Kentsmith9 (talk | contribs) m (→Imperial precision and rounding: typo) |
Kentsmith9 (talk | contribs) m (→Imperial precision and rounding: added new section on KM and MI) |
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== Additional losses for kilometer and miles == | |||
When the units are large enough, the display will convert the units to kilometers or miles depending upon which unit type is being displayed. | |||
In both cases of these large values, the base unit measurement does not change and continues to be meters as discussed earlier. The displayed value is translated from that base unit with the following two formulas: | |||
This results in the following: | '''Meters to Kilometers''' | ||
:<code>Integer( RoundedDisplayMeters / 10 +0.5 ) / 100</code><br /> | |||
'''Meters to Miles''' | |||
:<code>Integer( Integer( RoundedDisplayMeters * 3.28084 + 0.5 ) / 52.8 +0.5 ) ) / 100</code><br /> | |||
This results in the following (the steps have been removed for simplicity in the table: | |||
{| class="wikitable" style="text-align: center;" | {| class="wikitable" style="text-align: center;" | ||
|- | |- | ||
! colspan=" | ! colspan="3" | Kilometers and Miles | ||
|- | |- | ||
! Rounded length ( | ! Rounded length (m) | ||
! | ! Displayed result (km) | ||
! Displayed result (mi) | ! Displayed result (mi) | ||
|- | |- | ||
| 4994 | |||
| 4.99 | |||
| 3.10 | |||
|- | |||
| 4994 | |||
| 4.99 | |||
| 3.10 | |||
|- | |||
| 4994 | |||
| 4.99 | |||
| 3.10 | |||
|- | |||
| 4994 | |||
| 4.99 | | 4.99 | ||
| 3.10 | | 3.10 | ||
|- | |- | ||
| | | 4994 | ||
| | | 4.99 | ||
| | | 3.10 | ||
| | |- | ||
| 3. | | 4994 | ||
| 4.99 | |||
| 3.10 | |||
|- | |- | ||
| | | 4994 | ||
| 4.99 | |||
| | | 3.10 | ||
| 3. | |||
|- | |- | ||
| | | 4994 | ||
| 4.99 | |||
| | | 3.10 | ||
| 3. | |||
|- | |- | ||
|} | |} | ||
Revision as of 20:34, 1 June 2017
The Waze platform is based on metric units and each Waze application (WME and the client app) translates that into imperial units as required. Both display interfaces have a loss of accuracy in the displayed segment length due to rounding.
 |
The following information is only focused on the WME application and will not be covering the impact on the client app. |
Overview
All Waze segment length information is based on metric unit measurements.
When a user selects the metric unit measurement system from WME, the interface displays a whole metric unit rounded (up or down), not truncated.
When a user selects the imperial unit measurement system from WME, the interface simply translates the already rounded metric units into imperial units. WME displays two decimal places of accuracy for the translation from the rounded numbers, giving a false sense of precision. Note that any third decimal unit is also rounded as needed.
Metric precision and rounding
The internal units are stored with an accuracy of 0.01 meters (0.0328 ft) or about 3/8-inch accuracy. However, the displayed units will be rounded up or down as needed to produce only whole meters. When the segment length reaches more than 999 meters, it switches to kilometers and changes the precision to 0.01 km (or 10 m). This means, you might nudge the end of a segment slightly, but the displayed length may not change if the nudge was inside of the 10 meter range of the kilometer display.
 |
It has been noted that it is possible to initially see a granularity of only 1 millimeter when initially creating a segment before saving it, but that resolution seems to vanish after the first save. |
The meters displayed are rounded to the nearest whole number, with a minimum savable segment size of 1 meter (3.28 feet). Drawing or shrinking a segment any shorter than that will result in a save error. Segments shorter than 19.69 ft (6 m) will not accurately track speed data and should be avoided. See this discussion on minimum segment length for more information.
