Wednesday, June 28, 2017

A conclusion shopping around for a theory.

You sir are a donkey fucker. Okay, maybe you're not a donkey fucker, since there's no evidence of that. You sir, are a chicken fucker. Wait, no evidence there either. You sir are a squirrel fucker. -- Look, I have my conclusion, you fuck some kind of animal and when that type of animal is shot-down, I'm going to shop around for another type of animal. Because that's how this shit works apparently. --- Make some shit up, when that gets demolished, make different similar shit up, with generally the same conclusion.
You catch the analogy there goat-fucker?

Tuesday, June 27, 2017

Approximating an arc with cubic bezier curves, yet another metric.

C = 0.552

C = 0.55201372171

The idea is that rather than minimize the extrema of the error we can instead minimize the total error. Graph out formula for the error and calculate what would be under the curve as a whole. So rather than positive and negative error equal it would seek to minimize the error overall. It's not too different from the other metrics. But, rather than trying to keep the first pixel from being wrong, it tries to keep the pixels as a whole from being wrong for as long as possible. It's different than the number for the extrema because oddly the graph is symmetric at 0.5. It's not symmetric with regard to the y axis, and has different amounts areas of positive and negative and the error shifts as the value of c shifts.

Mortensen's value. Even extrema point.
0.55191502449 at 0.0000001 increments
Total error:1180.57375326880434046054832219597498652621901536765190
Samples: 10000001

My calculated value, brute force.
0.55201372171 at 0.0000001 increments
Total error:1159.83397426356807198675826572857280613256846239728729
Samples: 10000001

Naive geometric value, with purely positive error ((4/3)*(sqrt(2) - 1).
0.552284749 at 0.0000001 increments
Total error:1401.62730758375303300973494715872257045283590056376636
Samples: 10000001

As we can see the total error over a million samples gives us an improvement of 20. Compared to the naive value for all error being positive we gain 242 which is better than Mortensen's gain of 222.

We're talking literally fractions of percents here, but this number has another advantage. You can call it .552 which is a much shorter fraction. Besides the more slices I do the more I narrow in on the value, but it's still a bit off. I'm pretty sure on most of those digits but without actually doing the calculus I can't get much better than that.

0.552 at 0.0000001 increments
Total error:1160.26180861006145200701189677079769078925976995284068
Samples 10000001

You'll notice my value is only 0.4279 different than that in total error over a million samples. And since that truncation lowers it, it will only make it a bit closer to the even extrema point, which is a fine metric.

P_0 = (0,1), P_1 = (c,1), P_2 = (1,c), P_3 = (1,0)
P_0 = (1,0), P_1 = (1,-c), P_2 = (c,-1), P_3 = (0,-1)
P_0 = (0,-1), P_1 = (-c,-1), P_2 = (-1,-c), P_3 = (-1,0)
P_0 = (-1,0), P_1 = (-1,c), P_2 = (-c,1), P_3 = (0,1)
with c = 0.552

Under this metric the cubic value something like: 0.92103099 which might be more important because really flattening out the error might matter in that case a lot more than in the cubic case. I'll call it 0.921

Friday, June 16, 2017

Using a quad to emulate an arc, solving for C.

Basic geometry allows one to solve for the best solution to use a value of C to make a bezier curve close to an arc. The naive solution using Geometry is

This is the solution to the question of we have anchor points on the curve and the curve touches the circle at the center, what value of C for a control point on the quadrant curve (0,1),(C,C),(1,0). Gives us the best fit to the curve.

However Mortenson points out that we are better if we minimize the error rather than allow all the error to be on one side of the circle.

This issue allows a few more percent with the Cubic Bezier form. But, it's more important if we're using one fewer control points. The same is also true at one fewer yet. If we have a square, what square looks most similar to a circle.

The if the naive geometry solution is the same we get:

. Where the corners touch the circle but do not exceed it. The other way you could do it is to have them only touch at the corners and just make the curve larger than the circle.

And finally we have Mortensen's solution to it, by making the metric for closest be the average error across the entire graph.

Well, solving this for 1 control point means doing the same thing he did. Which isn't super-trivial because it means calculating min and max error and adjusting various things. So I wrote a program to do it.

Your C points in Quad Bezier curves are:

C= 0.92519820883625651516056680057654772234129017577799879993432335355559372311727101122467939843041708056568481020881580812152533756252840773920708961655740969447362217856208142868847332990974178763987890

Having the program I refigured it for Cubic:

Having a deviation in both directions of: ±0.00019607646987687817401874512914923 ....

