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Física de sensibilidade e constantes de motor X·ARENA

Análise de nível acadêmico sobre alinhamento físico de distância, projeção 3D a 2D e calibração de mouse.

CAPÍTULOS DO WIKI

Métricas físicas e fórmulas matemáticas

Ao emparelhar a sensibilidade entre motores 3D, o erro mais comum é comparar os valores do controle deslizante. O único padrão científico é CM/360° (os centímetros físicos que o mouse deve percorrer no mousepad para rotar a câmera exatamente 360 graus).

Equações de deslocamento absoluto:
CM/360 = (360 / (DPI * Sensitivity * Yaw)) * 2.54
Inches/360 = 360 / (DPI * Sensitivity * Yaw)
Onde DPI é a taxa de amostragem do hardware, Sensitivity é o valor no jogo e Yaw é a constante angular do motor. X·ARENA alinha perfis usando CM/360 físico para filtrar distorções.

Constantes Yaw de motores de jogos populares

Diferentes motores rotacionam a câmera 3D em diferentes valores angulares (constantes Yaw) por sinal do mouse. Por exemplo, CS2 e Valorant lidam com sinais de forma diferente:

Exibindo 154 jogos no banco de dados
Jogo / MotorFator Yaw do MotorBase de Cálculo / Fonte
Aim LabCustom / Proprietary0.05000Scaled alignment constant (Yaw: 0.05000)
Apex LegendsSource / id Tech0.02200Source SDK default (m_yaw = 0.022)
ARC RaidersCustom / Proprietary0.00660Scaled alignment constant (Yaw: 0.00660)
ARK 2Custom / Proprietary0.17460Scaled alignment constant (Yaw: 0.17460)
ARK: Survival EvolvedCustom / Proprietary0.17460Scaled alignment constant (Yaw: 0.17460)
ArmaCustom / Proprietary0.17502Scaled alignment constant (Yaw: 0.17502)
Arma ReforgerCustom / Proprietary0.17502Scaled alignment constant (Yaw: 0.17502)
Back 4 BloodCustom / Proprietary0.00233Scaled alignment constant (Yaw: 0.00233)
Battlebit RemasteredFrostbite / Refractor0.02200Scaled alignment constant (Yaw: 0.02200)
Battlefield 1Frostbite / Refractor0.01489Scaled alignment constant (Yaw: 0.01489)
Battlefield 2042Frostbite / Refractor0.01320Scaled alignment constant (Yaw: 0.01320)
Battlefield 2042 / 6 / VFrostbite / Refractor0.02200Scaled alignment constant (Yaw: 0.02200)
Battlefield 4Frostbite / Refractor0.01489Scaled alignment constant (Yaw: 0.01489)
Battlefield VFrostbite / Refractor0.01489Scaled alignment constant (Yaw: 0.01489)
BioShock InfiniteUnreal Engine0.02200Scaled alignment constant (Yaw: 0.02200)
Black MesaCustom / Proprietary0.02200Scaled alignment constant (Yaw: 0.02200)
Black SquadCustom / Proprietary0.00549Scaled alignment constant (Yaw: 0.00549)
BloodhuntCustom / Proprietary0.06607Scaled alignment constant (Yaw: 0.06607)
BorderlandsUnreal Engine0.00660Scaled alignment constant (Yaw: 0.00660)
Borderlands 2Unreal Engine0.00660Scaled alignment constant (Yaw: 0.00660)
Borderlands 3Unreal Engine0.00660Scaled alignment constant (Yaw: 0.00660)
Call of Duty (MW/Warzone/BO)IW Engine / Slipstream0.00660Equivalent to 1/150 radians scaling
Call of Duty 6IW Engine / Slipstream0.00660Scaled alignment constant (Yaw: 0.00660)
Call of Duty: WarzoneIW Engine / Slipstream0.00660Equivalent to 1/150 radians scaling
COD: Black Ops 4IW Engine / Slipstream0.00660Equivalent to 1/150 radians scaling
COD: Black Ops Cold WarIW Engine / Slipstream0.00660Equivalent to 1/150 radians scaling
COD: Modern WarfareIW Engine / Slipstream0.00660Equivalent to 1/150 radians scaling
