Ricci Flow for Shape Analysis and Surface Registration by Wei Zeng & Xianfeng David Gu

Author:Wei Zeng & Xianfeng David Gu
Language: eng
Format: epub
Publisher: Springer New York, New York, NY

Proof.

See Fig. 4.11 a. According to the Euclidean cosine law,

taking the derivative with respect to l k on both sides, we get

therefore

□

Fig. 4.11Derivative relation between edge length (or corner angle) and conformal factor

Namely,

(4.2)

Furthermore,

(4.3)

Now we can show a property for d ij .

Lemma 4.3.

For the triangle [v i ,v j ,v k ] with a circle packing,

Proof.

By the Pythagorean theorem,

Adding both sides, we complete the proof. □

Download

Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.