Mortensen gave this as,

Since we might well be using doubles I'd give it as:

C0.5519150244935106,1 1,0.5519150244935106 1,0
C1,-0.5519150244935106 0.5519150244935106,-1 0,-1
C-0.5519150244935106,-1 -1,-0.5519150244935106 -1,0
C-1,0.5519150244935106 -0.5519150244935106,1 0,1

And the c value for the quad bezier curve as:

Q0.9251982088362565 0.9251982088362565 1,0
Q0.9251982088362565 -0.9251982088362565 0,-1
Q-0.9251982088362565 -0.9251982088362565 -1,0
Q-0.9251982088362565 0.9251982088362565 0,1

This is much better than the more naive value: 0.91421356237 which is effectively unusable. While Mortensen's use for the cubic is great, it changes the quad naive to almost usable, generally not, but *almost* usable. The Mortensen-optimized value for quads is off by max 0.007767318 whereas the naive value is off by 0.010781424258 which is 28% better. Hm. That's the same value Mortensen got for the cubic.
Naive Quad: For comparison.

Saturday, June 3, 2017

1 dimensional fractals.

1 dimensional fractals all look the same. That's why they are fractals. Get it? Because they are all lines. And fractals look the same. And all 1d anything is a line which looks like all the other lines. HAHAHAHAHAHA!

Thursday, May 25, 2017

Entirely Hex Words

aa, ab, aba, abaca, abba, abbe, abed, accede, acceded, ace, aced, ad, add, added, ae, aff, ba, baa, baaed, baba, babe, bacca, baccae, bad, bade, baff, baffed, be, bead, beaded, bed, bedad, bedded, bee, beebee, beef, beefed, cab, cabbed, caca, cad, cade, caeca, caf, cafe, caff, ceca, cede, ceded, cee, da, dab, dabbed, dace, dad, dada, daff, daffed, de, dead, deaf, deb, decade, decaf, dee, deed, deeded, def, deface, defaced, ebb, ebbed, ed, ef, eff, efface, effaced, fa, fab, facade, face, faced, fad, fade, faded, faff, faffed, fe, fed, fee, feeb, feed

My favorite: effedface. Though 0xeffdface would fit in an int. 0xFADEDBEE 0xBEDAFFED 0xDECAFBAE 0xFEEDFACE 0xDEFACADE

32 bit hexwords.

