CS-184: Computer Graphics Today - Inst.eecs.berkeley.edu ...
CS-184: Computer Graphics Today - Inst.eecs.berkeley.edu ...
CS-184: Computer Graphics Today - Inst.eecs.berkeley.edu ...
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Undoing Homogenization<br />
We know<br />
We also know that there exist weights ,<br />
such that<br />
X = (! a i P i )/(! a j h j )<br />
i<br />
j<br />
Combining the above we have<br />
a j h j )<br />
!<br />
i<br />
!<br />
i<br />
S i = P i /h<br />
b i S i = X = (!<br />
i<br />
b i (P i /h i ) = (!<br />
i<br />
a i P i )/(!<br />
j<br />
a i P i )/(!<br />
j<br />
a j h j )<br />
a i<br />
9<br />
9<br />
Undoing Homogenization<br />
b i /h i = a i /(! a j h j )<br />
j<br />
a j h j )/h i = a i<br />
b i (!<br />
j<br />
b i (! a j h j )/h i − a i = 0<br />
j<br />
∀i<br />
∀i<br />
This is a linear system in<br />
∀i<br />
Unfortunately is is non-invertible, so...<br />
a i<br />
10<br />
10
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