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Re: Bump Function
*To*: mathgroup at smc.vnet.net
*Subject*: [mg32051] Re: Bump Function
*From*: paladin_billw at yahoo.com
*Date*: Fri, 21 Dec 2001 03:57:17 -0500 (EST)
*References*: <9vchll$3mm$1@smc.vnet.net>
*Sender*: owner-wri-mathgroup at wolfram.com
FWIW, here's a way to make smooth bumps that have a fixed value beyond
a threshold radius, can be scaled, centered anywhere, superimposed on
top of each other without ugly discontinuities, without wasting a lot
of time taking square roots. Enjoy:
(*bumpProfile is a function which determines the cross section of the
bump function, note the use of Min[] to level the function off beyond
a radius of 1*)
bumpProfile:=2^(4+4(Min[.895*#,.895]^2-1)^-1)&;
Plot[bumpProfile@x,{x,0,1}];
(*scalebump is a function for scaling the height and width of
bumpProfile*)
scalebump[r_,rmax_,h_]:=h*bumpProfile[N[r/rmax]];
(*roundbump converts the scaled bumpProfile from a function of one
variable to a function of (x^2+y^2), and performs a translation*)
roundbump[x_,y_,xcent_,ycent_,r_,h_]:=
scalebump[#,r,h]&@Dot[#,#]&@{x-xcent,y-ycent};
Plot3D[roundbump[x,y,0,0,1,1],{x,-1,1},{y,-1,1},PlotPoints->20];
(*Composite of 8 random bumps*)
With[{bumpdata=
With[{ nbumps=8, ranrngs={{-1,1},{-1,1},{.1,1},{0,1}} },
Flatten@{x,y,Map[Random[Real,#]&,ranrngs]}&/@Range@nbumps
]
},
Plot3D[
Evaluate[Plus@@#&[roundbump@@#&/@bumpdata]],
{x,-1,1},{y,-1,1},PlotRange->All,PlotPoints->50
]
];
On Fri, 14 Dec 2001 09:44:21 +0000 (UTC), Ajitkumar
<ajitkumar at math.mu.ac.in> wrote:
>Hi,
>
>Could somebody tell me how to plot the graph of bump functions. For
>example, if I want to draw the graph of the function say,
>
>f(x,y) = x^2+y^2 for x^2+y^2<1
> = 2 for x^2+y^2 >2
>
>
>Thanks
>Ajit Kumar
>Dept of Maths
>University of Mumbai
>Vidyanagari, Kalina
>Mumbai 400 098
>India
>Phone No. +91 652 6683
>Email- ajitkumar at math.mu.ac.in
> ajit_kumara at hotmail.com
> http://math.mu.ac.in/faculty/scholars/ajit.html
>
>
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