<s>
In	O
computer	O
graphics	O
,	O
a	O
T-spline	B-Algorithm
is	O
a	O
mathematical	O
model	O
for	O
defining	O
freeform	O
surfaces	O
.	O
</s>
<s>
A	O
T-spline	B-Algorithm
surface	O
is	O
a	O
type	O
of	O
surface	O
defined	O
by	O
a	O
network	O
of	O
control	B-Algorithm
points	I-Algorithm
where	O
a	O
row	O
of	O
control	B-Algorithm
points	I-Algorithm
is	O
allowed	O
to	O
terminate	O
without	O
traversing	O
the	O
entire	O
surface	O
.	O
</s>
<s>
Modeling	O
surfaces	O
with	O
T-splines	B-Algorithm
can	O
reduce	O
the	O
number	O
of	O
control	B-Algorithm
points	I-Algorithm
in	O
comparison	O
to	O
NURBS	B-Algorithm
surfaces	I-Algorithm
and	O
make	O
pieces	O
easier	O
to	O
merge	O
,	O
but	O
increases	O
the	O
book-keeping	O
effort	O
to	O
keep	O
track	O
of	O
the	O
irregular	O
connectivity	O
.	O
</s>
<s>
T-splines	B-Algorithm
can	O
be	O
converted	O
into	O
NURBS	B-Algorithm
surfaces	I-Algorithm
,	O
by	O
knot	O
insertion	O
,	O
and	O
NURBS	B-Algorithm
can	O
be	O
represented	O
as	O
T-splines	B-Algorithm
without	O
T	O
's	O
or	O
by	O
removing	O
knots	O
.	O
</s>
<s>
T-splines	B-Algorithm
can	O
therefore	O
,	O
in	O
theory	O
,	O
do	O
everything	O
that	O
NURBS	B-Algorithm
can	O
do	O
.	O
</s>
<s>
In	O
practice	O
,	O
an	O
enormous	O
amount	O
of	O
programming	O
was	O
required	O
to	O
make	O
NURBS	B-Algorithm
work	O
as	O
well	O
as	O
they	O
do	O
,	O
and	O
creating	O
the	O
equivalent	O
T-spline	B-Algorithm
functionality	O
would	O
require	O
similar	O
effort	O
.	O
</s>
<s>
To	O
smoothly	O
join	O
at	O
points	O
where	O
more	O
than	O
three	O
surface	O
pieces	O
meet	O
,	O
T-splines	B-Algorithm
have	O
been	O
combined	O
with	O
geometrically	O
continuous	O
constructions	O
of	O
degree	O
3	O
by	O
3	O
(	O
bi-cubic	O
)	O
and	O
,	O
more	O
recently	O
,	O
of	O
degree	O
4	O
by	O
4	O
(	O
bi-quartic	O
)	O
.	O
</s>
<s>
Subdivision	O
surfaces	O
,	O
NURBS	B-Algorithm
surfaces	I-Algorithm
,	O
and	O
polygon	B-Algorithm
meshes	I-Algorithm
are	O
alternative	O
technologies	O
.	O
</s>
<s>
Subdivision	O
surfaces	O
,	O
as	O
well	O
as	O
T-spline	B-Algorithm
and	O
NURBS	B-Algorithm
surfaces	I-Algorithm
with	O
the	O
addition	O
of	O
geometrically	O
continuous	O
constructions	O
,	O
can	O
represent	O
everywhere-smooth	O
surfaces	O
of	O
any	O
connectivity	O
and	O
topology	O
,	O
such	O
as	O
holes	O
,	O
branches	O
,	O
and	O
handles	O
.	O
</s>
<s>
However	O
,	O
none	O
of	O
T-splines	B-Algorithm
,	O
subdivision	O
surfaces	O
,	O
or	O
NURBS	B-Algorithm
surfaces	I-Algorithm
can	O
always	O
accurately	O
represent	O
the	O
(	O
exact	O
,	O
algebraic	O
)	O
intersection	B-Algorithm
of	O
two	O
surfaces	O
within	O
the	O
same	O
surface	O
representation	O
.	O
</s>
<s>
Polygon	B-Algorithm
meshes	I-Algorithm
can	O
represent	O
exact	O
intersections	B-Algorithm
but	O
lack	O
the	O
shape	O
quality	O
required	O
in	O
industrial	O
design	O
.	O
</s>
<s>
T-splines	B-Algorithm
do	O
not	O
yet	O
have	O
edge	O
weights	O
.	O
</s>
<s>
T-splines	B-Algorithm
were	O
initially	O
defined	O
in	O
2003	O
.	O
</s>
<s>
In	O
2007	O
the	O
U.S.	O
patent	O
office	O
granted	O
patent	O
number	O
7,274,364	O
for	O
technologies	O
related	O
to	O
T-Splines	B-Algorithm
.	O
</s>
<s>
T-Splines	B-Algorithm
,	O
Inc	O
.	O
was	O
founded	O
in	O
2004	O
to	O
commercialize	O
the	O
technologies	O
and	O
acquired	O
by	O
Autodesk	O
,	O
Inc	O
.	O
in	O
2011	O
.	O
</s>