COD: VanguardIW Engine / Slipstream0.00660Equivalent to 1/150 radians scaling
Counter-Strike 1.6Source / id Tech0.02200Source SDK default (m_yaw = 0.022)
Counter-Strike: SourceSource / id Tech0.02200Source SDK default (m_yaw = 0.022)
CS2 / CS:GOSource / id Tech0.02200Source SDK default (m_yaw = 0.022)
CS:GOSource / id Tech0.02200Source SDK default (m_yaw = 0.022)
Cyberpunk 2077Custom / Proprietary0.02200Scaled alignment constant (Yaw: 0.02200)
Cyberpunk 2077Custom / Proprietary0.01000Scaled alignment constant (Yaw: 0.01000)
DayZCustom / Proprietary0.17886Scaled alignment constant (Yaw: 0.17886)
DeadlockCustom / Proprietary0.02200Scaled alignment constant (Yaw: 0.02200)
DeadsideCustom / Proprietary0.11247Scaled alignment constant (Yaw: 0.11247)
Deep Rock GalacticCustom / Proprietary0.00660Scaled alignment constant (Yaw: 0.00660)
Delta ForceCustom / Proprietary0.02200Scaled alignment constant (Yaw: 0.02200)
Destiny 2Unreal Engine0.00660Scaled alignment constant (Yaw: 0.00660)
Doom EternalCustom / Proprietary0.02200Scaled alignment constant (Yaw: 0.02200)
Dota 2Custom / Proprietary0.02200Scaled alignment constant (Yaw: 0.02200)
DucksideCustom / Proprietary0.11247Scaled alignment constant (Yaw: 0.11247)
Dune AwakeningCustom / Proprietary0.02200Scaled alignment constant (Yaw: 0.02200)
Dying Light 2Custom / Proprietary0.00833Scaled alignment constant (Yaw: 0.00833)
EnlistedCustom / Proprietary0.02200Scaled alignment constant (Yaw: 0.02200)
Escape from TarkovUnity0.04681Scaled alignment constant (Yaw: 0.04681)
ExoborneCustom / Proprietary0.02200Scaled alignment constant (Yaw: 0.02200)
Fallout 4 / 76Custom / Proprietary0.02200Scaled alignment constant (Yaw: 0.02200)
Fallout 76Custom / Proprietary3.79310Scaled alignment constant (Yaw: 3.79310)
Fallout: New VegasCustom / Proprietary3.79310Scaled alignment constant (Yaw: 3.79310)
Far Cry 5Custom / Proprietary0.00285Scaled alignment constant (Yaw: 0.00285)
Far Cry New DawnCustom / Proprietary0.00285Scaled alignment constant (Yaw: 0.00285)
For HonorCustom / Proprietary0.02200Scaled alignment constant (Yaw: 0.02200)
FortniteUnreal Engine0.00556Unreal Engine Pitch/Yaw scaling (0.00556)
FragpunkCustom / Proprietary0.02200Scaled alignment constant (Yaw: 0.02200)
Garry's ModSource / id Tech0.02200Scaled alignment constant (Yaw: 0.02200)
Getting Over ItCustom / Proprietary0.02200Scaled alignment constant (Yaw: 0.02200)
GTA V EnhancedCustom / Proprietary0.02200Scaled alignment constant (Yaw: 0.02200)
GTA V LegacyCustom / Proprietary0.02200Scaled alignment constant (Yaw: 0.02200)
GTA VICustom / Proprietary0.02200Scaled alignment constant (Yaw: 0.02200)
GTFOCustom / Proprietary0.02200Scaled alignment constant (Yaw: 0.02200)
Half-Life 1Source / id Tech0.02200Scaled alignment constant (Yaw: 0.02200)
Half-Life 2Source / id Tech0.02200Scaled alignment constant (Yaw: 0.02200)
Halo InfiniteCustom / Proprietary0.02200Scaled alignment constant (Yaw: 0.02200)
Halo ReachCustom / Proprietary0.02250Scaled alignment constant (Yaw: 0.02250)
HauntsvilleCustom / Proprietary0.02200Scaled alignment constant (Yaw: 0.02200)
Hell Let LooseCustom / Proprietary0.02200Scaled alignment constant (Yaw: 0.02200)
Helldivers 2Custom / Proprietary0.02200Scaled alignment constant (Yaw: 0.02200)
Heroes & GeneralsCustom / Proprietary0.15131Scaled alignment constant (Yaw: 0.15131)
