How to calculate the viewing angle for curved monitors?

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Some higher-end computer monitors and TVs nowadays offer curved screen, which curvature is provided.

However, the viewer often sits closer to the screen than the centre of curvature, resulting in a viewing angle which is not a right angle anymore for every point offset from the center.

What is the formula to obtain the viewing angle as function of radius of curvature of the monitor and distance from the center of the monitor (or distance from the center of curvature) of the viewer? The coordinates on the monitor can be provided as linear distance along the curve.

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$$ w= r \sin \gamma = h \tan \beta $$

where $h$ is distance before mirror nearest end points shown and $w$ the half-width.

$$\tan \beta = \dfrac{r \sin \gamma}{h}$$

which is higher

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