The source files for generating the animations in this post are on GitHub.

本文之中文翻譯在此 (by Wayne Chen)

Timeslicing is a very useful technique to improve the performance of batched algorithms (multiple instances of the same algorithm): instead of running all instances of algorithms in a single frame, spread them across multiple frames.

For instance, if you have 100 NPCs in a game level, you typically don’t need to have every one of them make a decision in every single frame; having 50 NPCs make decisions in each frame would effectively reduce the decision performance overhead by 50%, 25 NPCs by 75%, and 20 NPCs by 80%.

Note that I said timeslicing the decisions, __not__ the whole update logic of the NPCs. In every frame, we’d still want to animate every NPC, or at least the ones closer and more noticeable to the player, based on the **latest decision**. The extra animation layer can usually hide the slight latency in the timesliced decision layer.

Also bear in mind that I will not be discussing how to finish a single algorithm across multiple frames, which is another form of timeslicing that is not within the scope of this post. Rather, this post will focus on spreading multiple instances of the same algorithm across multiple frames, where each instance is small enough to fit in a single frame.

Such timeslicing technique applies to batched algorithms that are not hyper-sensitive to latency. If even a single frame of latency is critical to certain batched algorithms, it’s probably not a good idea to timeslice them.

In this post, I’d like to cover:

- An example that involves running multiple instances of a simple algorithm in batch.
- How to timeslice such batched algorithms.
- A categorization for timeslicing based on the timing of input and output.
- A sample implementation of a timeslicer utility class.
- Finally, how threads can be brought into the mix.

The example I’m going to use is a simple logic that orients NPCs to face a target. Each NPC’s decision layer computes the desired orientation to face the target, and the animation layer tries to rotate the NPCs to match their desired orientation, capped at a maximum angular speed.

First, let’s see an animated illustration of what it might look like if this algorithm is run for every NPC in every frame (Update All).

The moving circle is the target, the black pointers represent NPCs and their orientation, and the red indicators represent the NPCs’ desired orientation.

And the code looks something like this:

void NpcManager::UpdateFrame(float dt) { for (Npc &npc : m_npcs) { npc.UpdateDesiredOrientation(target); npc.Animate(dt); } } void Npc::UpdateDesiredOrientation(const Object &target) { m_desiredOrientation = LookAt(target); } void Npc::Animate(float dt) { Rotation delta = Diff(m_desiredOrientation, m_currentOrientation); delta = Limit(delta, m_maxAngularSpeed); m_currentOrientation = Apply(m_currentOrientation, delta); }

As mentioned above, you typically don’t need to update all the NPCs’ decisions in one frame. We can achieve rudimentary timeslicing like this:

void NpcManager::UpdateFrame(float dt) { const unsigned kMaxUpdates = 4; unsigned npcUpdate = 0; while (npcUpdated < m_numNpcs && npcUpdated < kMaxUpdates) { m_aNpc[m_iNpcWalker].UpdateDesiredOrientation(target); m_iNpcWalker = (m_iNpcWalker + 1) % m_numNpc; ++npcUpdated; } for (Npc &npc : m_npcs) { npc.Animate(dt); } }

This straightforward approach could be enough. However, sometimes you just need more control over the timing of input and output. Using the more involved timeslicing logic presented below, you can have a choice of different timing of input and output to suit specific needs.

Before going any further, let’s take a look at the terminology that will be used throughout this post.

- Completing a
**batch**means finishing running the decision logic once for each NPC. - A
**job**represents the work to run an instance of decision logic for an NPC. - The
**input**is the data required to run a job. - The
**output**is the results from a job after it’s finished

Now the timeslicing logic.

Here are the steps of one way to timeslice batched algorithms. It’s probably not the absolute best in terms of efficiency or memory usage, but I find it logically clear and easy to maintain (which also means it’s good for presentational purposes). So unless you absolutely need to micro-optimize, I wouldn’t worry about it too much.

