Essays/Gauss-Bonnet/Bonnet05

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13 Examples

Verbs defining the shape of the surface under consideration as well as those defining
the number of points on the surface can be changed.


13.1 Example 1

This is the surface shown in Figure 1 which is used for checking verbs.


NB. ... example 1 (ijs) ...

NB. ... for v1 ...
s1=:1.43"_
f1=:2.10"_
i1=:10"_

NB. ... for v2 ...
s2=:0"_
f2=:2p1"_
i2=:56"_

p=:1.50"_
q=:1.65"_

load 'plot'

pd 'viewpoint _3 _5 0.7'
pd 'viewsize 1 1 0.5'

pd 'type surface'
pd (y1;y2;y3) vpgen''
pd 'pdf'
pd 'show'


GBplot01.jpg
Example 1: Surface


NB. ... integration (ijx) ...

   i1=:160"_
   i2=:100"_

   KSurface vpgen''
1.31589
   geocCurve vpgen''
1.31589


13.2 Example 2
NB. ... example 2 (ijs) ...

NB. ... for v1 ...
s1=:1.43"_
f1=:3.90"_
i1=:10"_

NB. ... for v2 ...
s2=:0"_
f2=:2p1"_
i2=:56"_

p=:1.40"_
q=:_0.75"_

load 'plot'

pd 'viewpoint _3 _5 0.7'
pd 'viewsize 1 1 0.5'

pd 'type surface'
pd (y1;y2;y3) vpgen''
pd 'pdf'
pd 'show'


GBplot02.jpg
Example 2: Surface


NB. ... integration (ijx) ...

   i1=:160"_
   i2=:100"_

   KSurface vpgen''
_0.350051
   geocCurve vpgen''
_0.350069


13.3 Example 3
NB. ... example 3 (ijs) ...

NB. ... for v1 ...
s1=:1.43"_
f1=:3.10"_
i1=:10"_

NB. ... for v2 ...
s2=:0"_
f2=:2p1"_
i2=:56"_

p=:1.40"_
q=:0.15"_

load 'plot'

pd 'viewpoint _3 _5 0.7'
pd 'viewsize 1 1 0.5'

pd 'type surface'
pd (y1;y2;y3) vpgen''
pd 'pdf'
pd 'show'


GBplot03.jpg
Example 3: Surface


NB. ... integration (ijx) ...

   i1=:160"_
   i2=:100"_

   KSurface vpgen''
_0.297497
   geocCurve vpgen''
_0.2975


13.4 Example 4
NB. ... example 4 (ijs) ...

NB. ... for v1 ...
s1=:0.001"_
f1=:2.80"_
i1=:20"_

NB. ... for v2 ...
s2=:0"_
f2=:2p1"_
i2=:56"_

p=:3.00"_
q=:_0.80"_

load 'plot'

pd 'viewpoint _3 _5 0.7'
pd 'viewsize 1 1 0.5'

pd 'type surface'
pd (y1;y2;y3) vpgen''
pd 'pdf'
pd 'show'


GBplot04.jpg
Example 4: Surface


NB. ... integration (ijx) ...

   i1=:320"_
   i2=:100"_

   (2^_41)&tsz@KSurface vpgen''
0
   (2^_44)&tsz@geocCurve vpgen''
0


13.5 Example 5
NB. ... example 5 (ijs) ...

NB. ... for v1 ...
s1=:0.3"_
f1=:1.20"_
i1=:20"_

NB. ... for v2 ...
s2=:0"_
f2=:2p1"_
i2=:56"_

p=:3.00"_
q=:0.90"_

load 'plot'

pd 'viewpoint _3 _5 0.7'
pd 'viewsize 1 1 0.5'

pd 'type surface'
pd (y1;y2;y3) vpgen''
pd 'pdf'
pd 'show'


GBplot05.jpg
Example 5: Surface


NB. ... integration (ijx) ...

   i1=:320"_
   i2=:100"_

   KSurface vpgen''
1.60017
   geocCurve vpgen''
1.60018


13.6 Example 6
NB. ... example 6 (ijs) ...

NB. ... for v1 ...
s1=:1.23"_
f1=:5.10"_
i1=:10"_

NB. ... for v2 ...
s2=:0"_
f2=:2p1"_
i2=:56"_

p=:1.40"_
q=:_0.15"_

load 'plot'

pd 'viewpoint _3 _5 0.7'
pd 'viewsize 1 1 0.5'

pd 'type surface'
pd (y1;y2;y3) vpgen''
pd 'pdf'
pd 'show'


GBplot06.jpg
Example 6: Surface


NB. ... integration (ijx) ...

   i1=:160"_
   i2=:100"_

   KSurface vpgen''
_0.364412
   geocCurve vpgen''
_0.364457



Download MoinMoin source: File:Bonnet05.ijs




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Contributed by Tom Allen