<s>
The	O
Grand	B-Application
Tour	I-Application
is	O
a	O
technique	O
developed	O
by	O
Daniel	O
Asimov	O
in	O
1985	O
,	O
which	O
is	O
used	O
to	O
explore	O
multivariate	B-General_Concept
statistical	I-General_Concept
data	I-General_Concept
by	O
means	O
of	O
an	O
animation	O
.	O
</s>
<s>
The	O
multivariate	B-General_Concept
data	I-General_Concept
that	O
is	O
the	O
original	O
input	O
for	O
any	O
grand	B-Application
tour	I-Application
visualization	O
is	O
a	O
(	O
finite	O
)	O
set	O
of	O
points	O
in	O
some	O
high-dimensional	O
Euclidean	O
space	O
.	O
</s>
<s>
The	O
grand	B-Application
tour	I-Application
converts	O
the	O
spatial	O
complexity	O
of	O
the	O
multivariate	B-General_Concept
data	I-General_Concept
set	O
into	O
temporal	O
complexity	O
by	O
using	O
the	O
relatively	O
simple	O
2-dimensional	O
views	O
of	O
the	O
projected	O
data	O
as	O
the	O
individual	O
frames	O
of	O
the	O
movie	O
.	O
</s>
<s>
A	O
grand	B-Application
tour	I-Application
"	O
method	O
"	O
is	O
an	O
algorithm	O
for	O
assigning	O
a	O
sequence	O
of	O
projections	O
onto	O
(	O
usually	O
)	O
2-dimensional	O
planes	O
to	O
any	O
given	O
dimension	O
of	O
Euclidean	O
space	O
.	O
</s>
<s>
This	O
allows	O
any	O
particular	O
multivariate	B-General_Concept
data	I-General_Concept
set	O
to	O
be	O
projected	O
onto	O
that	O
sequence	O
of	O
2-dimensional	O
planes	O
and	O
thereby	O
displayed	O
on	O
a	O
computer	O
screen	O
one	O
after	O
the	O
other	O
,	O
so	O
that	O
the	O
effect	O
is	O
to	O
create	O
a	O
movie	O
of	O
the	O
data	O
.	O
</s>
<s>
Asimov	O
showed	O
that	O
these	O
subspaces	O
can	O
be	O
selected	O
so	O
as	O
to	O
make	O
the	O
set	O
of	O
them	O
(	O
up	O
to	O
timet	O
)	O
increasingly	O
close	O
to	O
all	O
points	O
in	O
G(2,p )	O
,	O
so	O
that	O
if	O
the	O
grand	B-Application
tour	I-Application
movie	O
were	O
allowed	O
to	O
run	O
indefinitely	O
,	O
the	O
set	O
of	O
displayed	O
subspaces	O
would	O
correspond	O
to	O
a	O
dense	O
subset	O
of	O
G(2,p )	O
.	O
</s>
<s>
The	O
R	B-Language
package	O
implements	O
geodesic	O
interpolation	O
and	O
basis	O
generation	O
functions	O
that	O
allow	O
you	O
to	O
create	O
new	O
tour	O
methods	O
from	O
R	B-Language
.	O
</s>