- Start a new batch.
- Figure out all the jobs that need to be done. Associate each job with a unique
**key**that can be used to infer the required input for the job. - For each job, prepare an instance of job
**parameters**that is a collection of its key, input, and output. - Start and finish up to a max number of jobs per frame.
- Depending on the timing of output (more on this later),
**save**the**results**of a job, including the job’s output and its associated key, by pushing it to a**ring buffer**that represents the**history**of job results. The rest of the game logic to query latest results by key. - After all jobs are finished, the batch is finished. Rinse and repeat.

One advantage of looking up output by key is that different timesliced systems can work with each other just fine, even if they reference each other’s output. As far as a system is concerned, it’s looking up output from another system using a key, and the other system is reporting back the latest valid output available associated with the given key. Sort of like a mini database.

In our example, since each job is associated with an NPC, it seems fitting to use the NPCs as individual keys.

Next, here’s a categorization of timeslicing, based on the timing of reading input and saving output.

NOTE: The use of words “synchronous” and “asynchronous” here has nothing to do with multi-threading. The words are only used to distinguish the timing of operations. Everything presented before the “Threads” section later in this post is single-threaded.

**Asynchronous Input**: input is read by a job only when it’s started.**Synchronous Input**: input is read by all jobs when a new batch starts.**Asynchronous Output**: a job’s output is saved as soon as the job finishes.**Synchronous Output**: output of all jobs is saved when a batch finishes.

A ring buffer is used so that the rest of the game logic can be completely agnostic to the timing, and assume that the output (queried by key) is the latest.

Mixing and matching different timing of input and output gives 4 combinations. Async input / async output (AIAO), sync input / sync output (SISO), sync input / async output (SIAO), and async input / sync output (AISO). Let’s look at them one by one.

For demonstrational purposes, all animated illustrations below reflect a setup where only one job is started in each frame. The number should be set higher in a real game if it is introducing unacceptable latency.

For our specific example of NPCs turning to face the target, the AIAO combination probably makes the most sense. The input is read only when the job starts, so the job has the latest position of the target. The output is saved as soon as the job finishes with results of NPC’s desired orientation, so the NPC’s animation layer can react to the latest desired orientation immediately.

Here’s an animated illustration of what it could look like if we run the jobs at 10Hz (10 NPC jobs per second).

And here’s what it looks like if done at 30Hz.

You can see each that NPC waits until its job starts before getting the latest position of the target, and updates its desired orientation as soon as the job finishes.

For cases where asynchronous input from the AIAO combination as shown above is causing unwanted staggering, yet NPCs are still desired to react as soon as each of their job finishes, we can use the SIAO combination.

Here’s the 10Hz version.

And here’s the 30Hz version.

Note that when each job starts, it’s using the same target position as input, which has been synchronized at the start of each batch, while the output is saved for immediate NPC reaction as soon as each job finishes.

This is effectively the same as the first “basic first attempt” at timeslicing shown above.

The SISO combination is probably best explained by looking at the animated illustrations first. In order, below are the 10Hz and 30Hz versions of this combination.

It’s basically a “laggy” version of the very first animated illustration where every NPC is fully updated in every frame. All job input is synchronized upon batch start, and all output is saved out upon batch finish. Essentially this is kind of a “double buffer”, where the latest results aren’t reflected until all jobs in a batch are finished. For this reason, the history ring buffer must be **at least twice as large** as the max batch size for combinations with **synchronized output** to work properly.

The SISO combination is probably not ideal for our specific example. However, for cases like updating influence maps, heat maps, or any kind of game space analysis, the SISO combination could prove useful.

To be frank, I can’t think of a proper scenario to justify the use of the AISO combination. It’s only included here for comprehensive purposes. See the animated illustrations below in the order of the 10Hz version and 30Hz version. If you can think of a case where the AISO combination is a superior choice to the other three, please share your ideas in the comments or email me. I’d really like to know.

Now that we’ve seen all four combinations of timeslicing, it’s time to look at a sample implementation that does exactly what has been shown above.

Before going straight to the core timeslicing logic, let’s first look at how it plugs into the sample NPC code we saw earlier.

