Post on 10-May-2015
description
Smooth OperatorProgramming the little things that games can't do without
WGK 2012 · August 31, 2012
Leszek GodlewskiProgrammerleszek.godlewski@thefarm51.com
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Hello, target audience!
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● Beginner programmers● You can learn some cool stuff (hopefully)
● Beginner gameplay programmers● Intermediate programmers
● Maybe you'll learn a thing or two● Seasoned gameplay programmers
● You'll be bored to death :(
Far from done
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WORK INWORK INPROGRESSPROGRESS
All game footage in these slides is work in progress and is not representative of final quality of the game.
Why so smooth?
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● Rough and sharp things are, well, rough and sharp● We all like pleasant stuff● Jerky movement and rough transitions create
an impression of being unfinished, unprofessional, lacking polish
● Few processes in nature happen instantly● Kinematics: movement derives from velocity,
velocity derives from acceleration● Physical and chemical reactions all take time
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Organic motionVideo source: http://youtu.be/geg3ck3OT5Y
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Organic motionImage source: http://commons.wikimedia.org/wiki/File:1-D_kinematics.svg
Visual feedback of game logic
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● Gameplay logic is usually driven by a set of variables
● These variables are also used for visual feedback, either directly or indirectly (visual variables are derived from them in some way)● Discrete variables – potentially rough
transitions, often need smoothing out for appearance
● Continuous ones – usually less problematic
Visual feedback of game logic
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● Discrete transitions can be smoothed out for visuals by interpolation● It's not nearly as bad in reality as you may think
after taking a class in numerical methods!
Lerp
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● Mother of all interpolations! Used since antiquity
● Alpha term aka time● y = α · y0 + (1 – α) · y1● α [0; 1]∈
Why alpha is cool
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● It's simply percentage! (normalization FTW)● It's absurdly easy to convert lerps into
higher-order exponential interpolation! y = xz
Why alpha is cool
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● It's elementary to reverse its direction! αi = (1 – α0)
z
● It's trivial to make it time-dependent! α(t) = α(t - 1) + Δt · v
Moar interpolation!
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● Lerp can also be applied to vectors, Euler angles etc. (component-wise, using the same alpha term)
● Quaternions can be slerped● Polynomial interpolation, eg. cubic
(results in a C1 function), exponential, sine interpolation
● Ease-in, ease-out, ease-in-ease-out● Decelerating interpolation:
f(t) = f(t – 1) + α · [t – f(t – 1)]
What's that noise?
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● Entropy is a major natural force● In opposition to order and regularity● Humankind strives for the latter
● Need to simulate entropy for believable natural and organic features
● Lots of academic research on noise● Random number generators● Noise pattern algorithms
What's that noise?
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● Noises can be combined for procedural textures
● No memory/bandwidth limits● No mapping problem● Limitless possibilities of effects
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Case 1: Generic character animation
Case 1: Generic character animation
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● Skeletal animation data consists of key frames
● Need to interpolate (aka “inbetween”, or “tween”) between key frames for continuous motion independent of simulation speed
● But this is handled by animation playback code● Non-blended animation transitions look
bad● I mean, really, REALLY bad!● The effect is known as “popping”
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PoppingVideo clip: 01-popping.m4v
Popping
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Solution:● Interpolate the skeleton poses
resulting from the contributing animations
● Lerp bone translations● Slerp bone quaternions
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Animation blendingVideo clip: 02-blending.m4v
Animation blending
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Yeah, I know – nothing fancy, every game has it...
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Case 2: Camera target following
Case 2: Camera target following
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Challenges:● Camera can translate and rotate● Target can move as well!
● Fortunately, we can ignore target rotation● Target translation changes angle delta to
target!
Moving target problem
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angledelta
viewer
target angle delta
viewer
target
t = t0 t = t1
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Iteration 1: LerpVideo clip: 03-lerp.m4v
Iteration 1: Lerp
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● That's awful!● Direct result of lerping – no easing, motion feels
absolutely inorganic● Therefore we need an interpolation with ease
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Iteration 2: Decelerating interpolationVideo clip: 04-decel.m4v
Iteration 2: Decelerating interp.
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● Okay, so that actually looks fine!... sometimes● But only as long as the initial angle delta is
not extreme...● This is ease-out only● We need to ease-in, too!
