       Re: triangles

• To: mathgroup at smc.vnet.net
• Subject: [mg39285] Re: triangles
• From: "Peltio" <peltio at twilight.zone>
• Date: Sun, 9 Feb 2003 04:50:39 -0500 (EST)
• References: <b1ag0j\$ph6\$1@smc.vnet.net>
• Reply-to: "Peltio" <peltioNOSP at Miname.com.invalid>
• Sender: owner-wri-mathgroup at wolfram.com

```"Karen A. Wilk" ha scritto

>Hi!  Does anyone know what two 2-dimensional triangles multiplied
>together look like?

Has this something to do with fuzzy logic?
Just wondering.
Here are a few piecewise linear constructors (they were intended for
membership functions, that's what the MF stands for):

GammaShapedMF[x_, a_, b_] :=
Which[x<=a, 0, a <x< b, 1+(x-b)/(b-a),x>=b, 1]
LShapedMF[x_, a_, b_] :=
Which[x<=a, 1, a<x<b, 1-(x-a)/(b-a), x>=b, 0]
PiShapedMF[x_, a_, c1_, c2_, b_] :=
Min[GammaShapedMF[x, a, c1], LShapedMF[x, c2, b]]
DeltaShapedMF[x_, a_, c_, b_] :=
Min[GammaShapedMF[x, a, c], LShapedMF[x, c, b]]

Once you defined your triangular functions by means of a Which statement,
say

tri1[x_]:=DeltaShapedMF[x,2,4,6]
tri2[y_]:=DeltaShapedMF[y,1,3,5]

and once you chose the algebraic multiplication as the operator that
multiplies them together, I suppose that by plotting the function

f[x_,y_]=tri1[x]*tri2[y];

you'll find a cute pyramid. Here's a plot with a color function I like

LimitedGrayLevel[x_, maxBk_:0.3, maxWh_:0.90] :=
GrayLevel[maxBk + x(maxWh - maxBk)]
FuzzyGray[x_] := LimitedGrayLevel[1 - x, 0, .9]

Plot3D[ f[x,y], {x,0,8}, {y,0,8},
PlotPoints->25, BoxRatios->{1,1,1},
ColorFunction->FuzzyGray, PlotRange->All ]

Sigmoidal and gaussian MF make better plots, though : )

cheers,
Peltio