The timeslicer utility class allows users to provide a function that sets up keys for a new batch (writes to an array and returns new batch size), a function to set up input for job (writes to input based on key), and a function that is the logic to be timesliced (writes to output based on key and input).

class NpcManager { private: struct NpcJobInput { Point m_targetPos; }; struct NpcJobOutput { Orientation m_desiredOrientation; }; // timeslicing utility class Timeslicer < Npc*, // key NpcJobInput, // input NpcJobOutput, // output kMaxNpcs, // max batch size false, // sync input flag (false = async) false // sync output flag (false = async) > m_npcTimeslicer; // ...other stuff }; void NpcManager::Init() { // set up keys for new batch auto newBatchFunc = [this](Npc **aKey) unsigned { for (unsigned i = 0; i < m_numNpcs; ++i) { aKey[i] = GetNpc(i); } return m_numNpcs; }; // set up input for job auto setUpInputFunc = [this](Npc *pNpc, Input *pInput)->void { pInput->m_targetPos = GetTargetPosition(pNpc); } // logic to be timesliced auto jobFunc = [this](Npc *pNpc, const Input &input, Output *pOutput)->void { pOutput->m_desiredOrientation = LookAt(pNpc, input.m_targetPosition); }; // initialize timeslicer m_npcTimeslicer.Init ( newBatchFunc, setUpInputFunc, jobFunc ); } void NpcManager::UpdateFrame(float dt) { // timeslice decision logic m_timeslicer.Update(maxJobsPerFrame); // animate all NPCs based on latest decision results for (Npc &npc : m_npcs) { Output output; if (!m_timeSlicer.GetOutput(&npc, &output)) { npc.SetDesiredOrientation(output.m_desiredOrientation); } npc.Animate(dt); } }

And below is the timeslicer utility class in its entirety.

template < typename Input, typename Output, typename Key, unsigned kMaxBatchSize, bool kSyncInput, bool kSyncOutput > class Timeslicer { private: struct JobParams { Key m_key; Input m_input; Output m_output; }; struct JobResults { Key m_key; Output m_output; }; // number of jobs in current batch unsigned m_batchSize; // keep track of jobs in current frame unsigned m_iJobBegin; unsigned m_iJobEnd; // required to start jobs JobParams m_aJobParams[kMaxBatchSize]; // keep track of job results (statically allocated) static const unsigned kMaxHistorySize = kSyncOutput ? 2 * kMaxBatchSize // more on this later : kMaxBatchSize; typedef RingBuffer<JobResults, kMaxHistorySize> History; History m_history; // set up keys for new batch // (number of keys = batch size = jobs per batch) typedef std::function<unsigned (Key *)> NewBatchFunc; NewBatchFunc m_newBatchFunc; // set up input for job typedef std::function<void (Key, Input *)> SetUpInputFunc; SetUpInputFunc m_setUpInputFunc; // logic to be timesliced // (takes key and input, writes output) typedef std::function<void (Key, const Input &, Output *)> JobFunc; JobFunc m_jobFunc; public: void Init ( NewBatchFunc newBatchFunc, SetUpInputFunc setUpInputFunc, JobFunc jobFunc ) { m_newBatchFunc = newBatchFunc; m_setUpInputFunc = setUpInputFunc; m_jobFunc = jobFunc; Reset(); } void Reset() { m_batchSize = 0; m_iJobBegin = 0; m_iJobEnd = 0; } bool GetOutput(Key key, Output *pOutput) const { // iterate from newest history (last queued output) for (const JobResults &results : m_history.Reverse()) { if (key == results.m_key) { *pOutput = results.m_output; return true; } } return false; } void Update(unsigned maxJobsPerUpdate) { TryStartNewBatch(); StartJobs(maxJobsPerUpdate); FinishJobs(); } private: void TryStartNewBatch() { if (m_iJobBegin == m_batchSize) { // synchronous output saved on batch finish if (kSyncOutput) { for (unsigned i = 0; i < m_batchSize; ++i) { const JobParams ¶ms = m_aJobParams[i]; SaveResults(params); } } Reset(); Key aKey[kMaxBatchSize]; m_batchSize = m_newBatchFunc(aKey); for (unsigned i = 0; i < m_batchSize; ++i) { JobParams ¶ms = m_aJobParams[i]; params.m_key = aKey[i]; // synchronous input set up on new batch start if (kSyncInput) { m_setUpInputFunc(params.m_key, ¶ms.m_input); } } } } void StartJobs(unsigned maxJobsPerUpdate) { unsigned numJobsStarted = 0; while (m_iJobEnd < m_batchSize && numJobsStarted < maxJobsPerUpdate) { JobParams ¶ms = m_aJobParams[m_iJobEnd]; // asynchronous input set up on job start if (!kSyncInput) { m_setUpInputFunc(params.m_key, ¶ms.m_input); } m_jobFunc ( params.m_key, params.m_input, ¶ms.m_output ); ++m_iJobEnd; ++numJobsStarted; } } void FinishJobs() { while (m_iJobBegin < m_iJobEnd) { const JobParams ¶ms = m_aJobParams[m_iJobBegin++]; // asynchronous output saved on job finish if (!kSyncOutput) { SaveResults(params); } } } void SaveResults(const JobParams ¶ms) { JobResults results; results.m_key = params.m_key; results.m_output = params.m_output; if (m_history.IsFull()) { m_history.Dequeue(); } m_history.Enqueue(results); } };

