self.y == self.max_amplitude or self.up:
self.up = True
self.down = False
self.y -= VELOCITY
if self.y == self.min_amplitude:
self.up = False
self.down = True
molecules = []
for i in range(50):
FORCE = randint(10, 20)
molecules.append(Molecule(x, y, RADIUS, FORCE, K))
x += 20
clock = pygame.time.Clock()
run = True
while run:
clock.tick(100)
for event in pygame.event.get():
if event.type == pygame.QUIT:
run = False
win.fill(WHITE)
for molecule in molecules:
molecule.draw(win)
molecule.oscillate()
ts = []
for i in range(len(molecules)):
pa = molecules[max(0, i-1)]
pb = molecules[min(len(molecules)-1, i+1)]
ts.append((pb.y-pa.y) / (pb.x-pa.x))
for i in range(len(molecules)-1):
p0 = molecules[i].x, molecules[i].y
p3 = molecules[i+1].x, molecules[i+1].y
p1 = p0[0] + 10, p0[1] + 10 * ts[i]
p2 = p3[0] - 10, p3[1] - 10 * ts[i+1]
pygame.gfxdraw.bezier(win, [p0, p1, p2, p3], 4, BLACK)
for i in range(len(molecules)-1):
pygame.draw.line(win, AQUA, (molecules[i].x, molecules[i].y), (molecules[i].x, HEIGHT))
pygame.display.flip()
pygame.quit()
If you want to "fill" the water, you must calculate the points along the Bézier line and draw a filled polygon. How to calculate a Bézier curve is explained in Trying to make a Bezier Curve on PyGame library How Can I Make a Thicker Bezier in Pygame? and "X". You can use the following function:
def ptOnCurve(b, t):
q = b.copy()
for k in range(1, len(b)):
for i in range(len(b) - k):
q[i] = (1-t) * q[i][0] + t * q[i+1][0], (1-t) * q[i][1] + t * q[i+1][1]
return round(q[0][0]), round(q[0][1])
def bezier(b, samples):
return [ptOnCurve(b, i/samples) for i in range(samples+1)]
Use the bezier to stitch the wavy water polygon:
ts = []
for i in range(len(molecules)):
pa = molecules[max(0, i-1)]
pb = molecules[min(len(molecules)-1, i+1)]
ts.append((pb.y-pa.y) / (pb.x-pa.x))
pts = [(WIDTH, HEIGHT), (0, HEIGHT)]
for i in range(len(molecules)-1):
p0 = molecules[i].x, molecules[i].y
p3 = molecules[i+1].x, molecules[i+1].y
p1 = p0[0] + 10, p0[1] + 10 * ts[i]
p2 = p3[0] - 10, p3[1] - 10 * ts[i+1]
pts += bezier([p0, p1, p2, p3], 4)
Draw the polygon with pygame.draw.polygon():
pygame.draw.polygon(win, AQUA, pts)
Complete example:
from random import randint
import pygame
class Node:
def __init__(self, x, y, force, k, v):
self.x = x
self.y = y
self.y0 = y
self.force = force
self.k = k
self.v = v
self.direction = 1
def oscillate(self):
self.y += self.v * self.direction
if self.y0 - self.force / self.k > self.y or self.y0 + self.force / self.k < self.y:
self.direction *= -1
def draw(self, surf):
pygame.draw.circle(surf, "black", (self.x, self.y), 3)
window = pygame.display.set_mode((700, 500))
clock = pygame.time.Clock()
width, height = window.get_size()
no_of_nodes = 25
dx = width / no_of_nodes
nodes = [Node(i*dx, height//2, randint(15, 30), 1, 0.5) for i in range(no_of_nodes+1)]
def ptOnCurve(b, t):
q = b.copy()
for k in range(1, len(b)):
for i in range(len(b) - k):
q[i] = (1-t) * q[i][0] + t * q[i+1][0], (1-t) * q[i][1] + t * q[i+1][1]
return round(q[0][0]), round(q[0][1])
def bezier(b, samples):
return [ptOnCurve(b, i/samples) for i in range(samples+1)]
run = True
while run:
clock.tick(100)
for event in pygame.event.get():
if event.type == pygame.QUIT:
run = False
for molecule in nodes:
molecule.oscillate()
ts = []
for i in range(len(nodes)):
pa = nodes[max(0, i-1)]
pb = nodes[min(len(nodes)-1, i+1)]
ts.append((pb.y-pa.y) / (pb.x-pa.x))
pts = [(width, height), (0, height)]
for i in range(len(nodes)-1):
p0 = nodes[i].x, nodes[i].y
p3 = nodes[i+1].x, nodes[i+1].y
p1 = p0[0] + 10, p0[1] + 10 * ts[i]
p2 = p3[0] - 10, p3[1] - 10 * ts[i+1]
pts += bezier([p0, p1, p2, p3], 4)
window.fill("white")
pygame.draw.polygon(window, 'aqua', pts)
for molecule in nodes:
molecule.draw(window)
pygame.display.flip()
pygame.quit()
exit()

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