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Draws a 3D tetrahedron and allows a user to rotate it (mouse left button and wheel).

Python, 186 lines
 ``` 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("", cbClicked) canvas.bind("", cbMottion) canvas.bind("", resize) from platform import uname os = uname()[0] if ( os == "Linux" ): canvas.bind('', wheelUp) # X11 canvas.bind('', wheelDown) elif ( os == "Darwin" ): canvas.bind('', wheel) # MacOS else: canvas.bind_all('', 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.

 Created by Paulo Cavalcanti on Mon, 12 May 2014 (MIT)