If your game engine allows multi-threading, we can go one step further by offloading jobs to threads. Starting a job now creates a thread that runs the timesliced logic, and finishing a job now waits for the thread to finish. We need to use read/write locks to make sure the timeslicer plays nicely with the rest of game logic. Required changes to code are highlighted below.

class Timeslicer { // ...unchanged code omitted RwLock m_lock; struct JobParams { std::thread m_thread; Key m_key; Input m_input; Output m_output; }; bool GetOutput(Key key, Output *pOutput) const { ReadAutoLock readLock(m_lock); // iterate from newest history (last queued output) for (const JobResults &results : m_history.Reverse()) { if (key == results.m_key) { *pOutput = results.m_output; return true; } } return false; } void TryStartNewBatch() { WriteAutoLock writeLock(m_lock); if (m_iJobBegin == m_batchSize) { // synchronous output saved on batch finish if (kSyncOutput) { for (unsigned i = 0; i < m_batchSize; ++i) { const JobParams ¶ms = m_aJobParams[i]; SaveResults(params); } } Reset(); Key aKey[kMaxBatchSize]; m_batchSize = m_newBatchFunc(aKey); for (unsigned i = 0; i < m_batchSize; ++i) { JobParams ¶ms = m_aJobParams[i]; params.m_key = aKey[i]; // synchronous input set up on new batch start if (kSyncInput) { m_setUpInputFunc(params.m_key, ¶ms.m_input); } } } } void StartJobs(unsigned maxJobsPerUpdate) { WriteAutoLock writeLock(m_lock); unsigned numJobsStarted = 0; while (m_iJobEnd < m_batchSize && numJobsStarted < maxJobsPerUpdate) { JobParams ¶ms = m_aJobParams[m_iJobEnd]; // asynchronous input set up on job start if (!kSyncInput) { m_setUpInputFunc(params.m_key, ¶ms.m_input); } params.m_thread = std::thread([¶ms]()->void { m_jobFunc ( params.m_key, params.m_input, ¶ms.m_output ); }); ++m_iJobEnd; ++numJobsStarted; } } void FinishJobs() { WriteAutoLock writeLock(m_lock); while (m_iJobBegin < m_iJobEnd) { JobParams ¶ms = m_aJobParams[m_iJobBegin++]; params.m_thread.join(); // asynchronous output saved on job finish if (!kSyncOutput) { SaveResults(params); } } } };

If your game can afford to have one more frame of latency and you don’t want the timeslicer squatting a thread, you can tweak the update function a bit, where jobs are started at the end of update in the current frame, and are finished at the beginning of update in the next frame.

void TimeSlicer::Update(unsigned maxJobsPerUpdate) { FinishJobs(); TryStartNewBatch(); StartJobs(maxJobsPerUpdate); }

That’s it! We’ve seen how timeslicing batched algorithms can help with game performance, as well as the 4 combinations of input and output with different timing, each having its own use (well, maybe not the last one). We’ve also seen how the timeslicing logic can be further adapted to make use of threads.

