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I want to take measurements to create a topographic map of an acre of land for residential building design.

This requires height measurements to be taken over a grid on the order of every two meters. The resolution of each measurement (x, y, z) should be no worse than 10cm. All measurements need only be placed with respect to an arbitrary point of reference – i.e., absolute GPS location is not necessary.

I believe this is possible using a smartphone's camera and inertial sensors. For example, I could do it manually by going to each sample point and logging the angle and direction of the phone when its camera has centered a static reference target placed somewhere in the plot of land. But functionality similar to this has already been automated in software that uses the same data to, for example, stitch full-sphere panoramas and "VR" views.

Are there any apps that can automate the creation of a topographic map of this type? Solutions are welcome for iOS or Android. No price constraints.

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You are essentially wanting to perform whats called a 'Survey Level', but using your phone.

I'm not 100% a phone will give you enough referential accuracy over such a large distance. It might do! You may require some GNSS reveiver attachments/devices etc to compliment you.

Check out this article.

https://www.gpsworld.com/surveying-and-byod-yes-you-can-use-your-smartphone/

Alternative technologies could be a simple drone lidar survey that gives you a 3D point cloud.

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If you are in the US - substantial portions of the US have mapped at a 1M resolution (ie, spacing) by the USGS. A coverage map is here. If you're lucky, all you have to do is download the DEM - digital elevation map.

You are not likely to get the accuracy you desire with a software-only solution on a smartphone. You suggest a method where you could

do it manually by going to each sample point and logging the angle and direction of the phone when its camera has centered a static reference target placed somewhere in the plot of land

First, this requires that you know your location to the desired 10cm or better.* This is not possible with a cellphone GPS or a hiker's GPS. You need a survey grade GPS for this level of accuracy. Assuming you could find the location to this accuracy, you then need to know the direction and angle (elevation) to your target to a high degree of accuracy. In the best possible case of a circular property with the reference at the center, your largest distance to the target in is about 36m. This means you need to measure angle and elevation to better than 0.16°. This exceeds the accuracy of the sensor in the phone, let alone your ability to accurately locate the target in your view. The magnetic compass in your phone is not sufficiently accurate and making matters worse, is easily thrown off by local magnetic fields you might be carrying around.

If you're really not concerned about price, just go rent a survey grade GPS or a "total station" survey instrument.

*any error in your position location adds to the error in locating elevation relative to the target.

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