Parameterization II - Computer Graphics Laboratory
Parameterization II - Computer Graphics Laboratory
Parameterization II - Computer Graphics Laboratory
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x 1<br />
i<br />
Conformal <strong>Parameterization</strong> – DCP<br />
γi<br />
γ<br />
βi<br />
0<br />
x 0<br />
α<br />
[D [Desbrun b et t al., l 2002]<br />
β<br />
x 2<br />
For one triangle:<br />
90<br />
γ ( x − x ) + β(<br />
x − x ) = R ( x −x<br />
)<br />
cot cot<br />
2 0 1 0 1 2<br />
For complete one-ring of triangles<br />
(interior vertex):<br />
n<br />
(cot γ + cot β ) x − x = 0<br />
∑<br />
i=<br />
1<br />
i i i<br />
( )<br />
For incomplete one-ring of triangles<br />
(boundary vertex):<br />
n<br />
90<br />
i<br />
∑ γγi + ββi<br />
( x xi − x 0 ) = R x xi − x<br />
1 0<br />
∑<br />
1 i2<br />
i=<br />
1<br />
i2<br />
(cot cot ) ( )<br />
0<br />
25
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