Behaviour of N on gaining an extra frame

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Postby Raif » 2015.07.12 (20:09)

The demo replay circle seems to be a good representation of the collision diameter of the ninja.
59-0
Frame 212 vs 213
ImageImage
151-0 no jump
Frame 153 vs 154
ImageImage
151-0 with jump
Frame 153
Image

Going to have to agree with Eddy here. The ninja is too far away from the exit in 59-0 to gain a frame by jumping.

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Postby EddyMataGallos » 2016.01.20 (22:49)

Nice pictures there Raif.

I just found another example of this being useful to gain a frame, just in case somebody is interested:

81 frames run:


Just by running you get 82. This is 226626 map by Jeremoon.
ImageImage
Impressive flag by ska -|- N2High - My software for N2.0 -|- Awesome sig by Hendor
About me & Stats (Spoiler)

Hi, im Eddy, a Spanish highscorer and current Grandmaster of N. I've been playing N since 2006, I beat it on the 8th September 2008, and NReality later too. Started intermittently highscoring Metanet in 2010, although serious highscoring started in late 2011.

Current Stats
• Completed N on 8th Sept. 2008
• Completed NReality on 24th Dec. 2010
0th Place on Metanet 0th Rankings with 443 0ths.
0th Place on Metanet Top20 Rankings with 599 Scores.
0th Place on Metanet Top10 Rankings with 599 Scores.
1st Place on Metanet Top5 Rankings with 595 Scores.
0th Place on Metanet Level 0th Rankings with 361 0ths.
0th Place on Metanet Episode 0th Rankings with 82 0ths.
0th Place on Metanet Total Level Score: 72142.900 (20:02:22.900)
0th Place on Metanet Total Episode Score: 35669.900 (09:54:29.900)
0th Place on Metanet Total Point Rankings with 11669 Points.
0th Place in NReality 0th Rankings with 235 0ths.
0th Place for a grand total of 676 Total 0ths.
• Winner of some contests (BUST, 100, 9000, Bounty Hunters, SOAST) and of some rounds of some contests (ROPP, NErratic, Red Ball, NReality Team Arena)

{Info as of 01/Feb/2015} The info may be outdated.

Achievements
• 6th highscorer to reach 100 Metanet 0ths
• 4th highscorer to reach 200 Metanet 0ths
• 1st and only highscorer to reach 300 Metanet 0ths
• 1st and only highscorer to reach 400 Metanet 0ths
• 8th ever Grandmaster
• 2nd* highscorer to reach 599 top-20 Scores
• 1st highscorer to reach 599 top-10 Scores
• 10th highscorer to reach 70k Level Score
• 5th highscorer to reach 71k Level Score
• 2nd highscorer to reach 71.5k Level Score
• 1st highscorer to reach 72k Level Score

Relevant Dates
• First 0th: 31-3 on 04/Oct/10
• Reached 100 Metanet 0ths on 25/Feb/12
• Reached 200 Metanet 0ths on 30/Sep/12
• Reached 300 Metanet 0ths on 16/Mar/13
• Reached 400 Metanet 0ths on 04/Sept/14
• Reached highest amount of 0ths on Jan/2013
• Became the Grandmaster on 12/Apr/2012
• Reached 70k Level Score on 25/Dec/11
• Reached 71k Level Score on 13/Jan/11
• Reached 71.5k Level Score on 01/Aug/12
• Reached 72k Level Score on 04/Jul/14
• Completed N 1.4 on 08/Sept/08
• Completed NReality on 24/Dec/10
• Reached 100 NReality 0ths on Oct/2011
• Reached 200 NReality 0ths on Nov/2011
• Reached 100 Top-20 Scores on Aug/10
• Reached 200 Top-20 Scores on Nov/11
• Reached 300 Top-20 Scores on Nov/11
• Reached 400 Top-20 Scores on Dec/11
• Reached 500 Top-20 Scores on Jan/12
• Reached 599 Top-20 Scores on 04/Apr/12
• Reached 599 Top-10 Scores on 18/Nov/12

Deds & Images (Spoiler)

