381 - A10 - Splines

402 days ago by Professor381

# Using the Matlab builtin function x = [0 1 2.5 3.6 5 7 8.1 10]; y = sin(x); xx = 0:.05:10; yy = spline(x,y,xx); plot(x,y,'o',xx,yy) 
       
                                                                        

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# Now, let's do this parametrically # Using the Matlab builtin function t = [0 1 2 5 7 8 10]; x = [0 4 4 3 2 -1 0]; y = [0 0 3 5 0 -3 1]; tt = 0:.05:10; xx = spline(t,x,tt); yy = spline(t,y,tt); plot(x,y,'o',xx,yy) 
       
Traceback (click to the left of this block for traceback)
...
SyntaxError: invalid syntax
Traceback (most recent call last):    xx = spline(t,x,tt);
  File "", line 1, in <module>
    
  File "/tmp/tmpQgFDuR/___code___.py", line 4
    t = [_sage_const_0  _sage_const_1  _sage_const_2  _sage_const_5  _sage_const_7  _sage_const_8  _sage_const_10 ];
                                    ^
SyntaxError: invalid syntax
# Using Sage for a functional set of points xs = [0, 1, 2.5, 3.6, 5, 7, 8.1, 10] ys = [0, 1, 2.5, 3.6, 5, 7, 8.1, 10] pts = [] for k in range(len(xs)): ys[k] = sin(xs[k]) # comment this out if you want to just use the y-values entered above or change to another formula to model with cubic pieces pts.append((xs[k],ys[k])) end f = spline(pts) G = plot(f,(x,0,10)) G += points(pts,size=20,color='red') show(G) 
       
var('t') ts = [0, 1, 2, 5, 7, 8, 10] xs = [0, 4, 4, 3, 2, -1, 0] ys = [0, 0, 3, 5, 0, -3, 1] pts = [] ptsx = [] ptsy = [] for k in range(len(xs)): pts.append((xs[k],ys[k])) ptsx.append((ts[k],xs[k])) ptsy.append((ts[k],ys[k])) end f = spline(ptsx) h = spline(ptsy) G = parametric_plot((f,h),(t,min(ts),max(ts))) G += points(pts,size=20,color='red') show(G)