Accuracy of Offset Projection
getDistanceScales offers a cheap way to project lng/lat or meter offset to pixels. It is useful when using the GPU to project a cluster of coordinates near an origin point, without suffering the precision loss of WebGL.
This article discusses the usage and accuracy of the distance scales.
Meter offset to pixels
Regular meter offset to pixels projection:
uniform vec3 unitsPerMeter;
vec3 meters_offset_to_pixels_offset(vec3 meters) {
return meters * unitsPerMeter;
}
When getDistanceScales is called with flag highPrecision: true, it generates additional multipliers to compensate for precision loss over latitude change. More precise meter offset to pixels projection:
uniform vec3 unitsPerMeter;
uniform vec3 unitsPerMeter2;
vec3 meters_offset_to_pixels_offset_adjusted(vec3 meters) {
return meters * (unitsPerMeter + unitsPerMeter2 * meters.y);
}
Accuracy at San Francisco (37N, z = 12):
| R | X unadjusted | X adjusted |
|---|---|---|
| 100 meters | off by -0.000 pixels, 0.001% | off by 0.000 pixels, 0.001% |
| 1000 meters | off by -0.008 pixels, 0.012% | off by 0.000 pixels, 0.001% |
| 5000 meters | off by -0.200 pixels, 0.060% | off by 0.002 pixels, 0.001% |
| 10000 meters | off by -0.804 pixels, 0.121% | off by 0.003 pixels, 0.000% |
| 30000 meters | off by -7.277 pixels, 0.366% | off by -0.021 pixels, 0.001% |
Accuracy at high latitude (75N, z = 12):
| R | X unadjusted | X adjusted |
|---|---|---|
| 100 meters | off by -0.001 pixels, 0.006% | off by 0.000 pixels, 0.001% |
| 1000 meters | off by -0.130 pixels, 0.061% | off by 0.001 pixels, 0.001% |
| 5000 meters | off by -3.290 pixels, 0.309% | off by -0.001 pixels, 0.000% |
| 10000 meters | off by -13.200 pixels, 0.620% | off by -0.044 pixels, 0.002% |
| 30000 meters | off by -119.884 pixels, 1.877% | off by -1.473 pixels, 0.023% |
LngLat offset to pixels
Regular lng_lat offset to pixels projection:
uniform vec3 unitsPerDegree;
vec3 lnglat_offset_to_pixels_offset(vec3 lngLatZ) {
return lngLatZ * unitsPerDegree;
}
When getDistanceScales is called with flag highPrecision: true, it generates additional multipliers to compensate for precision loss over latitude change. More precise meter offset to pixels projection:
uniform vec3 unitsPerDegree;
uniform vec3 unitsPerDegree2;
vec3 lnglat_offset_to_pixels_offset_adjusted(vec3 lngLatZ) {
return lngLatZ * (unitsPerDegree + unitsPerDegree2 * lngLatZ.y);
}
Accuracy at San Francisco (37N, z = 12):
| R | Y unadjusted | Y adjusted |
|---|---|---|
| 0.001 degrees | off by -0.000 pixels, 0.001% | off by -0.000 pixels, 0.000% |
| 0.01 degrees | off by -0.005 pixels, 0.007% | off by -0.000 pixels, 0.000% |
| 0.05 degrees | off by -0.125 pixels, 0.034% | off by -0.000 pixels, 0.000% |
| 0.1 degrees | off by -0.499 pixels, 0.068% | off by -0.001 pixels, 0.000% |
| 0.3 degrees | off by -4.508 pixels, 0.204% | off by -0.022 pixels, 0.001% |
Accuracy at high latitude (75N, z = 12):
| R | Y unadjusted | Y adjusted |
|---|---|---|
| 0.001 degrees | off by -0.001 pixels, 0.003% | off by -0.000 pixels, 0.000% |
| 0.01 degrees | off by -0.081 pixels, 0.034% | off by -0.000 pixels, 0.000% |
| 0.05 degrees | off by -2.038 pixels, 0.172% | off by -0.005 pixels, 0.000% |
| 0.1 degrees | off by -8.172 pixels, 0.345% | off by -0.039 pixels, 0.002% |
| 0.3 degrees | off by -74.258 pixels, 1.046% | off by -1.055 pixels, 0.015% |