I hope you find this useful.

]]>Also, this post is part 2 of a series (part 1) leading up to a geometric interpretation of Fourier transform and spherical harmonics.

Drawing analogy from vector projection, we have seen what it means to “project” a curve onto another in the previous post. This time, we’ll see how to find a the closest vector on a plane via vector projection, and then we’ll see how it translates to finding the best approximation of a curve via curve “projection”. This handy analogy can help us take another step closer to a geometric interpretation of Fourier transform and spherical harmonics later.

Given vectors , , and , the closest vector on the plane formed (or “spanned” in linear algebra jargon) by and is the projection of onto the plane. This projection, denoted , is a combination of scaled and , in the form of , that has the least error from .

The error is measured by the magnitude of the difference vector:

As pointed out in the previous post, minimizing this error is essentially equivalent to minimizing the root mean square error (RMSE):

This is what the relationship of , , , and looks like visually:

The projection of onto the plane spanned by and , is the vector on the plan that has the least error from , and the difference vector is orthogonal to the plane.

So how do we compute ? In the previous post we’ve seen how to project a vector onto another, so would computing be as simple as projecting onto , and then project the result again onto ? Not really. Here’s why:

As you can see in the figure above, isn’t parallel to nor . Projecting onto would give you a vector that is parallel to , and a subsequent projection onto would leave you with a result that is parallel to , which is definitely not .

One way to do it is to calculate a vector orthogonal to the plane, i.e. a plane normal , by taking the cross product of the two vectors that span the plane: . Then, take out the part in that is parallel to by subtracting the projection of onto from . What is left of is the part of that is parallel to the plane, i.e. the projection:

But, I want to talk about another way of performing the projection, which is easier to translate to curves later. and are not necessarily orthogonal to each other. Let’s find two orthogonal vectors that lie on the plane spanned by and . Then, we split into two parts, one parallel to one vector and one parallel to the other vector. Finally, we combine these two parts together to obtain a vector that is essentially the part of that is parallel to the plane.

As a simple illustration, if the plane is the X-Z plane, then the obvious two orthogonal vectors of choice would be and . To project a vector onto the X-Z plane, we split it into a part that is parallel to , which is , and a part that is parallel to , which is . Combining those two parts together would give us . This makes sense, because projecting a vector onto the X-Z plane is just as simple as dropping the Y component.

Now, given two arbitrary vectors and that span a plane, we can generate two orthogonal vectors, denoted and , by using a method called the Gram-Schmidt process. The first vector would simply be the . To compute the second vector , we take away from its part that is parallel to ; what’s left of is orthogonal to :

To compute , we combine the parts of that are parallel to and , respectively:

The Gram-Schmidt process is actually more general than described above. It can apply to higher dimensions. Given vectors, denoted to , in an -dimensional space (), and if the vectors are linearly independent, i.e. they span an -dimensional subspace, then we can generate vectors that are orthogonal to each other, denoted through , spanning the same subspace, using the Gram-Schmidt process.

The first vector would simply be . To compute the second vector , we take away from its part that is parallel to . To compute the third vector , we take away from its part that is parallel to **all previously generated orthogonal vectors**, and . Repeat this process until we have reached and produced :

Projecting an -dimensional vector onto this -dimensional subspace would involve combining the parts of the vector parallel to each of the orthogonal vectors. In our example above that involves 3D vectors, and . In higher dimensions, no simple 3D cross products can save you there.

Now we are done with vectors. Let’s take a look at curves!

Let’s say our interval of interest is . Given a 3rd-order polynomial curve , what’s the best approximation using a 2st-order polynomial curve, or a 1th-order polynomial curve (flat line)? How about simply dropping the higher-order terms, so we get and ? Here’s what they look like:

At first glance, I’d say and are not what we want. We can definitely find a parabolic curve and a line that approximate better. Look at just how far apart and are from at . Clearly, and are not the 2nd-order and 1st-order polynomial curves that have the least RMSEs from . Simply dropping higher-order terms turns out to be a naive approach. The right way to do it is just like what we did with vectors: projection.