abasedly aba5ed17
abatable aba7ab1e
abatises aba715e5
abbacies abbac1e5
abbatial abba71a1
abbesses abbe55e5
abettals abe77a15
abigails ab16a115
ableists ab1e1575
abscised ab5c15ed
abscises ab5c15e5
abscissa ab5c155a
abseiled ab5e11ed
accessed acce55ed
accesses acce55e5
accidias acc1d1a5
accidies acc1d1e5
accolade acc01ade
accosted acc057ed
acetylated ace7718d
acetylates ace77185
acetylic ace7711c
acidoses ac1d05e5
acidosis ac1d0515
acidotic ac1d071c
acolytes ac0177e5
addicted add1c7ed
adelgids ade161d5
aecidial aec1d1a1
affected affec7ed
affiliated aff1118d
affiliates aff11185
afflicts aff11c75
affordable af4dab1e
affordably af4dab17
afforested af4e57ed
agiotage a6107a6e
agitable a617ab1e
agitatedly a6178d17
albedoes a1bed0e5
alcaides a1ca1de5
alcaldes a1ca1de5
alcaydes a1ca7de5
aldolase a1d01a5e
alfalfas a1fa1fa5
algicide a161c1de
algidity a161d177
algology a1601067
alidades a11dade5
alliable a111ab1e
allodial a110d1a1
allotted a11077ed
allottee a11077ee
allseeds a115eed5
alogical a1061ca1
asbestic a5be571c
ascetics a5ce71c5
asocials a50c1a15
assagais a55a6a15
assailed a55a11ed
assegais a55e6a15
assessed a55e55ed
assesses a55e55e5
assisted a55157ed
associated a550c18d
associates a550c185
assoiled a55011ed
astasias a57a51a5
astilbes a5711be5
atalayas a7a1a7a5
attaboys a77ab075
attendees a710dee5
attested a77e57ed
atticist a771c157
babbitts babb1775
babesias babe51a5
babydoll bab7d011
babysits bab75175
bacalaos baca1a05
baccalas bacca1a5
badassed bada55ed
badasses bada55e5
bagasses ba6a55e5
bagatelles ba6811e5
baggages ba66a6e5
baggiest ba661e57
bailable ba11ab1e
bailiffs ba111ff5
ballades ba11ade5
balladic ba11ad1c
ballasts ba11a575
ballboys ba11b075
balletic ba11e71c
balliest ba111e57
ballista ba11157a
balloted ba1107ed
basaltes ba5a17e5
basaltic ba5a171c
baseball ba5eba11
baseless ba5e1e55
baseload ba5e10ad
basicity ba51c177
basidial ba51d1a1
basified ba51f1ed
basifies ba51f1e5
basilect ba511ec7
basilica ba5111ca
basseted ba55e7ed
bassetts ba55e775
bassists ba551575
bastiles ba5711e5
bastille ba57111e
batistes ba7157e5
battalia ba77a11a
battiest ba771e57
baysides ba751de5
beadiest bead1e57
beasties bea571e5
beatable bea7ab1e
beatific bea71f1c
beatless bea71e55
bebloods beb100d5
bedabble bedabb1e
beddable beddab1e
bedotted bed077ed
bedsides bed51de5
bedstead bed57ead
beefalos beefa105
beefiest beef1e57
beefless beef1e55
befitted bef177ed
befleaed bef1eaed
befogged bef066ed
befooled bef001ed
begalled be6a11ed
beladied be1ad1ed
beladies be1ad1e5
belittle be11771e
bellboys be11b075
bellcast be11ca57
beltless be171e55
besieged be51e6ed
besieges be51e6e5
besotted be5077ed
besteads be57ead5
biacetyl b1ace771
biasedly b1a5ed17
bibelots b1be1075
biblical b1b11ca1
biblists b1b11575
bicycled b1c7c1ed
bicycles b1c7c1e5
bicyclic b1c7c11c
biddable b1ddab1e
biddably b1ddab17
bifacial b1fac1a1
bifidity b1f1d177
bifocals b1f0ca15
bigfoots b16f0075
bilabial b11ab1a1
bilgiest b1161e57
billable b111ab1e
billeted b111e7ed
billetee b111e7ee
billfold b111f01d
bilsteds b1157ed5
bioassay b10a55a7
biocidal b10c1da1
biocides b10c1de5
biocycle b10c7c1e
biogases b106a5e5
biologic b101061c
biolyses b10175e5
biolysis b1017515
biolytic b101771c
biosolid b105011d
biotical b1071ca1
biotites b10717e5
biotitic b107171c
biscotti b15c0771
bisected b15ec7ed
bistable b157ab1e
biteable b17eab1e
bitsiest b1751e57
bittiest b1771e57
blasties b1a571e5
blastoffs b1a52ff5
bloodied b100d1ed
bloodies b100d1e5
bloodily b100d117

Hex words, as in words that can be spelled purely in hex.`

aa aa
aal aa1
aalii aa111
aaliis aa1115
aals aa15
aas aa5
ab ab
aba aba
abaca abaca
abacas abaca5
abaci abac1
abaft abaf7
abas aba5
abase aba5e
abased aba5ed
abasedly aba5ed17
abases aba5e5
abasia aba51a
abasias aba51a5
abatable aba7ab1e
abate ab8
abated ab8d
abates ab85
abatis aba715
abatises aba715e5
abattis aba7715
abattises aba7715e5
abaya aba7a
abayas aba7a5
abba abba
abbacies abbac1e5
abbacy abbac7
abbas abba5
abbatial abba71a1
abbe abbe
abbes abbe5
abbess abbe55
abbesses abbe55e5
abbey abbe7
abbeys abbe75
abbot abb07
abbotcies abb07c1e5
abbotcy abb07c7
abbots abb075
abdicable abd1cab1e
abdicate abd1c8
abdicated abd1c8d
abdicates abd1c85
abed abed
abele abe1e
abeles abe1e5
abelia abe11a
abelias abe11a5
abet abe7
abets abe75
abettal abe77a1
abettals abe77a15
abetted abe77ed
abide ab1de
abided ab1ded
abides ab1de5
abigail ab16a11
abigails ab16a115
abilities ab11171e5
ability ab11177
abiological ab101061ca1
abioses ab105e5
abiosis ab10515
abiotic ab1071c
abiotically ab1071ca117
ablate ab18
ablated ab18d
ablates ab185
able ab1e
abled ab1ed
ablegate ab1e68
ablegates ab1e685
ableist ab1e157
ableists ab1e1575
ables ab1e5
ablest ab1e57
ably ab17
abo ab0
abode ab0de
aboded ab0ded
abodes ab0de5

Wednesday, January 4, 2017

Reinventing the world without reinventing the wheel

I just made this up. Dibs.

"Reinventing the world without reinventing the wheel" - Tatarize.