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'
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'
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'
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'
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'
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'
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