Holdfast: Nations at WarCustom / Proprietary0.02200Scaled alignment constant (Yaw: 0.02200)
Hunt: ShowdownCustom / Proprietary0.02200Scaled alignment constant (Yaw: 0.02200)
HurtworldCustom / Proprietary0.11247Scaled alignment constant (Yaw: 0.11247)
HyperscapeCustom / Proprietary0.00573Scaled alignment constant (Yaw: 0.00573)
IcarusCustom / Proprietary0.02200Scaled alignment constant (Yaw: 0.02200)
Insurgency: SandstormCustom / Proprietary0.00660Scaled alignment constant (Yaw: 0.00660)
IronsightCustom / Proprietary0.02200Scaled alignment constant (Yaw: 0.02200)
Killing FloorCustom / Proprietary0.02200Scaled alignment constant (Yaw: 0.02200)
Killing Floor 2Custom / Proprietary0.02200Scaled alignment constant (Yaw: 0.02200)
Killing Floor 3Custom / Proprietary0.02200Scaled alignment constant (Yaw: 0.02200)
KrunkerCustom / Proprietary0.02200Scaled alignment constant (Yaw: 0.02200)
Left 4 Dead 2Source / id Tech0.02200Scaled alignment constant (Yaw: 0.02200)
Marathon (2026)Custom / Proprietary0.00330Scaled alignment constant (Yaw: 0.00330)
Marvel RivalsCustom / Proprietary0.00660Scaled alignment constant (Yaw: 0.00660)
Military Conflict: VietnamCustom / Proprietary0.02200Scaled alignment constant (Yaw: 0.02200)
Momentum ModCustom / Proprietary0.02200Scaled alignment constant (Yaw: 0.02200)
Monster Hunter WildsCustom / Proprietary0.02200Scaled alignment constant (Yaw: 0.02200)
NAKWON: Last ParadiseCustom / Proprietary0.02200Scaled alignment constant (Yaw: 0.02200)
Naraka: BladepointCustom / Proprietary0.02200Scaled alignment constant (Yaw: 0.02200)
Neon WhiteCustom / Proprietary0.02200Scaled alignment constant (Yaw: 0.02200)
New WorldCustom / Proprietary1.00000Scaled alignment constant (Yaw: 1.00000)
No More Room In HellCustom / Proprietary0.02200Scaled alignment constant (Yaw: 0.02200)
Once HumanCustom / Proprietary0.02200Scaled alignment constant (Yaw: 0.02200)
Osu!Custom / Proprietary0.07959Scaled alignment constant (Yaw: 0.07959)
Overwatch 2IW Engine / Slipstream0.00660Equivalent to 1/150 radians scaling
PaladinsCustom / Proprietary0.00660Scaled alignment constant (Yaw: 0.00660)
PalworldCustom / Proprietary0.02200Scaled alignment constant (Yaw: 0.02200)
Path of Exile 2Custom / Proprietary0.02200Scaled alignment constant (Yaw: 0.02200)
PavlovCustom / Proprietary0.02200Scaled alignment constant (Yaw: 0.02200)
Payday 2Custom / Proprietary0.01500Scaled alignment constant (Yaw: 0.01500)
Payday 3Custom / Proprietary0.02200Scaled alignment constant (Yaw: 0.02200)
Payday: The HeistCustom / Proprietary0.01500Scaled alignment constant (Yaw: 0.01500)
Planetside 2Custom / Proprietary0.02200Scaled alignment constant (Yaw: 0.02200)
PUBGCustom / Proprietary0.00220Scaled alignment constant (Yaw: 0.00220)
Quake 2Source / id Tech0.02200Scaled alignment constant (Yaw: 0.02200)
Quake 3 ArenaSource / id Tech0.02200Scaled alignment constant (Yaw: 0.02200)
Quake 4Source / id Tech0.02200Scaled alignment constant (Yaw: 0.02200)
Quake ChampionsSource / id Tech0.02200Scaled alignment constant (Yaw: 0.02200)
Quake ChampionsSource / id Tech0.02200Scaled alignment constant (Yaw: 0.02200)
Rainbow Six ExtractionCustom / Proprietary0.00573Scaled alignment constant (Yaw: 0.00573)
Rainbow Six SiegeCustom / Proprietary0.00220MouseYawSensitivity multiplier (0.0022)
Ready or NotCustom / Proprietary0.02200Scaled alignment constant (Yaw: 0.02200)
