Cartography/imaging: understanding projection between heterogeneous 2D coordinate systems
Assumptions; the question is very agnostic to any languages or tooling, although I am approaching with
CSharp and SkiaSharp specifically, but is neither here nor there concerning the core question. Which is: projecting between a world coordinate system and canvas resolution coordinates.
The world coordinate system is very large, 1.5M whole numbers, represented as decimal for centimeters and fractional cm precision; neither here nor there except to understand the A coordinate system. The B coordinate space of course is the target bitmap, in whatever resolution, may be 8K, 16K even 32K, bandwidth and memory permitting, square.
Thus far the naive attempt is to apply a simple world per bitmap ratio, or pixels per world, depending upon the point or rectangle bounds conversion. But there is always an error. Example image: the circle and points are accurate relative to themselves; but are inaccurate to the target bitmap in question, the scaling being something like 183 units per px error involved applying any ratios to the source coordinates. This error can vary depending on the source bitmap resolution, of course. So the algorithm should be robust keeping that in mind.
Overall, my goal is to gain the understanding, calculations involved, to do the projection more precisely regarding world to canvas, without the sort of translation issues. And adapt that into the implementation details.
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I was curious and ran it through for some GPT feedback. I am not hundred percent convinced this algorithm would necessarily provide the
t I want; owing to the fact, the scaling factor is something like 1/183 px/world, and that it seems as though X-Y the error is cumulatively increasing over that range; even more strange orthogonal to the distance the further Y-X travel from canvas zero.
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That's
1/183 assuming 1.5M world coordinate system (hard fact) versus 8192x bitmap canvas. Of course factors vary depending upon the bitmap resolution; I can start from as much as approximately ~64Kx if necessary, but that gets expensive to SKIA, etc.From first glance, sounds like a rounding/truncation error in your conversion?
That's exactly what's going on. How do I contend with that? Rounding issues beyond 6 places is not acceptable, especially in this scenario. Contingencies at my disposal are to start from larger resolution image source, but the performance hit is huge.
Windows Calculator reports
8192 / 1500000 being 0.00546448087431693989071038251366, which I need every single digit from that ratio for precision to be what we want, whereas dotnet csharp reporting more like 0.0054613333333333337, give or take depending decimal, float, etc, but all losing their stuff after about six places.How exactly are you doing the scaling? double should be good up to about 15 significant figures, decimal significantly beyond that (28-29)
If I do that division in windows calculator, I get 0.00546133333333333333333333333333, which exactly matches what I get from C#
canton7
REPL Result: Success
Console Output
Compile: 428.124ms | Execution: 36.436ms | React with ❌ to remove this embed.
So I'm not sure where you got 0.00546448087431693989071038251366 from. It's exactly 1/183, if that helps narrow it down