Thanks to ska for dedicating this map to me
Thanks to BluePretzel for dedicating this map to me
Thanks to da_guru for dedicating this map to me
Thanks to zoasBE for dedicating this full episode to me!: 00-0 00-100-2 00-3 00-4
Thanks to zoasBE for dedicating this mappack to me
Thanks to zoasBE for partially dedicating this map to me
Thanks to VODKALOVER for dedicating this map to me
Thanks to runningninja for dedicating this map to me
Thanks to zoasBE for dedicating this map to me
Thanks to zoasBE for partially dedicating this map to me
Thanks to trance for dedicating this map to me
Thanks to zoasBE for dedicating this map to me
Thanks to zoasBE for dedicating this map to me
Thanks to llabesab for dedicating this map to me
Thanks to the23 for dedicating this map to me
Thanks to Traveleravi for dedicating this map to me
Thanks to 123leonidas321 for dedicating this map to me
Thanks to the23 for dedicating this map to me
Thanks to Uniden for dedicating this map to me
Thanks to Uniden for dedicating this map to me
Thanks to Ors_II for dedicating this map to me
Thanks to Sunset for dedicating this map to me
Thanks to blue_rocks for dedicating this map to me
Thanks to Leonhard for dedicating this map to me
Thanks to blue_rocks for dedicating this map to me
Thanks to Daggafork for dedicating this map to me
Thanks to VODKALOVER for dedicating this map to me
Thanks to blue_rocks for dedicating this map to me
Thanks to blue_rocks for dedicating this map to me
Thanks to Armaghan_Ali for dedicating this map to me
Thanks to Armaghan_Ali for dedicating this map to me
Thanks to Armaghan_Ali for dedicating this map to me
Thanks to RandomDigits/SpartaX18 for dedicating this map to me
Sorry if Im missing any ded.

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ImageThanks to leo.
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Postby ska » 2016.01.24 (06:14)

EddyMataGallos wrote:Nice pictures there Raif.

I just found another example of this being useful to gain a frame, just in case somebody is interested:

81 frames run:


Just by running you get 82. This is 226626 map by Jeremoon.
hmmm... how curious...

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Postby Raif » 2020.04.11 (23:39)

I've finally got an explanation for this after analyzing the ninja's position in NED in a test map (included below). In NED if you exit demo playback, the current coordinates of the ninja are seen in the map editor.

Here's what I've found:

Movement on the ground
- The max speed of the ninja on the ground is 4.85 px/frame.
- The max speed is never attained exactly so the speed fluctuates.
- For example if the ninja is running at 4.84 px/frame, it will accelerate at slightly above 0.10 px/frame^2 to give a speed of ~4.94 px/frame on the next frame.
- The ninja will now decelerate (because it is now moving above the max speed). The deceleration is at slightly below 0.05 px/frame^2 to give back a speed around ~4.84 px/frame^2 two frames later.
- The ninja will now accelerate again because the speed is below 4.85 px/frame, setting up a loop of three frames.
- Because the the acceleration is greater than twice the deceleration, the ninja's average speed will slowly increase until it reaches 4.90 px/frame - upon which it will loop back 4.85.
- While running on the ground at max speed the ninja's average speed will vary between 4.85 and 4.90 px/frame.

Movement in the air
- The max speed of the ninja in the air is 4.90 px/frame.
- Once again the speed fluctuates, but in air the acceleration will be 0.05 px/frame^2 (half of that on the ground). The deceleration is the same at 0.05 px/frame^2.
- This means that the while moving through the air at max speed the ninja's average speed will vary between 4.875 and 4.925 px/frame.
- Once again the average speed will slowly increase until it reaches 4.925 and then loop back to 4.875 px/frame.

What this means
- Moving through air is faster than moving on the ground.
- The act of jumping and the number of jumps is irrelevant, what matters is maximizing time spent in the air.
- Once you've reached max speed, jumping will never be detrimental - you should always jump.

To illustrate the point, below is a graph of the average speed in my test map: (a) while simply holding right, and (b) an MBD with an optimized set of jumps.

The optimized set of jumps saved ~3.19 pixels over the "holding right" tactic over the course of the map. Since the ninja moves at ~4.9 px/frame this is equivalent to an improvement of 0.65 frames.

In my test map, the edge of the exit is located at 734 pixels. In the "holding right" tactic the ninja is located x-coordinate 732.15 just before he enters the exit. 732.15 + 3.19 is greater than 734 so in this case jumping saved a frame (but obviously may not do so in all maps).

Image

Test map (and optimized demo):

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Postby macrohenry » 2020.05.13 (12:23)

This is super interesting, I hadn't even expected the ninja's speed to fluctuate. Thanks for the analysis.
This has probably been discussed before but, knowing all this, is there any chance to save a frame on 59-0 by maximizing your time in the air?
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Postby EddyMataGallos » 2020.05.13 (22:19)

Raif and I discussed this on Discord when he did the analysis, and if I recall correctly there was way too much to be saved in 59-0 even by optimizing airtime. I should mention for completeness that this is also how it works in N++, at least, the fact that airtime max speed is slightly higher (we have proved it using test maps), dunno about the fluctuations (since we don't have something as powerful as Ned in N++ we can't really know positions with this much precision).
ImageImage
Impressive flag by ska -|- N2High - My software for N2.0 -|- Awesome sig by Hendor
About me & Stats (Spoiler)

Hi, im Eddy, a Spanish highscorer and current Grandmaster of N. I've been playing N since 2006, I beat it on the 8th September 2008, and NReality later too. Started intermittently highscoring Metanet in 2010, although serious highscoring started in late 2011.