Iterations 3..n
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Fast-forward through some trial, lots of error and a bit of despair...
Iteration n + 1
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How about this:● At start, compute initial angle delta
Δ0 = Θc(0) - Θt(0)● Store the current angle delta to target Δ(t)● Compensate for target translation by adding
the delta of deltas to camera rotation (we need to go deeper!)
Θc(t) = Θc(t – 1) + Δ(t) – Δ(t – 1)● Interpolate over Δ0 with a simple ease-in-
ease-out
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Iteration n + 1Video clip: 05-compensation.m4v
Iteration n + 1
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● Phew! That'll do.● The delta of deltas compensates almost
perfectly for target movement● Only the most extreme of cases may still
cause problems (very fast-moving target, very short distance to target)
● Ease-in-ease-out makes for a nice, smooth feeling
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Case 3: Flashlight
Case 3: Flashlight
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Challenges:● Spotlight must be aligned correctly with the
1st person mesh● But 1st person mesh is drawn in a different FOV!
● Spotlight must change size and colour according to the flashlight state
● Normal light – static shape, dynamic colour● Focused light – dynamic shape and colour● Dead battery – static shape, dynamic colour,
blinking
Light alignment vs FOV
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Light alignment vs FOV
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Light alignment vs FOV
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Light alignment vs FOV
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Light alignment vs FOV
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Light alignment vs FOV
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Off to an easy start● Light is obviously rendered at global
FOV● Configurable offset from camera● Dynamic light influence switched off
for 1st person meshes to avoid artifacts
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Oops! Gimbal lock!Video clip: 06-gimbal.m4v
Oops! Gimbal lock!
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● Quick fix: use quaternions instead for composing the rotations together
QuatToRotator( QuatProduct( QuatInvert( QuatFromRotator(Rotation)), QuatFromRotator(SocketRotation) ))
From logic to visuals
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● Logic control variables● Current item state (discrete)● Remaining battery power (continuous)
● Light cone size (continuous)● Derived from state transition and, if focused, from
battery power● Light brightness and colour (continuous)
● Derived from state transition and battery power● Light blink state (when the battery is dying)
Light cone size
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● Recap: drive light volume mesh scale and spotlight cone angle by state and battery power
● For state, let's try a helper variable and a lerp (0: unfocused, 1: focused)
if (IsFlashLightBeamActive()) FocusAlpha = FMin(1.f, FocusAlpha + DeltaTime * FocusSpeed);else FocusAlpha = FMax(0.f, FocusAlpha - DeltaTime * FocusSpeed);
Bonus!
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● FocusAlpha may be easily applied to drive visuals by beam focus, such as FOV
FREE!!!FREE!!!
Light cone size
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● Recap: drive light volume mesh scale and spotlight cone angle by state and battery power
● Final light cone scale:ConeScale = Lerp(1.f, ((1.f – PowerBlinkThreshold) * Power ** 2.f + PowerBlinkThreshold) * FocusSizeMultiplier, FocusAlpha);
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Light cone sizeVideo clip: 07-size.m4v
Light brightness & colour
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● Recap: drive spotlight brightness by state and battery power, and colour by battery power only
● Brightness is a piece of cake:NewBrightness = Lerp( UnfocusedBrightness, FocusedBrightness, FocusAlpha * Power);
Light brightness & colour
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● Recap: drive spotlight brightness by state and battery power, and colour by battery power only
● Colour is just as easy:NewColor = LerpColor( LowBatteryLightColour, FullBatteryLightColour, Power);
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Light brightness & colourVideo clip: 08-colour.m4v
Light blinking
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● A little noise will come in handy:if (bDeadBattery) bBlinking = Power < 0.925 && Rand(100) < 8;else if (Power <= PowerBlinkThreshold) bBlinking = Power <= 0.f || FRand() < (1.f - Power / PowerBlinkThreshold);
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Light blinkingVideo clip: 09-blinking.m4v
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Flashlight in actionVideo clip: 10-flashlight.m4v
General tips
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● Fractions are your best friends!● Alpha term is usually just a floating point
division away● Bias and scaling is easy
● Easing is cheap● Use whenever motion or transition feels robotic
● Ordinary rand() is often noisy enough● Plenty of other noise functions available if not
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Questions?
Thank you!
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leszek.godlewski@thefarm51.com
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