Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

The two triangles $xyz$ and $x^{\prime}y^{\prime}z^{\prime}$, shown below, have opposite orientations. A closed curve $abcd$ is embedded in the first triangle ($abcd$). The vertices of the corresponding closed discrete curve $a^{\prime}b^{\prime}c^{\prime}d^{\prime}$ are computed by the method of barycentric coordinates. As shown below $a^{\prime}b^{\prime}c^{\prime}d^{\prime}$ will have opposite orientation as $abcd$.

I'd like to know:

  1. why the difference in orientation of the embedding triangles leads to a difference in the orientations of the embedded discrete curves.

  2. if reversing the orientation of the triangle $xyz$ to match that of $x^{\prime}y^{\prime}z^{\prime}$ is sufficient to is sufficient to ensure that $abcd$ and $a^{\prime}b^{\prime}c^{\prime}d^{\prime}$ have the same orientations.

two triangles with opposite orientations

share|improve this question
add comment

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.