Current Stats
• Completed N on 8th Sept. 2008
• Completed NReality on 24th Dec. 2010
0th Place on Metanet 0th Rankings with 443 0ths.
0th Place on Metanet Top20 Rankings with 599 Scores.
0th Place on Metanet Top10 Rankings with 599 Scores.
1st Place on Metanet Top5 Rankings with 595 Scores.
0th Place on Metanet Level 0th Rankings with 361 0ths.
0th Place on Metanet Episode 0th Rankings with 82 0ths.
0th Place on Metanet Total Level Score: 72142.900 (20:02:22.900)
0th Place on Metanet Total Episode Score: 35669.900 (09:54:29.900)
0th Place on Metanet Total Point Rankings with 11669 Points.
0th Place in NReality 0th Rankings with 235 0ths.
0th Place for a grand total of 676 Total 0ths.
• Winner of some contests (BUST, 100, 9000, Bounty Hunters, SOAST) and of some rounds of some contests (ROPP, NErratic, Red Ball, NReality Team Arena)

{Info as of 01/Feb/2015} The info may be outdated.

Achievements
• 6th highscorer to reach 100 Metanet 0ths
• 4th highscorer to reach 200 Metanet 0ths
• 1st and only highscorer to reach 300 Metanet 0ths
• 1st and only highscorer to reach 400 Metanet 0ths
• 8th ever Grandmaster
• 2nd* highscorer to reach 599 top-20 Scores
• 1st highscorer to reach 599 top-10 Scores
• 10th highscorer to reach 70k Level Score
• 5th highscorer to reach 71k Level Score
• 2nd highscorer to reach 71.5k Level Score
• 1st highscorer to reach 72k Level Score

Relevant Dates
• First 0th: 31-3 on 04/Oct/10
• Reached 100 Metanet 0ths on 25/Feb/12
• Reached 200 Metanet 0ths on 30/Sep/12
• Reached 300 Metanet 0ths on 16/Mar/13
• Reached 400 Metanet 0ths on 04/Sept/14
• Reached highest amount of 0ths on Jan/2013
• Became the Grandmaster on 12/Apr/2012
• Reached 70k Level Score on 25/Dec/11
• Reached 71k Level Score on 13/Jan/11
• Reached 71.5k Level Score on 01/Aug/12
• Reached 72k Level Score on 04/Jul/14
• Completed N 1.4 on 08/Sept/08
• Completed NReality on 24/Dec/10
• Reached 100 NReality 0ths on Oct/2011
• Reached 200 NReality 0ths on Nov/2011
• Reached 100 Top-20 Scores on Aug/10
• Reached 200 Top-20 Scores on Nov/11
• Reached 300 Top-20 Scores on Nov/11
• Reached 400 Top-20 Scores on Dec/11
• Reached 500 Top-20 Scores on Jan/12
• Reached 599 Top-20 Scores on 04/Apr/12
• Reached 599 Top-10 Scores on 18/Nov/12

Deds & Images (Spoiler)

Thanks to ska for dedicating this map to me
Thanks to BluePretzel for dedicating this map to me
Thanks to da_guru for dedicating this map to me
Thanks to zoasBE for dedicating this full episode to me!: 00-0 00-100-2 00-3 00-4
Thanks to zoasBE for dedicating this mappack to me
Thanks to zoasBE for partially dedicating this map to me
Thanks to VODKALOVER for dedicating this map to me
Thanks to runningninja for dedicating this map to me
Thanks to zoasBE for dedicating this map to me
Thanks to zoasBE for partially dedicating this map to me
Thanks to trance for dedicating this map to me
Thanks to zoasBE for dedicating this map to me
Thanks to zoasBE for dedicating this map to me
Thanks to llabesab for dedicating this map to me
Thanks to the23 for dedicating this map to me
Thanks to Traveleravi for dedicating this map to me
Thanks to 123leonidas321 for dedicating this map to me
Thanks to the23 for dedicating this map to me
Thanks to Uniden for dedicating this map to me
Thanks to Uniden for dedicating this map to me
Thanks to Ors_II for dedicating this map to me
Thanks to Sunset for dedicating this map to me
Thanks to blue_rocks for dedicating this map to me
Thanks to Leonhard for dedicating this map to me
Thanks to blue_rocks for dedicating this map to me
Thanks to Daggafork for dedicating this map to me
Thanks to VODKALOVER for dedicating this map to me
Thanks to blue_rocks for dedicating this map to me
Thanks to blue_rocks for dedicating this map to me
Thanks to Armaghan_Ali for dedicating this map to me
Thanks to Armaghan_Ali for dedicating this map to me
Thanks to Armaghan_Ali for dedicating this map to me
Thanks to RandomDigits/SpartaX18 for dedicating this map to me
Sorry if Im missing any ded.

Image
ImageThanks to leo.
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