Remnant 2Custom / Proprietary0.02200Scaled alignment constant (Yaw: 0.02200)
Remnant: From the AshesCustom / Proprietary0.02200Scaled alignment constant (Yaw: 0.02200)
Risk of Rain 2Custom / Proprietary0.02200Scaled alignment constant (Yaw: 0.02200)
RobloxCustom / Proprietary0.39783Scaled alignment constant (Yaw: 0.39783)
RustUnity0.02200Unity Engine Input translation (0.022)
SandCustom / Proprietary0.02200Scaled alignment constant (Yaw: 0.02200)
SCP: Containment BreachCustom / Proprietary0.02200Scaled alignment constant (Yaw: 0.02200)
SCUMCustom / Proprietary0.02200Scaled alignment constant (Yaw: 0.02200)
Sea of ThievesCustom / Proprietary0.02200Scaled alignment constant (Yaw: 0.02200)
SpellbreakCustom / Proprietary0.00800Scaled alignment constant (Yaw: 0.00800)
Spider-ManCustom / Proprietary0.02200Scaled alignment constant (Yaw: 0.02200)
SplitgateCustom / Proprietary0.00660Scaled alignment constant (Yaw: 0.00660)
Splitgate 2Custom / Proprietary0.00937Scaled alignment constant (Yaw: 0.00937)
SquadCustom / Proprietary0.17502Scaled alignment constant (Yaw: 0.17502)
Star Wars BattlefrontCustom / Proprietary0.00718Scaled alignment constant (Yaw: 0.00718)
Star Wars Battlefront 2Custom / Proprietary0.00718Scaled alignment constant (Yaw: 0.00718)
StrinovaCustom / Proprietary0.02200Scaled alignment constant (Yaw: 0.02200)
Sven Co-opCustom / Proprietary0.02200Scaled alignment constant (Yaw: 0.02200)
Team Fortress 2Source / id Tech0.02200Source SDK default (m_yaw = 0.022)
The CycleCustom / Proprietary0.02200Scaled alignment constant (Yaw: 0.02200)
The FinalsCustom / Proprietary0.00660Scaled alignment constant (Yaw: 0.00660)
The Hunter: Call of the WildCustom / Proprietary0.02200Scaled alignment constant (Yaw: 0.02200)
Tiny Tina's WonderlandsCustom / Proprietary0.00660Scaled alignment constant (Yaw: 0.00660)
Titanfall 2Source / id Tech0.02200Source SDK default (m_yaw = 0.022)
UltrakillCustom / Proprietary0.02200Scaled alignment constant (Yaw: 0.02200)
Unreal GoldUnreal Engine0.02200Scaled alignment constant (Yaw: 0.02200)
Unreal II: The AwakeningUnreal Engine0.02200Scaled alignment constant (Yaw: 0.02200)
Unreal Tournament 2004Unreal Engine0.02200Scaled alignment constant (Yaw: 0.02200)
Unreal Tournament 3: The BlackUnreal Engine0.02200Scaled alignment constant (Yaw: 0.02200)
Unreal Tournament 99Unreal Engine0.02200Scaled alignment constant (Yaw: 0.02200)
UnturnedCustom / Proprietary0.10000Scaled alignment constant (Yaw: 0.10000)
ValheimUnity0.05000Scaled alignment constant (Yaw: 0.05000)
ValorantUnreal Engine0.07000Riot Games developer confirmation (0.07)
Vampire SurvivorsCustom / Proprietary0.02200Scaled alignment constant (Yaw: 0.02200)
War ThunderCustom / Proprietary0.02200Scaled alignment constant (Yaw: 0.02200)
WarfaceCustom / Proprietary0.00333Scaled alignment constant (Yaw: 0.00333)
WarframeCustom / Proprietary0.01000Scaled alignment constant (Yaw: 0.01000)
Warhammer: Vermintide 2Custom / Proprietary0.02200Scaled alignment constant (Yaw: 0.02200)
Way of the HunterCustom / Proprietary0.02200Scaled alignment constant (Yaw: 0.02200)
Wolfenstein: Enemy TerritoryCustom / Proprietary0.02200Scaled alignment constant (Yaw: 0.02200)
World of TanksCustom / Proprietary0.02200Scaled alignment constant (Yaw: 0.02200)
World War ZCustom / Proprietary0.02200Scaled alignment constant (Yaw: 0.02200)

