def minkdemo(list1,list2):
'''
Returns the Minkowski sum of two lists.
'''
output = []
for stuff1 in list1:
for stuff2 in list2:
temp = [stuff1[i] + stuff2[i] for i in range(len(stuff1))]
output.append(temp)
return output
@interact
def minksumvis(x1tri = slider(-1,1,1/10,0, label = 'Triangle point x coord.'), yb = slider(1,4,1/10,2, label = 'Blue point y coord.')):
t_list = [[1,0],[x1tri,1],[0,0]]
kite_list = [[3, 0], [1, 0], [0, 1], [1, yb]]
triangle = polygon([[q[0]-6,q[1]] for q in t_list], alpha = .5, rgbcolor = (1,0,0))
t_vert = point([x1tri-6,1], rgbcolor = (1,0,0))
b_vert = point([kite_list[3][0]-4,yb], rgbcolor = (0,0,1))
kite = polygon([[q[0]-4,q[1]] for q in kite_list], alpha = .5,rgbcolor = (0,0,1))
p12 = minkdemo(t_list, kite_list)
p12 = [[q[0],q[1]] for q in p12]
p12poly = Polyhedron(p12)
edge_lines = Graphics()
verts = p12poly.vertices()
for an_edge in p12poly.vertex_adjacencies():
edge_lines += line([verts[an_edge[0]], verts[an_edge[1][0]]])
edge_lines += line([verts[an_edge[0]], verts[an_edge[1][1]]])
triangle_sum = Graphics()
for vert in kite_list:
temp_list = []
for q in t_list:
temp_list.append([q[i] + vert[i] for i in range(len(t_list[0]))])
triangle_sum += polygon(temp_list, alpha = .5, rgbcolor = (1,0,0))
kite_sum = Graphics()
for vert in t_list:
temp_list = []
for q in kite_list:
temp_list.append([q[i] + vert[i] for i in range(len(t_list[0]))])
kite_sum += polygon(temp_list, alpha = .3,rgbcolor = (0,0,1))
labels = text('+', (-4.3,.5), rgbcolor = (0,0,0))
labels += text('=', (-.2,.5), rgbcolor = (0,0,0))
show(labels + t_vert + b_vert+ triangle + kite + triangle_sum + kite_sum + edge_lines, axes=False, figsize = [11.0*.7, 4*.7], xmin = -6, ymin = 0, ymax = 4)
