<s>
Geometric	B-Application
constraint	I-Application
solving	I-Application
is	O
constraint	B-Application
satisfaction	I-Application
in	O
a	O
computational	O
geometry	O
setting	O
,	O
which	O
has	O
primary	O
applications	O
in	O
computer	B-Application
aided	I-Application
design	I-Application
.	O
</s>
<s>
A	O
problem	O
to	O
be	O
solved	O
consists	O
of	O
a	O
given	O
set	O
of	O
geometric	O
elements	O
and	O
a	O
description	O
of	O
geometric	O
constraints	B-Algorithm
between	O
the	O
elements	O
,	O
which	O
could	O
be	O
non-parametric	O
(	O
tangency	O
,	O
horizontality	O
,	O
coaxiality	O
,	O
etc	O
)	O
or	O
parametric	O
(	O
like	O
distance	O
,	O
angle	O
,	O
radius	O
)	O
.	O
</s>
<s>
The	O
goal	O
is	O
to	O
find	O
the	O
positions	O
of	O
geometric	O
elements	O
in	O
2D	O
or	O
3D	O
space	O
that	O
satisfy	O
the	O
given	O
constraints	B-Algorithm
,	O
which	O
is	O
done	O
by	O
dedicated	O
software	O
components	O
called	O
geometric	O
constraint	B-Algorithm
solvers	O
.	O
</s>
<s>
Geometric	B-Application
constraint	I-Application
solving	I-Application
became	O
an	O
integral	O
part	O
of	O
CAD	B-Application
systems	O
in	O
the	O
80s	O
,	O
when	O
Pro/Engineer	O
first	O
introduced	O
a	O
novel	O
concept	O
of	O
feature-based	O
parametric	O
modeling	O
concept	O
.	O
</s>
<s>
There	O
are	O
additional	O
problems	O
of	O
geometric	B-Application
constraint	I-Application
solving	I-Application
that	O
are	O
related	O
to	O
sets	O
of	O
geometric	O
elements	O
and	O
constraints	B-Algorithm
:	O
dynamic	O
moving	O
of	O
given	O
elements	O
keeping	O
all	O
constraints	B-Algorithm
satisfied	O
,	O
detection	O
of	O
over	O
-	O
and	O
under-constrained	O
sets	O
and	O
subsets	O
,	O
auto-constraining	O
of	O
under-constrained	O
problems	O
,	O
etc	O
.	O
</s>
<s>
A	O
general	O
scheme	O
of	O
geometric	B-Application
constraint	I-Application
solving	I-Application
consists	O
of	O
modeling	O
a	O
set	O
of	O
geometric	O
elements	O
and	O
constraints	B-Algorithm
by	O
a	O
system	O
of	O
equations	O
,	O
and	O
then	O
solving	O
this	O
system	O
by	O
non-linear	O
algebraic	O
solver	O
.	O
</s>
<s>
For	O
the	O
sake	O
of	O
performance	O
,	O
a	O
number	O
of	O
decomposition	B-Application
techniques	I-Application
could	O
be	O
used	O
in	O
order	O
to	O
decrease	O
the	O
size	O
of	O
an	O
equation	O
set	O
:	O
decomposition-recombination	O
planning	O
algorithms	O
,	O
tree	O
decomposition	O
,	O
C-tree	O
decomposition	O
,	O
graph	O
reduction	O
,	O
re-parametrization	O
and	O
reduction	O
,	O
computing	O
fundamental	O
circuits	O
,	O
body-and-cad	O
structure	O
,	O
or	O
the	O
witness	O
configuration	O
method	O
.	O
</s>
<s>
Some	O
other	O
methods	O
and	O
approaches	O
include	O
the	O
degrees	O
of	O
freedom	O
analysis	O
,	O
symbolic	O
computations	O
,	O
rule-based	O
computations	O
,	O
constraint	B-Algorithm
programming	O
and	O
constraint	B-Algorithm
propagation	O
,	O
and	O
genetic	O
algorithms	O
.	O
</s>
<s>
Geometric	B-Application
constraint	I-Application
solving	I-Application
has	O
applications	O
in	O
a	O
wide	O
variety	O
of	O
fields	O
,	O
such	O
as	O
computer	B-Application
aided	I-Application
design	I-Application
,	O
mechanical	O
engineering	O
,	O
inverse	B-General_Concept
kinematics	I-General_Concept
and	O
robotics	O
,	O
architecture	O
and	O
construction	O
,	O
molecular	O
chemistry	O
,	O
and	O
geometric	O
theorem	O
proving	O
.	O
</s>
<s>
The	O
primary	O
application	O
area	O
is	O
computer	B-Application
aided	I-Application
design	I-Application
,	O
where	O
geometric	B-Application
constraint	I-Application
solving	I-Application
is	O
used	O
in	O
both	O
parametric	O
history-based	O
modeling	O
and	O
variational	O
direct	O
modeling	O
.	O
</s>
<s>
DCM	O
(	O
Dimensional	O
Constraint	B-Algorithm
Manager	O
)	O
,	O
a	O
commercial	O
solver	O
from	O
D-Cubed	O
(	O
subsidiary	O
of	O
Siemens	O
PLM	O
Software	O
)	O
,	O
integrated	O
in	O
AutoCAD	B-Algorithm
,	O
SolidWorks	B-Application
,	O
Creo	B-Application
,	O
and	O
many	O
other	O
popular	O
CAD	B-Application
systems	O
;	O
</s>
<s>
LGS	O
,	O
a	O
commercial	O
solver	O
developed	O
by	O
LEDAS	O
and	O
currently	O
owned	O
by	O
Bricsys	B-Language
,	O
integrated	O
in	O
Cimatron	O
E	O
and	O
BricsCAD	B-Language
;	O
</s>
<s>
C3D	B-Language
Solver	I-Language
,	O
a	O
commercially	O
available	O
solver	O
which	O
is	O
a	O
part	O
of	O
C3D	B-Language
Toolkit	I-Language
,	O
integrated	O
into	O
KOMPAS-3D	O
;	O
</s>
<s>
GeoSolver	O
,	O
a	O
GNU	B-License
Public	I-License
License	I-License
Python	B-Language
package	O
for	O
geometric	B-Application
constraint	I-Application
solving	I-Application
.	O
</s>
