Commit 088afdab by Jim Hefferon

### all slides; fix angle plot so it shows signed angle

parent 148032c0
 ... ... @@ -194,6 +194,8 @@ def plot_before_after_action(a, b, c, d, pts, colors=None): p = plot(G) return p # Find the signed angle between the planar vector v and Mv # See http://math.stackexchange.com/a/879474/12012 def find_angles(a,b,c,d,num_pts,lower_limit=None,upper_limit=None): """Apply the matrix to points around the upper half circle, and return the angle between the input and output vectors. ... ... @@ -215,12 +217,42 @@ def find_angles(a,b,c,d,num_pts,lower_limit=None,upper_limit=None): v = vector(RDF, pt) w = v*M try: angle = arccos(w*v/(1.0*w.norm()*v.norm())) dot = v[0]*w[0] + v[1]*w[1] # dot product det = v[0]*w[1] - v[1]*w[0] # determinant angle = atan2(det, dot) # atan2(y, x) or atan2(sin, cos) except: angle = None r.append((t,angle)) return r # This finds the positive angle between the vectors. # def find_angles(a,b,c,d,num_pts,lower_limit=None,upper_limit=None): # """Apply the matrix to points around the upper half circle, and # return the angle between the input and output vectors. # a, b, c, d reals Upper left, ur, ll, lr of matrix. # num_pts positive integer number of points # lower_limit=0, upper_limit=pi ignore angles outside these limits # """ # if lower_limit is None: # lower_limit=0 # if upper_limit is None: # upper_limit=pi # r = [] # M = Matrix(RDF, [[a, b], [c, d]]) # for i in range(num_pts): # t = i*pi/num_pts # if ((tupper_limit)): # continue # pt = (cos(t), sin(t)) # v = vector(RDF, pt) # w = v*M # try: # angle_size = arccos(w*v/(1.0*w.norm()*v.norm())) # except: # angle = None # r.append((t,angle)) # return r MARKERSIZE = 2 TICKS = ([0,pi/4,pi/2,3*pi/4,pi], [0,pi/2,pi]) def color_angles_list(a, b, c, d, num_pts, colors): ... ...
 ... ... @@ -27,7 +27,7 @@ p=plot_before_after_action(2,2,0,2,[(cos(pi/6),sin(pi/6))],['orange']) p.set_axes_range(-0.1,2.1,-0.1,2.75) p.save("graphics/five_ii_a_skew4.pdf") p = plot_color_angles(2,2,0,2) p.set_axes_range(0,pi,0,pi) p.set_axes_range(0,pi,-pi,pi) p.save("graphics/five_ii_a_skew5.pdf", figsize=3, tick_formatter=[pi,pi]) ... ... @@ -38,8 +38,12 @@ q.save("graphics/five_ii_a_generic1.pdf") p = plot_circle_action(1,3,2,4) p.set_axes_range(-3, 3, -4.5, 4.5) p.save("graphics/five_ii_a_generic2.pdf") # positive angle: # p = plot_color_angles(1,3,2,4) # p.set_axes_range(0,pi,0,pi) # p.save("graphics/five_ii_a_generic3.pdf", figsize=3, tick_formatter=[pi,pi]) p = plot_color_angles(1,3,2,4) p.set_axes_range(0,pi,0,pi) p.set_axes_range(0,pi,-pi,pi) p.save("graphics/five_ii_a_generic3.pdf", figsize=3, tick_formatter=[pi,pi]) ... ... @@ -51,6 +55,6 @@ p = plot_circle_action(-1,0,0,2) p.set_axes_range(-2.5, 2.5, -2.5, 2.5) p.save("graphics/five_ii_a_diagonal2.pdf") p = plot_color_angles(-1,0,0,2) p.set_axes_range(0,pi,0,pi) p.set_axes_range(0,pi,-pi,pi) p.save("graphics/five_ii_a_diagonal3.pdf", figsize=3, tick_formatter=[pi,pi])
 ... ... @@ -376,14 +376,14 @@ Here is the diagram, specialized for this case. \Re^2_{\wrt{B}} @>t_{\pi/6}>\hat{H}> \Re^2_{\wrt{D}} \end{CD} \end{equation*} To get $H$ we move down from the upper left, across, and then back up. To get $\hat{H}$ we move up from the upper left, across, and then down. \end{frame} \begin{frame} With respect to the standard basis real vectors represent themselves, so the matrix representing moving up is easy. \begin{equation*} \rep{id}{B,\stdbasis_2} \begin{mat} =\begin{mat} 1 &1 \\ 1 &-1 \end{mat} ... ...
Markdown is supported
0% or
You are about to add 0 people to the discussion. Proceed with caution.
Finish editing this message first!