Meters are rounded with the following formula:
Integer( TrueSegmentLength + 0.5 )
This results in the following:
| Meters | |||
|---|---|---|---|
| True length (m) | Formula Steps | Displayed result (m) | |
| 4.49 | Integer(4.49 + 0.5) | Integer(4.99) | 4 |
| 4.50 | Integer(4.5 + 0.5) | Integer(5.0) | 5 |
| 4.99 | Integer(4.99 + 0.5) | Integer(5.49) | 5 |
| 5.00 | Integer(5 + 0.5) | Integer(5.5) | 5 |
| 5.49 | Integer(5.49 + 0.5) | Integer(5.99) | 5 |
| 5.50 | Integer(5.5 + 0.5) | Integer(6.0) | 6 |
The formula for the kilometer range is more complex. Note the precision is still based on the 2 decimal places for the meters:
Integer( ( TrueSegmentLength + 0.5 ) / 10 ) / 100- Int = Integer in the table below
This results in the following:
| Kilometers | |||||
|---|---|---|---|---|---|
| True length (m) | Formula Steps | Displayed result (km) | |||
| 1004.99 | Int( ( 1004.99 + 5 ) / 10 ) / 100 | Int( 1009.99 / 10 ) / 100 | Int( 100.999 ) / 100 | 100 / 100 | 1.00 |
| 1005.00 | Int( ( 1005 + 5 ) / 10 ) / 100 | Int( 1010 / 10 ) / 100 | Int( 101 ) / 100 | 101 / 100 | 1.01 |
| 1009.99 | Int( ( 1009.99 + 5 ) / 10 ) / 100 | Int( 1014.99 / 10 ) / 100 | Int( 101.499 ) / 100 | 101 / 100 | 1.01 |
| 1010.00 | Int( ( 1010 + 5 ) / 10 ) / 100 | Int( 1015 / 10 ) / 100 | Int( 101.5 ) / 100 | 101 / 100 | 1.01 |
| 1014.99 | Int( ( 1014.99 + 5 ) / 10 ) / 100 | Int( 1019.99 / 10 ) / 100 | Int( 101.999 ) / 100 | 101 / 100 | 1.01 |
| 1015.00 | Int( ( 1015 + 5 ) / 10 ) / 100 | Int( 1020 / 10 ) / 100 | Int( 102 ) / 100 | 102 / 100 | 1.02 |
 |
Drawing of the reality of segment lengths compared to the stepped output of the whole numbers including the rounding. |
Imperial precision and rounding
When changing the WME display to imperial, there is no change to the underlying segment unit value. The WME interface simply translates all the already rounded metric displayed values into the equivalent imperial values out to two decimal places. This has the negative impact of purporting a high degree of precision when in fact it is without basis.
The translation from metric to imperial is done by the following formula:
Integer( RoundedDisplayMeters * 328.084 + 0.5 ) / 100
This results in the following:
| Feet | ||||
|---|---|---|---|---|
| Rounded length (m) | Formula Steps | Displayed result (ft) | ||
| 4 | Integer( 4 * 328.084 + 0.5 ) / 100 | Integer( 1312.836) / 100 | 1312 / 100 | 13.12 |
| 5 | Integer( 5 * 328.084 + 0.5 ) / 100 | Integer( 1640.920) / 100 | 1640 / 100 | 16.4 |
| 6 | Integer( 6 * 328.084 + 0.5) / 100 | Integer( 1969.004) / 100 | 1969 / 100 | 19.69 |
Additional losses for kilometer and miles
When the units are large enough, the display will convert the units to kilometers or miles depending upon which unit type is being displayed.
In both cases of these large values, the base unit measurement does not change and continues to be meters as discussed earlier. The displayed value is translated from that base unit with the following two formulas:
Meters to Kilometers
Integer( RoundedDisplayMeters / 10 +0.5 ) / 100
Meters to Miles
Integer( Integer( RoundedDisplayMeters * 3.28084 + 0.5 ) / 52.8 +0.5 ) ) / 100
This results in the following (the steps have been removed for simplicity in the table:
| Kilometers and Miles | ||
|---|---|---|
| Rounded length (m) | Displayed result (km) | Displayed result (mi) |
| 4994 | 4.99 | 3.10 |
| 4994 | 4.99 | 3.10 |
| 4994 | 4.99 | 3.10 |
| 4994 | 4.99 | 3.10 |
| 4994 | 4.99 | 3.10 |
| 4994 | 4.99 | 3.10 |
| 4994 | 4.99 | 3.10 |
| 4994 | 4.99 | 3.10 |
Now look at what happened to the original unit as measured in feet after it is rounded in metric and then converted back to imperial. You can see the back and forth translations amplify the error, yet continue to provide a false sense of accuracy with the two decimal places:
This results in the following:
| The Amplified False Accuracy with Feet | |||
|---|---|---|---|
| True length (ft) | True length (m) | Rounded metric | Displayed result (ft) |
| 14.73 | 4.49 | 4 | 13.12 |
| 14.76 | 4.50 | 5 | 16.4 |
| 16.37 | 4.99 | 5 | 16.4 |
| 16.40 | 5.00 | 5 | 16.4 |
| 18.01 | 5.49 | 5 | 16.4 |
| 18.04 | 5.50 | 6 | 19.69 |
Because WME will show the value 5 meters or 16.4 feet for wide range of values both above and below 5 meters, that value cannot reliably be used to ensure a segment is above or below a server threshold of 5 meters or 16.4 feet. Therefore, to guarantee you are above a 5 meter threshold you must select 6 meters or 19.69 feet. Similarly, if you want to ensure you are below a 5 meter threshold you must select 4 meters or 13.12 feet.
Custom precision script for WME
Users in the Waze editing community have developed scripts that can be loaded into the browser to enable additional functionality not available in the basic WME available from Waze. One such script is the WME True Segment Length. This script will display the true length of the segment in both metric and imperial units with two decimal places of accuracy.