{"id":475,"date":"2016-04-20T10:57:33","date_gmt":"2016-04-20T14:57:33","guid":{"rendered":"https:\/\/blogs.mathworks.com\/graphics\/?p=475"},"modified":"2016-04-20T10:57:33","modified_gmt":"2016-04-20T14:57:33","slug":"fplot-and-friends","status":"publish","type":"post","link":"https:\/\/blogs.mathworks.com\/graphics\/2016\/04\/20\/fplot-and-friends\/","title":{"rendered":"FPLOT and Friends"},"content":{"rendered":"\r\n

Another new feature that I really like in R2016a<\/a> is the upgraded fplot function and all of the new members of the fplot family.<\/p>

The fplot function<\/a> has been around for a long time. The basic idea is that you pass it a function which takes X coordinates as inputs and returns Y coordinates as outputs. Then fplot will use that function to draw a curve.<\/p>

fplot(@(x) sin(x))\r\n<\/pre>\"\" 
This is really useful for getting a \"quick feel\" for the shape of a function, or a family of functions.<\/p>
fplot(@(x) besselj(x,1),[0 2*pi])\r\nhold on<\/span>\r\nfplot(@(x) besselj(x,2),[0 2*pi])\r\nfplot(@(x) besselj(x,3),[0 2*pi])\r\nfplot(@(x) besselj(x,4),[0 2*pi])\r\nfplot(@(x) besselj(x,5),[0 2*pi])\r\nhold off<\/span>\r\nlegend show<\/span>\r\n<\/pre>\"\" 
In addition to functions, if you have the Symbolic Math Toolbox<\/a>, fplot can also accept symbolic variables now. This gives it even more power. For example, I can reproduce that plot with a single call to fplot by calling besselj<\/a> with a symbolic variable for the domain and a vector for the order.<\/p>
syms x<\/span>\r\nfplot(besselj(x,1:5),[0,2*pi])\r\nlegend show<\/span>\r\n<\/pre>\"\" 
The new version of fplot has a lot of nice refinements, such as the nice legend entries in those last two examples.<\/p>
When we first showed the new fplot to Cleve, he gave it one of his favorite functions<\/a>.<\/p>
$$tan(sin(x)) + sin(tan(x))$$<\/p>
This is what the previous version of fplot did with that.<\/p>
\"\" <\/p>
And here's the R2016a version.<\/p>
fplot(@(x) tan(sin(x)) + sin(tan(x)))\r\n<\/pre>\"\" 
As you can see, it does a better of resolving the details in those tricky bits. And it labeled the asymptotes for use, although it missed the one at $-\\pi\/2$. The reason Cleve likes this function is that it's a bit of a torture test!<\/p>
And we can get even more detail if we zoom in.<\/p>
xlim(pi\/2 + [-.2 .2])\r\n<\/pre>\"\" 
Another big enhancement is that fplot can now do parametric curves as well as plotting Y as a function of X. To do this, we just pass it two functions. The first function takes the parameter value as input and returns X coordinates. The second function takes the parameter value as input and returns Y coordinates.<\/p>
For example, I can use it to recreate the cubic Bézier curve from this blog post<\/a>. This is a bit simpler than the way I did it in that post. Especially if you're not familiar with things like Kronecker tensor products<\/a>. Note, you'll need the placelabel function I wrote in that earlier blog post.<\/p>
clf\r\npt1 = [ 5;-10];\r\npt2 = [18; 18];\r\npt3 = [38; -5];\r\npt4 = [45; 15];\r\nplacelabel(pt1,'pt_1'<\/span>);\r\nplacelabel(pt2,'pt_2'<\/span>);\r\nplacelabel(pt3,'pt_3'<\/span>);\r\nplacelabel(pt4,'pt_4'<\/span>);\r\nxlim([0 50])\r\naxis equal<\/span>\r\nhold on<\/span>\r\n\r\ncubic_bezier = @(t,a,b,c,d) a*      (1-t).^3 ...<\/span>\r\n                        + 3*b*t   .*(1-t).^2 ...<\/span>\r\n                        + 3*c*t.^2.*(1-t)    ...<\/span>\r\n                        +   d*t.^3          ;\r\n\r\nfplot(@(t)cubic_bezier(t,pt1(1),pt2(1),pt3(1),pt4(1)), ...<\/span>\r\n      @(t)cubic_bezier(t,pt1(2),pt2(2),pt3(2),pt4(2)), ...<\/span>\r\n      [0 1])\r\n\r\nhold off<\/span>\r\n<\/pre>\"\" 
But one of the coolest features of the new version of fplot is hiding at the bottom of the doc page<\/a>. If you look down there, you'll see this:<\/p>
\r\n
See Also<\/h2>\r\n
Functions<\/h3>\r\n