In the vector example above, we were operating in the 3D geometric space. Now we are working with a more abstract 3rd-order polynomial space where lives in. The lower-order polynomial curve that has the least RMSE from is the projection of into that lower-order polynomial space. Let’s start with finding the 2nd-order polynomial curve that has the least RMSE from .

The 2nd-order polynomial subspace is 3-dimensional, since a 2nd-order polynomial curve has the form . Let’s first find 3 curves that span the subspace. An easy pick would be , , and . Now we need to use them to generate a set of orthogonal curves, , , and using the Gram-Schmidt process:

If you forgot how to “project” a curve onto another, please refer to the previous post.

Here are the results:

You can say that , , and are a set of orthogonal axes spanning the 2nd-order polynomial subspace. Now we split into three orthogonal parts by projecting it onto , , and :

Here’s what , , and look like alongside :

and might not look like they are close to , but they are the closest curves you can get along the axes and that have the least RMSEs from .

Now, we can combine the three orthogonal parts of to form the 2nd-order polynomial curve that is the best approximation of :

This looks way better than the result of simply dropping the 3rd-order term, as shown in the figure above.

Since the three parts are already orthogonal, we can actually obtain the 1st-order polynomial curve that best approximates by simply dropping from :

Also looking good, compared to simply dropping the 3rd-order and 2nd-order terms.

That’s it. In this post, we’ve seen how to generate a set of orthogonal curves from a set of curves spanning a lower-dimensional subspace of curves, and use the orthogonal curves to find the best approximation of a curve via curve “projection”.

We now have all the tools we need to move onto Fourier transform and spherical harmonics in the next post. Finally, something game-related!

]]>Also, this post is part 1 of a series (part 2) leading up to a geometric interpretation of Fourier transform and spherical harmonics.

Fourier transform and spherical harmonics are mathematical tools that can be used to represent a function as a combination of periodic functions (functions that repeat themselves, like sine waves) of different frequencies. You can approximate a complex function by using a limited number of periodic functions at certain frequencies. Fourier transform is often used in audio processing to post-process signals as combination of sine waves of different frequencies, instead of single streams of sound waves. Spherical harmonics can be used to approximate baked ambient lights in game levels.

We’ll revisit these tools in later posts, so it’s okay if you’re still not clear how they can be of use at this point. First, let’s start somewhere more basic.

If you have two vectors and , **projecting onto ** means stripping out part of that is orthogonal to , so the result is the part of that is parallel to . Here is a figure I borrowed from Wikipedia:

The **dot product** of and is a scalar equal to the product of magnitude of both vectors and the cosine of the angle (, using the figure above) between the vectors:

Another way of calculating the dot product is adding together the component-wise products. If and , then:

A follow-up to the alternate formula above is the formula for vector magnitude. The magnitude of a vector is the square root of the dot product of the vector with itself:

The geometric meaning of the dot product is the magnitude of the projection of onto **scaled** by . Dot product is commutative, i.e. , which means that is also equal to the magnitude of the projection of onto scaled by .

So if you want to get the magnitude of the projection of onto , you need to divide the dot product by the magnitude of :

To get the actual projected vector of onto , multiply the magnitude with the unit vector in the direction of , denoted by :

One important property of dot product is: if it’s positive, the two vectors point in roughly the same direction (); if it’s zero, the vectors are orthogonal (); if it’s negative, the vectors point away from each other ().

For the dot product of two unit vectors, like , it’s just . If it’s 1, then the two vectors point in exactly the same direction (); if it’s -1, then the two vectors point in exactly opposite directions (). So, in order to measure how close the directions two vectors point in, we can normalize both vectors and take their dot product.

Let’s say we have three vectors: , , and . If we want to determine which of and points in a direction closer to where points, we can just compare the dot products of their normalized versions, and . Whichever vector’s normalized version has a larger dot product with points in a direction closer to that of .

A metric often used to measure the difference between two data objects is the root mean square error (RMSE) which is the square root of the average of component-wise errors. For vectors, that means:

It kind of makes sense, because it is exactly the magnitude of the vector that is the difference between and scaled by :

It’s also the square root of the dot product of the difference vector with it self scaled by :

Here’s an important property of projection:

The projection of a vector onto another vector is the vector parallel to that has the **minimal RMSE** with respect to . In other words, gives you **the best scaled version of to approximate **.

