#!/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())
Diff to Previous Revision
--- revision 1 2014-05-12 16:49:11
+++ revision 2 2014-05-14 21:03:40
@@ -2,11 +2,6 @@
# coding: UTF-8
#
## @package _12_tet
-#
-# @author Paulo Roma
-# @since 01/05/2014
-# @see http://www.orimosenzon.com/wiki/index.php/Python_samples
-# @see http://mathworld.wolfram.com/RotationMatrix.html
#
# Draws a 3D tetrahedron and allows a user to rotate it
# (mouse left button and wheel).
@@ -17,6 +12,11 @@
# 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
@@ -146,7 +146,7 @@
"""Map mouse wheel displacements to rotations about Z axis."""
global tet
- tet = matMul(ROT_Z(EPS(event.delta)),tet)
+ tet = matMul(ROT_Z(EPS(event.delta/120)),tet)
drawTet(tet,tetColor)
def resize(event):
