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| | QW physics: moving in air, bunnyhop. | | QW physics: moving in air, bunnyhop. |
| − | !!!!!!!Article is not correct at the moment. It will be fixed soon!!!
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| | With commands | | With commands |
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| − | Those values are defined by variables
| + | //TODO |
| − | cl_sidespeed, cl_forwardspeed, cl_backspeed, cl_upspeed.
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| − | Also command +speed increases them 2 times.
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| − | If 2 opposite commands are (for example +forward and +back) then only earliest is really active.
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| − | Valuses forwardmove, sidemove, upmove are sent to server and
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| − | also used in client to predict movement.
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| − | Code that processes player movement must be equal in client and server.
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| − | For example I have
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| − | cl_forwardspeed 400 (ezquake default) and
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| − | also there is following line in my config which is executed at the client start:
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| − | +mlook;wait;+speed;wait;
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| − | Thus when pressing +forward
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| − | forwardmove = 2 * 400 = 800.
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| − | Movement of layers is processed in function PM_PlayerMove.
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| − | Probably to reduce traffic quake clients remove several bits and
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| − | forwardmove = 800 become 508 в PM_PlayerMove.
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| − | Lets see player movement in air.
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| − | So called vector of wished speed is calculated.
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| − | In air it is horizontal and is summed up from 2 components:
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| − | horyzontal vector with length forwardmove wich is directed along player view but horizontally
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| − | and of vector with length sidemove which is horizontal and perpendicular to 1st component.
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| − | (Need picture.)
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| − | upmove is not used while in air. Only gravitation affects player movement in air.
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| − | Next , if length of received vector of wishspeed is grater than server restriction
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| − | its length is decreased to meet restrictions.
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| − | This length is 320 for usual TDM and
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| − | changes from 230 to 450 depending on player class in TF.
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| − | Next step. We are in function PM_PlayerAccelerate() and
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| − | we have vector of wished direction with length 1
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| − | and value of wished speed.
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| − | First of all value of wished speed is restricted by 30:
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| − | wishspd = min(wishspd, 30);
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| − | Then value of projection of current velocity to wished direction is calculated:
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| − | currentspeed = DotProduct (pmove.velocity, wishdir);
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| − | Вычисляем разницу между желаемой скоростью и проекцией теущей скорости.
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| − | Then difference between wished speed and projection of current velocity
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| − | is calculated. If result is not positive then velocity does not change.
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| − | addspeed = wishspd - currentspeed;
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| − | if (addspeed <= 0)
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| − | return;
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| − | Then calculated value
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| − | accelspeed = accel * wishspeed * pm_frametime =
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| − | 10 *320 * 0.014 = 44.8.
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| − | (wishspeed - is not wishspd here)
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| − | Then minimal value between is taken:
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| − | accelspeed = min(accelspeed, addspeed);
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| − | Final step: vector with length accelspeed and direction wishdir is added to current velocity.
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| − | VectorMA(pmove.velocity, accelspeed, wishdir, pmove.velocity);
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| − | Simpliest cases.
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| − | If player is in air and does not press buttons his horizontal speed does not change.
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| − | If player has zero speed pressin +forward gives him speed 30 directed horizontally forward.
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| − | Now we can look into bunnyhop.
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| − | Wewill concider speed greater than server restriction (320 in TDM)
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| − | because player can gain that speed while he is on ground.
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| − | And of course we concder that player does not set too small values of
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| − | cl_sidespeed, cl_forwardspeed, cl_backspeed.
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| − | Nice fact about QW is that it does not matter where player looking to.
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| − | Only his wishdir is important.
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| − | Let angle between horizontal velocity v и wishdir is gamma.
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| − | wishspd = min(wishspd, 30) = 30 with conditions given above.
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| − | addspeed = wishspd - currentspeed = 30 - v * cos(gamma)
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| − | Final value of accelspeed >=0.
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| − | When bunnyhopping we want to increase speed so we must have
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| − | cos(gamma) > 0
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| − | addspeed = 30 - v * cos(gamma) > 0
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| − | When bunnyhopping value accel * wishspeed * pm_frametime is not important.
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| − | Really 44.8 > 30 - v * cos(gamma) if cos(gamma) > -14.8/v
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| − | that is only if we are decaccelerating.
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| − | So when bunnyhopping we have accelspeed = addspeed;
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| − | Increase of speed in one frame is
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| − | dv_frame = addspeed * cos(gamma) = (30 - v * cos(gamma)) * cos(gamma).
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| − | Graphic of dv_frame(cos(gamma)) is parabola
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| − | (Need picture)
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| − | Upper (best) point is when соs(gamma_best) = 15 / v;
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| − | Best possible increase in one frame is
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| − | dv_frame_best = (30 - v * 15 / v) * 15 / v = 225 / v.
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| − | pm_frametime = 0.013, if 77fps phisics is active
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| − | and pm_frametime = 0.014, if 72fps phisics (TF2003 standard, old TDM standard).
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| − | Ultimately speed increase is described by following differential equation:
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| − | dv/dt = 225/(v * pm_frametime)
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| − | Acceleration with 77fps phisics is about 7% bigger than with 72fps.
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| − | v(t) ~ sqrt(t - t0).
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| − | Theoretically speed of 2000 can be reached within 111 seconds with 77fps phisics.
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| − | It was experimentally proved that player can overcome sv_maxvelocity which is by default.
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| − | Player must keep best direction of wishdir.
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| − | He rotates to make it.
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| − | Player can look up or down while bunnyhopping: it does not matter for physics.
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| − | Correct angle speed is
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| − | omega = addspeed * sin(gamma) / v = (15 / v) * sqrt(1 - (15 / v)^2).
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| − | So the greater is speed the less is best angle speed.
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| − | Comments and corrections are welcome.
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