Fix algebra error in scan formula and replace 2s minimum scan time with exponential dropoff

[UnorderedSigh]

Content (Artwork / Missions / Jobs)
Fixes #9201 wherein @Amazinite didn't like having a minimum scan time and @ziproot discovered a big math error.

Summary

There are two problems with the Ship::Scan logic right now. An algebra error and a 2 second minimum scan time.

Math Error

The first is a big math error here described by @ziproot

EDIT: I just tested with 10 million scan power. That took two seconds. So it seems like the scan speed cap is too hard to hit.

Two constants were wrong in Ship.cpp because of an algebra error.

When deriving the scaling factor formula, I inverted the scan formula incorrectly.

This:
// factor = pow(sqrt(scanEfficiency) * framesToFullScan / SCAN_TIME, 1.5) / referenceSize

Should be this:
// factor = pow(sqrt(scanEfficiency) * framesToFullScan / SCAN_TIME, -1.5) / referenceSize

(Notice the -)

If you correct that in Ship.cpp by recalculating the constants, the scan rates are correct: 3-10 seconds for a gunship to scan a human ship.

-       const double SCAN_CARGO_FACTOR = 3;
+       const double SCAN_CARGO_FACTOR = pow(1.0 / sqrt(5), -1.5) / 600;
-       const double SCAN_OUTFIT_FACTOR = 10;
+       const double SCAN_OUTFIT_FACTOR = pow(1.0 / sqrt(15), -1.5) / 740;

Exponential Drop-Off Instead of a Hard Cap

However, @Amazinite doesn't like the idea of a minimum scan time at all. Instead, I'm replacing it with an exponential dropoff in scan rate. I'm using the brownish-yellow color here, which is an exponent of 5.

Testing Done

Free Worlds Scanning Mission

@Pointedstick's test save from #7640 has a scanner-equipped Splinter at the "go scan that Cruiser" mission in the Free Worlds campaign. The mission is doable with one scanner, and easy with three.

Morgan.Atrasco.txt

Illegal Missions

Here's another one from @movingpictures: a Heavy Shuttle up to no good, flying through heavily patrolled space:

Lenny.Lightfingers

Here's four from me: Sparrow, Heavy Shuttle, Clipper, and Blackbird, outfitted for smuggling, all with illegal missions through well-patrolled space, and you don't have enough fuel to reach the destination.

Aimet Taepip~3029-04-20 Sparrow Test.txt
Aimet Taepip~3029-04-18 Heavy Shuttle Test.txt
Aimet Taepip~3029-04-18 Clipper Test.txt
Aimet Taepip~3029-04-18 Blackbird Test.txt

Big Ship Illegal Mission and AI Bugs

Aimet Taepip~3029-04-19 Ranoerek Test.txt

It generally takes the full ten seconds to scan my Ranoerek.

[UnorderedSigh]

If #9551 is merged, then the formulae must be updated again:

• sqrt(5) => sqrt(500)
• sqrt(15) => sqrt(1500)

[ziproot]

Um, now scanning is too powerful.

EDIT: I'm stupid. Ignore this.

[ziproot]

I have tested using your build and the provided save files, and everything appears to take as long as it should.

[UnorderedSigh]

Um, now scanning is too powerful. EDIT: I'm stupid. Ignore this.

Hai space is why I made a 2 second minimum scan time. Now a big ship will have maybe 1-2 seconds, and small ships are doomed. I could start the exponential drop-off at 4 seconds instead of 2, but then players won't be able to insta-scan enemies.

For tuning scanners, we need to focus only on human space before or during the main campaign. Anywhere else aliens can scan you, that scanning isn't for of missions or jobs yet. It's just present for lore reasons. Once we know standard human scanners work well, we can move on to balancing alien scanners.

Surely, hiding illegal goods from more advanced races will require more advanced techniques than a large cargo hold.

[ziproot]

By "I'm stupid" I meant "I forgot to disable my plugin which had the workaround of multiplying scan efficiency by 100" so the Hai scanners were more powerful than they should have been.
On the other hand, I'm not sure if Amazinite was really stuck at 10 seconds because of the algebra error or if they were really hitting the hard cap almost immediately.

[UnorderedSigh]

By "I'm stupid" I meant "I forgot to disable my plugin which had the workaround of multiplying scan efficiency by 100" so the Hai scanners were more powerful than they should have been. On the other hand, I'm not sure if Amazinite was really stuck at 10 seconds because of the algebra error or if they were really hitting the hard cap almost immediately.

It was the algebra error.

[ziproot]

In that case, wouldn't #9201 be addressed simply by fixing the algebra error?

[UnorderedSigh]

In that case, wouldn't #9201 be addressed simply by fixing the algebra error?

No, people also want to insta-scan AI ships by packing massive piles of scanners. Read through the comments and you'll see such a discussion.

[quyykk]

comments usually appear first, and not last. I'd say move this up

[UnorderedSigh]

I rearranged the comments. Does it make more sense now?

[UnorderedSigh]

IMO if you add a comment saying which formula was used I think that would be enough. There's really no need to calculate this value at runtime.
It's calculated once, at compile time.

Keeping the calculation in the code, and the formula next to it, let's the reader know what was done and why. When it comes time to tweak things, you can change the relevant part of the calculation instead of figuring it out a second time.

[quyykk]

Keeping the calculation in the code, and the formula next to it, let's the reader know what was done and why. When it comes time to tweak things, you can change the relevant part of the calculation instead of figuring it out a second time.

That's why you have the comment with the formula though? What's there to figure out?

It's calculated once, at compile time.

Also no, pow is not constexpr. Neither is sqrt nevermind the compiler is smarter than me, you're right

[UnorderedSigh]

Your scan times will be dangerously low in Hai space unless you use these:

• Hai scan opacity and holographic amenity outfits #9562

[UnorderedSigh]

Last tested and known to work Thu, 23 Nov 2023 00:45:43 UTC.

[Amazinite]

Feeling much better. Just some stylistic notes.