# 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)
1
|--------------------------------------------------------------------|
| ## #### + + ## + ###
|
| ## # ## #
|
| # # # ##
|
| # # # #
|
0.5 |-+# # # #
+-|
| # # # #
|
| # # # #
|
|# # # #
|
|# # #
# |
0 |-+ # #
#+-|
| # #
# |
| # #
# |
| # #
#|
| #F #
#|
-0.5 |-+ # #
+-|
| # #
|
| # #
|
| # #
|
| + +## # + +
|
-1
|--------------------------------------------------------------------|
0 2 4 6 8
10
1 |--------------------------------------------------------------------|
| ## #### + + ## + ### |
| ## # ## # |
| # # # ## |
| # # # # |
0.5 |-+# # # # +-|
| # # # # |
| # # # # |
|# # # # |
|# # # # |
0 |-+ # # #+-|
| # # # |
| # # # |
| # # #|
| #F # #|
-0.5 |-+ # # +-|
| # # |
| # # |
| # # |
| + +## # + + |
-1 |--------------------------------------------------------------------|
0 2 4 6 8 10
|
# 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
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# 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)
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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)
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