Rotatable Tetrahedron (Python recipe) by Paulo Cavalcanti

ActiveState Code (http://code.activestate.com/recipes/578876/)

#!/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())