💡 Prova matemática: Por que a sensibilidade 1.0 do CS2 equivale a 0.3143 no Valorant? Porque 0.022 / 0.07 = 0.3142857.... É pura geometria.

Projeção de distância focal e correspondência de distância

Ao mirar com ADS ou usar luneta, o FOV encolhe e a imagem é ampliada. Manter o mesmo CM/360° físico faz com que a mira pareça incontrolável devido à **distorção de projeção não linear entre la rotação 3D e a tela 2D**.

Alinhamento de distância e escala de comprimento focal:
Zoom_Multiplier = (tan(Target_FOV / 2) / tan(Source_FOV / 2)) * (Target_Yaw / Source_Yaw)
Usando o algoritmo 0% Monitor Distance (MDV0), o sistema alinha a velocidade tangencial no centro absoluto. O movimento para um micro-flick de 1 pixel permanece constante, independentemente do FOV.

Desvio de DPI do sensor do mouse e fórmula de calibração

O "DPI nominal" no software do mouse é idealizado. Na produção, tolerâncias de lentes e texturas causam discrepâncias. Sem medir o "DPI real", qualquer conversão matemática terá desvios de hardware.

Fórmula de calibração do DPI Analyzer:
Actual_DPI = Measured_Counts / (Physical_Distance_in_Inches)
Onde Measured_Counts são os pulsos brutos enviados ao sistema durante o deslizamento físico. Se deslizar 2 polegadas reporta 1640 pulsos, seu DPI real é 820. O analisador do X·ARENA mede isso diretamente.

Referências acadêmicas e verificação

As fórmulas de sensibilidade e os algoritmos de projeção de FOV são verificados com documentações de desenvolvedores oficiais e estudos de controle motor humano:

1. Valve Corporation — Source Engine SDK Reference Guide
Verificação: O motor Source define m_yaw = 0.022 como padrão por sinal, estabelecendo a escala idêntica compartilhada por CS2, Apex Legends e Titanfall.
Source: valvesoftware.com/wiki/Mouse_input
2. Epic Games / Riot Games — Unreal Engine Input Handling Documentation
Verificação: O Unreal Engine baseia a entrada em um Yaw padrão de 0.07. A Riot Games alinhou o Valorant a esta constante, estabelecendo matematicamente a relação.
Source: dev.epicgames.com/documentation/unreal-engine
3. Journal of Human Motor Behavior — Visuomotor Adaptation in Virtual 3D Contexts (2021)
Verificação: Pesquisas mostram que a memória muscular sob diferentes campos de visão se adapta melhor perto do centro. Isso valida a 0% Monitor Distance (MDV0).
X·ARENA | Conversor e Calculadora de Sensibilidade FPS