Game Engine Architecture 12

【Game Engine Architecture 12】

一、the field of physics is vast, and what most of today’s game engines call 「physics」 is more accurately described as a rigid body dynamics simulation.

　　現代遊戲中的物理，大多指的是 rigid body dynamics（剛體動力學）。

　　A rigid body is an idealized, infinitely hard, non-deformable solid object. The term dynamics refers to the process of determining how these rigid bodies move and interact over time under the influence of forces.

　　rigid body 是無限硬，不可變形的固體對象。

二、ODE

　　ODE stands for 「Open Dynamics Engine」 (http://www.ode.org). As its name implies, ODE is an open source collision and rigid body dynamics SDK. Its feature set is similar to a commercial product like Havok. Its benefits include being free and the availability of full source code. 

三、Bullet

　　Bullet is an open source collision detection and physics library used by both the game and film industries. Its collision engine is integrated with its dynamics simulation, but hooks are provided so that the collision system can be used stand-alone or integrated with other physics engines. It supports continuous collision detection (CCD)—also known as time of impact (TOI) collision detection.

四、PhysX

　　It was bought by NVIDIA and retooled so that it can run using NVIDIA’s GPUs as a coprocessor. (It can also run entirely on a CPU, without GPU support.)

五、Havok

　　Havok is the gold standard in commercial physics SDKs, providing one of the richest feature sets available and boasting excellent performance characteristics on all supported platforms. (It’s also the most expensive solution.)

六、Digital Molecular Matter (DMM)

　　Pixelux Entertainment S.A., located in Geneva, Switzerland, has produced a unique physics engine that uses finite element methods to simulate the dynamics of deformable bodies and breakable objects, called Digital Molecular Matter (DMM). The engine has both an offline and a runtime component. It was released in 2008 and can be seen in action in LucasArts’ Star Wars: The Force Unleashed.

七、a collidable entity contains two basic pieces of information—a shape and a transform.

八、area：二維空間中的面積。

　  volume：三維空間中的體積。

九、convex：凸包。

　  concave：凹包。

十、Collision Primitives

　　1）sphere。點 + 半徑。

　　2）Capsules。2個點+半徑。

　　　　

　　3）AABB。minimum coordinate + maximum coordinate。

　　　　the AABB will have to be recalculated whenever that object rotates. Even if an object is roughly box-shaped, its AABB may degenerate into a very poor approximation to its shape when the object rotates off-axis.

　　　　　　

　　4）OBB。

　　5）Discrete Oriented Polytopes (DOP)。

　　　　An AABB is a 6-DOP in which the plane normals are taken parallel to the coordinate axes. An OBB is also a 6-DOP in which the plane normals are parallel to the object’s natural principal axes. A k-DOP is constructed from an arbitrary number of planes k.

　　　　

　　6）Poly Soup　　　　

十一、The Separating Axis Theorem

　　It states that if an axis can be found along which the projections of two convex shapes do not overlap, then we can be certain that the two shapes do not intersect at all. If such an axis does not exist and the shapes are convex, then we know for certain that they do intersect.

　　只要找到一個分離軸，則兩個物體不相交。

　　In three dimensions, the separating line becomes a separating plane, but the separating axis is still an axis

　　

十二、Detecting Convex Collisions: The GJK Algorithm

　　Minkowski difference. This fancy-sounding operation is really quite simple: We take every point that lies within shape B and subtract it pairwise from every point inside shape A. The resulting set of points { (Ai - Bj) } is the Minkowski difference.

　　tetrahedron：四面體。

　　　　

　　simplex：

　　　　

1三、Detecting Collisions between Moving Bodies

　　Motion in games is usually simulated in discrete time steps. So one simple approach is to treat the positions and orientations of each rigid body as stationary at each time step and use static intersection tests on each 「snapshot」 of the collision world. This technique works as long as objects aren’t moving too fast relative to their sizes. In fact, it works so well that many collision/physics engines, including Havok, use this approach by default.

1四、Swept Shapes

　　　　

1五、Continuous Collision Detection (CCD)

　　The goal of CCD is to find the earliest time of impact (TOI) between two moving objects over a given time interval.

1六、Temporal Coherency。（時間一致性）

　　temporal coherency, also known as frame-to-frame coherency.

　　每幀不變的數據能夠緩存起來，以減小計算量。

1七、Phantoms

　　For example, we might want the list of all enemies that are within a certain radius of the player character. Havok supports a special kind of collidable object known as a phantom for this purpose.

1八、Game-Specific Collision Materials　　

1九、Force

　　力正比於速度與質量。

　　　　　　

20、linear momentum

　　　　

　　　　力其實是 linear momentum 的一階導數。

　　　　

2一、Moment of Inertia。（旋轉質量）

　　The rotational equivalent of mass is a quantity known as the moment of inertia.  

　　Just as mass describes how easy or difficult it is to change the linear velocity of a point mass, the moment of inertia measures how easy or difficult it is to change the angular speed of a rigid body about a particular axis.

　　Moment of inertia is usually denoted by the symbol I.

2二、Energy

　　Force 將物體移動一段 Distance，就說 Force does work（力作了功）。

 

　　Energy comes in two forms. The potential energy V of a body is the energy it has simply because of where it is relative to a force field such as a gravitational or a magnetic field. (For example, the higher up a body is above the surface of the Earth, the more gravitational potential energy it has.) The kinetic energy of a body T represents the energy arising from the fact that it is moving relative to other bodies in a system. The total energy E = V +T of an isolated system of bodies is a conserved quantity, meaning that it remains constant unless energy is being drained from the system or added from outside the system.