Also note that if is larger than , it means has a smaller RMSE than with respect to ; thus, points in a direction closer to that o than does.

Now we’re finished with vectors. It’s time to move onto curves.

Let’s consider these three curves:

When working with curves, as opposed to vectors, we need to additionally specify an interval of of interest. For simplicity, we will consider for the rest of this post.

Below is a figure showing what they look like side-by-side within our interval of interest:

Just like vectors, “projecting” a curve onto another curve gives you the best scaled version of to approximate , and the “projection” has minimal RMSE with respect to . To compute the RMSE of curves, we need to first figure out how to compute the “dot product” of two curves.

Recall that the dot product of vectors is equal to the sum of component-wise products:

Mirroring that, let’s sum up the products of samples of curves at regular intervals, and we normalize the sum by dividing it with the number of samples, so we don’t get drastically different results due to different number of samples. If we take 10 samples between to compute the dot product of and , we get:

The more samples we use, the more accuracy we get. What if we take an infinite number of samples so we get the most accurate result possible?

This basically turns into an integral:

So there we have it, one common definition of the “dot product” of two curves:

**The integral of the product of two curves over the interval of interest**.

Copying the formula from vectors, the RMSE between two curves and is:

In integral form, it becomes:

The “mean” part of the error is omitted since it’s a division by 1, the length of our interval of interest.

To find out which one of the “normalized” version of and has less RMSE with respect to the normalized version of , we take the dot products of the normalized versions of the curves:

The dot product of and is larger than that of and . That means has a lower RMSE than with respect to .

Drawing analogy from vectors, is conceptually “pointing in a direction” closer to that of than does.

Now let’s try finding the best scaled version of that has minimal RMSE with respect to , by computing the projection of onto :

And this is what , , and look like side-by-side:

The projected curve is a scaled-up version of that is a better approximation of than itself; it is the best scaled version of that has the least RMSE with respect to .

Now that you know how to “project” a curve onto another, we will see how to approximate a curve with multiple simpler curves while maintaining minimal error.

]]>本文屬於My Career系列文

Here is the original English post.

本文之英文原文在此

註：為方便複製至PTT，本文排版採BBS格式，不習慣者請見諒

Uncharted 4已經發售，終於可以分享我負責開發的部分了

我主要是負責單人模式的夥伴AI、多人模式的戰友AI、還有一些遊戲邏輯

沒有收錄到最終遊戲的部分和一些瑣碎的細工我就略過不提

** = 崗位系統 = **

在本文開始前，我想要先談談我們用來指派NPC移動位置的崗位系統

這個系統的核心邏輯不是我負責的，我寫的是使用這個系統的客戶端程式

崗位是可行走空間中的離散位置

大部分是用工具自動生成的，也有一些是設計師手動擺置的

基於不同需求，我們設計不同的崗位平分系統

(e.g. 潛行崗位、戰鬥崗位)

然後我們選擇評分最高的崗位，指派NPC移動過去

** = 夥伴跟隨 = **

夥伴跟隨系統是繼承自The Last of Us

基本概念就是，夥伴在玩家周圍找個跟隨點

這些可能的跟隨點從玩家位置扇狀分開

並且要滿足以下的路徑線段淨空條件:

– 玩家到跟隨點

– 跟隨點到前方投射點

– 前方投設點到玩家

攀爬是Uncharted 4的新功能，這是The Last of Us 沒有的

為了與現有的跟隨系統整合，我利用攀爬崗位讓夥伴可以跟著玩家一起攀爬

這個功能比我想像中的還要難搞

單純根據玩家的攀爬狀態來切換夥伴的攀爬狀態，結果不甚理想

只要玩家快速在攀爬與非攀爬的狀態之間切換，夥伴就會在兩個狀態間快速跳換

於是我加入了遲滯現象(hysteresis)

