Draws a 3D tetrahedron and allows a user to rotate it (mouse left button and wheel).
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 | #!/usr/bin/env python
# coding: UTF-8
#
## @package _12_tet
#
# Draws a 3D tetrahedron and allows a user to rotate it
# (mouse left button and wheel).
#
# The Tetrahedron is represented by a 3 x 4 matrix.
# Each column represents a 3D vertex.
#
# note: a m x n matrix is represented by a list of lines:
# [[l_1] [l_2] .. [l_m]].
# m = len(mat), n = len(mat[0]), mat(i,j) = mat[i][j]
#
# @author Paulo Roma
# @since 01/05/2014
# @see http://www.orimosenzon.com/wiki/index.php/Python_samples
# @see http://mathworld.wolfram.com/RotationMatrix.html
try:
from tkinter import * # python 3
except ImportError:
from Tkinter import * # python 2
from math import *
def createZeroMat(m,n):
"""Return a matrix (m x n) filled with zeros."""
ret = [0] * m
for i in range(m):
ret[i] = [0] * n
return ret
def matMul(mat1, mat2):
"""Return mat1 x mat2 (mat1 multiplied by mat2)."""
m = len(mat1)
n = len(mat2[0])
common = len(mat2)
ret = createZeroMat(m,n)
if len(mat1[0]) == len(mat2):
for i in range(m):
for j in range(n):
for k in range(common):
ret[i][j] += mat1[i][k] * mat2[k][j]
return ret
def matTrans(mat):
"""Return mat (n x m) transposed (m x n)."""
m = len(mat[0])
n = len(mat)
ret = createZeroMat(m,n)
for i in range(m):
for j in range(n):
ret[i][j] = mat[j][i]
return ret
def translate(x,y,dx,dy):
"""Translate vector(x,y) by (dx,dy)."""
return x+dx, y+dy
def drawTet(tet,col):
"""Draw a tetrahedron."""
w = canvas.winfo_width()/2
h = canvas.winfo_height()/2
canvas.delete(ALL) # delete all edges
nv = len(tet[0]) # number of vertices in tet (4)
# draw the 6 edges of the tetrahedron
for p1 in range(nv):
for p2 in range(p1+1,nv):
canvas.create_line(translate(tet[0][p1], tet[1][p1], w, h),
translate(tet[0][p2], tet[1][p2], w, h), fill = col)
def init():
"""Initialize global variables."""
global ROT_X, ROT_Y, ROT_Z
global eps, EPS, tet
global lastX, lastY, tetColor, bgColor
tet = matTrans([[0,-100,0],[-100,100,0],[100,100,0],[0,0,200]])
# counter-clockwise rotation about the X axis
ROT_X = lambda x: matTrans([[1,0,0], [0,cos(x),-sin(x)], [0,sin(x),cos(x)] ])
# counter-clockwise rotation about the Y axis
ROT_Y = lambda y: matTrans([[cos(y),0,sin(y)], [0,1,0], [-sin(y),0,cos(y)]])
# counter-clockwise rotation about the Z axis
ROT_Z = lambda z: matTrans([[cos(z),sin(z),0], [-sin(z),cos(z),0], [0,0,1]])
eps = lambda d: pi/300 if (d>0) else -pi/300
EPS = lambda d: d*pi/300
lastX = 0
lastY = 0
tetColor = 'black'
bgColor = 'white'
def cbClicked(event):
"""Save current mouse position."""
global lastX, lastY
lastX = event.x
lastY = event.y
def cbMottion(event):
"""Map mouse displacements in Y direction to rotations about X axis,
and mouse displacements in X direction to rotations about Y axis."""
global tet
# Y coordinate is upside down
dx = lastY - event.y
tet = matMul(ROT_X(EPS(-dx)),tet)
dy = lastX - event.x
tet = matMul(ROT_Y(EPS(dy)),tet)
drawTet(tet,tetColor)
cbClicked(event)
def wheelUp(event):
"""Map mouse wheel up displacements to rotations about Z axis."""
global tet
tet = matMul(ROT_Z(EPS(1)),tet)
drawTet(tet,tetColor)
def wheelDown(event):
"""Map mouse wheel down displacements to rotations about Z axis."""
global tet
tet = matMul(ROT_Z(EPS(-1)),tet)
drawTet(tet,tetColor)
def wheel(event):
"""Map mouse wheel displacements to rotations about Z axis."""
global tet
tet = matMul(ROT_Z(EPS(event.delta/120)),tet)
drawTet(tet,tetColor)
def resize(event):
"""Redraw the tetrahedron, in case of a window change due to user resizing it."""
drawTet(tet,tetColor)
def main():
global canvas
root = Tk()
root.title('Tetrahedron')
root.geometry('+0+0')
init()
canvas = Canvas(root, width=400, height=400, background=bgColor)
canvas.pack(fill=BOTH,expand=YES)
canvas.bind("<Button-1>", cbClicked)
canvas.bind("<B1-Motion>", cbMottion)
canvas.bind("<Configure>", resize)
from platform import uname
os = uname()[0]
if ( os == "Linux" ):
canvas.bind('<Button-4>', wheelUp) # X11
canvas.bind('<Button-5>', wheelDown)
elif ( os == "Darwin" ):
canvas.bind('<MouseWheel>', wheel) # MacOS
else:
canvas.bind_all('<MouseWheel>', wheel) # windows
drawTet(tet,tetColor)
mainloop()
if __name__=='__main__':
sys.exit(main())
|
How to manipulate a 3D shape (in the present case, a tetrahedron) using only python Tkinter.
Tags: rotatable, tetrahedron