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alecjacobson / geometry-processing-parameterization

Parameterization assignment for Geometry Processing course
https://github.com/alecjacobson/geometry-processing
Mozilla Public License 2.0
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Question in deriving equation #51

Closed MaxwellFang closed 5 years ago

MaxwellFang commented 5 years ago

image I am not sure how to derive from the second line to the third line, the best derivation I got is sum_{i, j} ui ortho(uj - ui). Also, if the third line is correct since the two vectors multiplied are orthogonal to each other, which leads the result to 0.

alecjacobson commented 5 years ago

Thank you for pointing this out. The derivation had some typos. Please see the updated readme for a more explicit and cleaner version:

image
MaxwellFang commented 5 years ago

Thank you for the explanation. Just one more question, why the last line contains an absolute value? Even in later discussion, U^T A U doesn't seem taking the absolute value either. Is that also a typo? Thank you

alecjacobson commented 5 years ago

It's not an absolute value it's the determinant.

On Mon, Apr 22, 2019, 11:52 PM MaxwellFang notifications@github.com wrote:

Thank you for the explanation. Just one more question, why the last line contains an absolute value? Even in later discussion, U^T A U doesn't seem taken the absolute value either. Is that also a typo? Thank you

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MaxwellFang commented 5 years ago

Thanks for the explanation, I am going to close this issue