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Update README.md
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alinnman authored May 16, 2024
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Expand Up @@ -72,8 +72,8 @@ The result will be a tuple of **two** coordinates (intersections of two circles
The intersections are calculated using an algorithm based on [this article](https://math.stackexchange.com/questions/4510171/how-to-find-the-intersection-of-two-circles-on-a-sphere) <br/>
This is a short outline of the algorithm. Two circles $A$ and $B$ define the circles of equal altitude defined from the sighting data as described above. The circles relate to a *sight pair* $S_{p_{1,2}} = \{s_1, s_2\}$ which we will come back to later.

$A = \{ p \in \mathbb{R}^3 \mid p \cdot a = \cos \alpha \land |p| = 1 \}$ <br/>
$B = \{ p \in \mathbb{R}^3 \mid p \cdot b = \cos \beta \land |p| = 1 \}$
$A = \left{ p \in \mathbb{R}^3 \mid p \cdot a = \cos \alpha \land |p| = 1 \right}$ <br/>
$B = \left{ p \in \mathbb{R}^3 \mid p \cdot b = \cos \beta \land |p| = 1 \right}$

We aim for finding the intersections $p_1$ and $p_2$ for te circles $A$ and $B$

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