Sorry for the Delay, our group was facing a technical error
First method
We use the Pythagoras Theorem to derive a formula for finding the distance between two points in 2- and 3- dimensional space.
This allows for an accurate measure of the closest straight line to the screen
Let P = (x 1, y 1) and Q = (x 2, y 2) be two points on the Cartesian plane
Then from the Pythagoras Theorem we find that the distance between P and Q is
In a similar way, it can be proved that if P = (x 1, y 1, z1) and Q = (x 2, y 2, z2) are two points in the 3-dimensional space, the distance between P and Q is
2nd method
Trigon is also a good way of measuring the distance and the angles involved in calculating whether or not someone is in the optimum viewing range. This is especially useful with 3d trigon, as we can arrive at a more conducive result with 2 planes instead of one
We have to calculate the following:
-Current viewing angle: Based on the inputs, this is the viewing angle or arc for your set up.
-Maximum recommended viewing distance: Based on data from Electro home, which suggests a viewing distance of three to six screen widths for video. This corresponds to the point at which most people will begin having trouble picking out details and reading the screen. Probably too far away to be effective for home theatre, OK for everyday TV viewing. Most people are comfortable watching TV between this distance and half this distance.
-Maximum SMPTE recommended viewing distance: SMPTE standard EG-18-1994 recommends a minimum viewing angle of 30 degrees for movie theatres. This seems to be becoming a de facto standard for front projection home theatres also. Viewing from this distance or closer will result in a more immersive experience, and also lessen eye strain caused by watching a smaller image in a dark room.
-Maximum and Recommended THX viewing distances: THX also publish standards for movie theatres to adhere to for THX certification. THX requires that the back row of seats in a theatre have at least a 26 degree viewing angle and recommends a 36 degree viewing angle.
-SMPTE and THX screen widths: Based on the viewing distance supplied to the calculator, these are the minimum screen widths required to meet the SMPTE and THX recommendations discussed above.
-Viewing Distances based on Visual Acuity: These distances are calculated based on the resolving power of the human eye (reference), or visual acuity. The human eye with 20/20 vision can detect or resolve details as small as 1/60th of a degree of arc. These distances represent the point beyond which some of the detail in the picture is no longer able to be resolved and "blends" with adjacent detail.
This guideline would be difficult to exceed in a home theatre, with most vertical viewing angles in the 15-20 degree range. See the diagram below for an example.
The THX cinema standards have no references to a "best" or "optimal" vertical viewing angle. However, normal human vision's optimal cone of vision has a radius of approximately 15 degrees. From this I'd suggest that anything in the range of 10-20 degrees would be good, with larger values causing increased eye and neck strain.
- Ho Zhen Hao
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