## 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"_

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

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

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

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

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

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

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

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

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

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

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

pd 'type surface'
pd (y1;y2;y3) vpgen''
pd 'pdf'
pd 'show'```
 Example 6: Surface

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

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

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

Prev Page: Essays/Gauss-Bonnet/Bonnet04

Contributed by TomAllen

Essays/Gauss-Bonnet/Bonnet05 (last edited 2008-12-08 10:45:44 by anonymous)