<s>
Descriptive	B-Language
geometry	I-Language
is	O
the	O
branch	O
of	O
geometry	O
which	O
allows	O
the	O
representation	O
of	O
three-dimensional	O
objects	O
in	O
two	O
dimensions	O
by	O
using	O
a	O
specific	O
set	O
of	O
procedures	O
.	O
</s>
<s>
The	O
theoretical	O
basis	O
for	O
descriptive	B-Language
geometry	I-Language
is	O
provided	O
by	O
planar	B-Algorithm
geometric	I-Algorithm
projections	I-Algorithm
.	O
</s>
<s>
Italian	O
architect	O
Guarino	O
Guarini	O
was	O
also	O
a	O
pioneer	O
of	O
projective	O
and	O
descriptive	B-Language
geometry	I-Language
,	O
as	O
is	O
clear	O
from	O
his	O
Placita	O
Philosophica	O
(	O
1665	O
)	O
,	O
Euclides	O
Adauctus	O
(	O
1671	O
)	O
and	O
Architettura	O
Civile	O
(	O
1686	O
—	O
not	O
published	O
until	O
1737	O
)	O
,	O
anticipating	O
the	O
work	O
of	O
Gaspard	O
Monge	O
(	O
1746	O
–	O
1818	O
)	O
,	O
who	O
is	O
usually	O
credited	O
with	O
the	O
invention	O
of	O
descriptive	B-Language
geometry	I-Language
.	O
</s>
<s>
Gaspard	O
Monge	O
is	O
usually	O
considered	O
the	O
"	O
father	O
of	O
descriptive	B-Language
geometry	I-Language
"	O
due	O
to	O
his	O
developments	O
in	O
geometric	O
problem	O
solving	O
.	O
</s>
<s>
Descriptive	B-Language
geometry	I-Language
uses	O
the	O
image-creating	O
technique	O
of	O
imaginary	O
,	O
parallel	O
projectors	O
emanating	O
from	O
an	O
imaginary	O
object	O
and	O
intersecting	O
an	O
imaginary	O
plane	O
of	O
projection	O
at	O
right	O
angles	O
.	O
</s>
<s>
Aside	O
from	O
the	O
Orthographic	O
,	O
six	O
standard	O
principal	O
views	O
(	O
Front	O
;	O
Right	O
Side	O
;	O
Left	O
Side	O
;	O
Top	O
;	O
Bottom	O
;	O
Rear	O
)	O
,	O
descriptive	B-Language
geometry	I-Language
strives	O
to	O
yield	O
four	O
basic	O
solution	O
views	O
:	O
the	O
true	B-Application
length	I-Application
of	O
a	O
line	O
(	O
i.e.	O
,	O
full	O
size	O
,	O
not	O
foreshortened	O
)	O
,	O
the	O
point	O
view	O
(	O
end	O
view	O
)	O
of	O
a	O
line	O
,	O
the	O
true	O
shape	O
of	O
a	O
plane	O
(	O
i.e.	O
,	O
full	O
size	O
to	O
scale	O
,	O
or	O
not	O
foreshortened	O
)	O
,	O
and	O
the	O
edge	O
view	O
of	O
a	O
plane	O
(	O
i.e.	O
,	O
view	O
of	O
a	O
plane	O
with	O
the	O
line	O
of	O
sight	O
perpendicular	O
to	O
the	O
line	O
of	O
sight	O
associated	O
with	O
the	O
line	O
of	O
sight	O
for	O
producing	O
the	O
true	O
shape	O
of	O
a	O
plane	O
)	O
.	O
</s>
<s>
By	O
the	O
90°	O
circuitous	O
stepping	O
process	O
,	O
projecting	O
in	O
any	O
direction	O
from	O
the	O
point	O
view	O
of	O
a	O
line	O
yields	O
its	O
true	B-Application
length	I-Application
view	O
;	O
projecting	O
in	O
a	O
direction	O
parallel	O
to	O
a	O
true	B-Application
length	I-Application
line	O
view	O
yields	O
its	O
point	O
view	O
,	O
projecting	O
the	O
point	O
view	O
of	O
any	O
line	O
on	O
a	O
plane	O
yields	O
the	O
plane	O
's	O
edge	O
view	O
;	O
projecting	O
in	O
a	O
direction	O
perpendicular	O
to	O
the	O
edge	O
view	O
of	O
a	O
plane	O
will	O
yield	O
the	O
true	O
shape	O
(	O
to	O
scale	O
)	O
view	O
.	O
</s>
<s>
There	O
is	O
heuristic	O
value	O
to	O
studying	O
descriptive	B-Language
geometry	I-Language
.	O
</s>
<s>
It	O
does	O
so	O
without	O
the	O
need	O
for	O
adjacent	O
orthographic	O
views	O
and	O
therefore	O
may	O
seem	O
to	O
render	O
the	O
circuitous	O
,	O
stepping	O
protocol	O
of	O
Descriptive	B-Language
Geometry	I-Language
obsolete	O
.	O
</s>
<s>
However	O
,	O
since	O
descriptive	B-Language
geometry	I-Language
is	O
the	O
science	O
of	O
the	O
legitimate	O
or	O
allowable	O
imaging	O
of	O
three	O
or	O
more	O
dimensional	O
space	O
,	O
on	O
a	O
flat	O
plane	O
,	O
it	O
is	O
an	O
indispensable	O
study	O
,	O
to	O
enhance	O
computer	O
modeling	O
possibilities	O
.	O
</s>
<s>
To	O
get	O
a	O
true	B-Application
view	I-Application
(	O
length	O
in	O
the	O
projection	O
is	O
equal	O
to	O
length	O
in	O
3D	O
space	O
)	O
of	O
one	O
of	O
the	O
lines	O
:	O
SU	O
in	O
this	O
example	O
,	O
projection	O
3	O
is	O
drawn	O
with	O
hinge	O
line	O
H2	O
,	O
3	O
parallel	O
to	O
S2U2	O
.	O
</s>
<s>
To	O
get	O
points	O
Q	O
and	O
T	O
on	O
these	O
lines	O
giving	O
this	O
shortest	O
distance	O
,	O
projection	O
5	O
is	O
drawn	O
with	O
hinge	O
line	O
H4	O
,	O
5	O
parallel	O
to	O
P4R4	O
,	O
making	O
both	O
P5R5	O
and	O
S5U5	O
true	B-Application
views	I-Application
(	O
any	O
projection	O
of	O
an	O
end	O
view	O
is	O
a	O
true	B-Application
view	I-Application
)	O
.	O
</s>
<s>
General	O
solutions	O
are	O
a	O
class	O
of	O
solutions	O
within	O
descriptive	B-Language
geometry	I-Language
that	O
contain	O
all	O
possible	O
solutions	O
to	O
a	O
problem	O
.	O
</s>
<s>
1-3	O
below	O
demonstrate	O
(	O
1	O
)	O
Descriptive	B-Language
geometry	I-Language
,	O
general	O
solutions	O
and	O
(	O
2	O
)	O
simultaneously	O
,	O
a	O
potential	O
standard	O
for	O
presenting	O
such	O
solutions	O
in	O
orthographic	O
,	O
multiview	O
,	O
layout	O
formats	O
.	O
</s>