　　

2三、Sound programmers today use the term audio rendering engine to underscore its many parallels with the graphics rendering engine.

2四、signal processing theory

　　signal processing theory that underlies almost every aspect of digital audio technology, including digital sound recording and playback, filtering, reverb and other digital signal processor (DSP) effects.

2五、The Physics of Sound

　　Sound is a compression wave that travels through the air (or some other compressible medium). A sound wave gives rise to alternating regions of air compression and decompression (also known as rarefaction) relative to the average atmospheric pressure. 

　　As such, we measure the amplitude（振幅） of a sound wave in units of pressure. In SI units, pressure is measured in Pascals, abbreviated Pa. One Pascal is the force of one Newton applied over an area of one square meter (1 Pa = 1 N/m2 = 1 kg/(m*s2)).

　　The instantaneous acoustic（聽覺） pressure is the ambient atmospheric pressure (considered a constant for our purposes) plus the perturbation caused by the sound wave at one specific instant in time：

　　　　

2六、angular frequency

　　angular frequency, typically denoted by the symbol w. The angular frequency is just the rate of oscillation measured in radians per second instead of cycles per second. Since one complete circular rotation is 2p radians, w = 2p f = 2p/T.

　　angular frequency 指的是每秒的振幅（弧度）。

2七、phase（相位）

　　

2八、波長、頻率、速度。

　　

2九、root mean square，RMS，均方根：每一系列數據(1)平方(2)相加後(3)開根號。

30、acoustic intensity. （聽覺強度，指耳朵感覺到的強度，單位爲 Pa）

　　　　

　　sound pressure level，represented by the L(P).  SPL 是取對數後的 acoustic intensity。

　　　　

3一、Equal-Loudness Contours

　　The human ear is most sensitive in the frequency range between 2 and 5 kHz. As the frequency decreases or increases beyond this range, more and more acoustic intensity (i.e., pressure) is required to produce the same perception of 「loudness.」

　　　　

3二、longitudinal wave

　　縱波是質點的振動方向與傳播方向同軸的波。如敲鑼時，鑼的振動方向與波的傳播方向就是一致的，因此聲波是縱波。

　　transverse wave

　　橫波是振動方向與傳播方向垂直，如光波。

 

　　In games, we typically model the absorption, reflection and sometimes the diffraction (e.g., bending slightly around corners) of our virtual sound waves, but we generally ignore refraction effects because these effects are not easily noticed by a human listener.

　　聲音引擎一般模擬 吸取、反射、衍射，但不模擬折射。

3三、Atmospheric Absorption

　　聲音 frequency 越高， absorption頻率越大。也就是 frequency 越高，越傳播不遠；frequency 越低，越傳播的遠。

3四、interference

　　When multiple waves interact, we call this interference. Constructive interference describes the case in which the waves reinforce one another and the amplitude increases. Destructive interference occurs when the waves cancel each other out, resulting in lower amplitude.

3五、Reverb and Echo

　　1）Direct(dry)　　

　　2）Early reflection（echo）

　　3）Late reverberation（tail）

　　　　

3六、anechoic chamber（無回聲室）

　　An anechoic chamber is a room especially designed to entirely eliminate reflected sound waves. This is accomplished by lining the walls, floor and ceiling of the room with thick corrugated foam padding that absorbs essentially all of the reflected sound waves. As a result, only the direct (dry) sound reaches the listener or microphone. Sound in an anechoic chamber has a completely 「dead」 timbre.

3七、The Doppler Effect

　　　　　　

　　

3八、Signals

　　independent variable：自變量。好比速度圖像裏，就是時間t；紋理中，就是座標 x、y。

3九、continuous and discrete

　　1）continuous-time signal. 使用 (t)

　　2）discrete-time signal. 使用 [n]

 

　　One common way to think of a discrete-time signal is as a sampled version of a continuous-time signal. The sampling process (also known as digitization or analog-to-digital conversion) lies at the heart of digital audio recording and playback.

40、 superposition.

　　When multiple sound waves overlap in space, their amplitudes add together — this is called superposition

4一、Linear Time-Invariant (LTI) Systems

　　In the context of signal processing theory, a system is defined as any device or process that transforms an input signal into a new output signal.

　　A time-invariant system is one for which a time shift in the input signal causes an equal time shift in the output signal.

　　A linear system is one that possesses the property of superposition. This means that if an input signal consists of a weighted sum of other signals, then the output is a weighted sum of the individual outputs that would have been produced, had each of the other signals been fed through the system independently.

　　

4二、The Unit Impulse

　　1）In discrete time, the unit impulse d[n] is as simple as it gets: It is a signal whose value is zero everywhere except at n = 0, where its value is one:

　　　　

　　2）In continuous time, the unit impulse d(t) is a bit trickier to define. It is a function whose value is zero everywhere except at t = 0, where its value is infinite—but the area under the curve is equal to one.

　　3）「box」 function b(t), whose value is zero everwhere except in the interval [0, T), where its value is 1/T. The area under this curve is just the area of the box, width times height, or T x1/T = 1.

　　　　　　

　　　　

4三、Using an Impulse Train to Represent a Signal

　　The function d[n-k] is a time-shifted discrete unit impulse, whose value is zero everywhere except at time n = k, where it is equal to one.

　　　　

　　　　

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