只有在玩家切換了攀爬狀態，並且保持此狀態移動一定距離之後，夥伴才跟進

廣泛來說，遲滯現象是個解決行為跳換的好方法

** = 夥伴帶領 = **

遊戲中的某些特定場景，我們要讓夥伴帶領玩家前進

我把The Last of Us的帶領系統移植過來

設計師使用spline曲線在關卡中標記他們想讓夥伴帶領玩家的大致路線

如果有多個帶領路線，設計師則會用腳本語言切換主要的帶領路線

玩家的位置投射到spline曲線上，再往前延伸設定為帶領參考點

當帶領參考點超越被標記為等待點的spline曲線控制點，夥伴會前往下個等待點

如果玩家走回頭路

夥伴只有在帶領參考點離此次推進至最遠的等待點一段距離，才會回頭

這也是利用遲滯現象來避免行為跳換

我也把動態移動速度調整的功能整合進帶領系統

根據夥伴和玩家之間的距離，一些”速度平面”沿著spline曲線放置

夥伴有三種移動模式: 走路、跑步、衝刺

根據玩家撞到的速度平面，夥伴會選擇不同的移動模式

另外，夥伴的行進動畫速度也會基於玩家距離做微調

目的是避免切換移動模式的時後，有太突然的移動速度變化

** = 夥伴掩體共用 = **

在The Last of Us中，玩家和夥伴可以在各不離開掩體的狀況下重疊

我們稱這個為掩體共用

The Last of Us中的Joel伸手跨過Ellie和Tess按在掩體上

看起來很自然，因為夥伴的身型都比玩家嬌小

但是同樣的動作就不適合身型差不多的Nate、Sam、Sully、和Elena

而且Uncharted 4的遊戲節奏較快

讓Nate伸手去按掩體只會讓動作流暢性打折扣

所以我們決定就單純讓夥伴靠緊掩體，玩家稍微繞彎避開伙伴

我用的邏輯很簡單

如果玩家位置往移動方向投射的點，落在夥伴掩體周圍的一個方框內

夥伴就會取消目前的掩體行為，並且快速靠緊掩體

** = 救星戰友 = **

我負責多人模式的戰友(sidekicks)，而救星戰友是其中最特別的

單人模式中的NPC，沒有一個人的行為跟救星戰友一樣

他們會復甦被擊倒的同伴，也會複製玩家的掩蔽行為

救星戰友會嘗試複製玩家的掩蔽行為，並且盡量待在離玩家很近的地方

所以當玩家被擊倒的時候，他們就可以迅速跑過來復甦

如果玩家有裝備救星戰友的復甦包額外功能

他們會在採取復甦行動之前，朝被擊倒的復甦目標丟復甦包

復甦包丟擲基本上就是延用手榴彈的拋物線淨空測試和擲彈動作

只是我把手榴彈換成復甦包而已

** = 隱蔽草叢 = **

在隱蔽草叢中蹲行也是Uncharted 4才有的新功能

要實作這個功能，我們需要某種能夠標記場景的手段

遊戲邏輯才可以判斷玩家是否身處隱蔽草叢中

我們一開始是讓美術人員在Maya中標記背景模型的表面

但美術人員和設計師之間的溝通時間太長，很難頻繁改進關卡

於是我們決定用另外一種方法標記隱蔽草叢

我在場景編輯器中的nav mesh增加了隱密草叢的額外tag

讓設計師可以直接在編輯器中精準標記隱蔽草叢

有了這個額外的標記

我們也可以用這個資訊來為隱蔽崗位評分

** = 感知 = **

Uncharted 4沒有像The Last of Us有聆聽模式

所以我們必須要找另外一種方法，讓玩家有辦法得知附近的敵人威脅

好讓玩家不會在未知的敵對環境中產生迷失感

我利用敵人的感知資料，加入了威脅標示

當敵人開始注意(白色)、起疑(黃色)、和發現(橘色)玩家

這些標示會適時地提醒玩家

另外，我在威脅標示開始累積的同時播放背景雜音，以製造張力

當玩家被發現的時候，則播放大聲的提示音效

這些音效的安排和做用跟The Last of Us類似

** = 調查 = **

這是在我們送廠壓片前，我負責的最後一個功能

我平常在Naughty Dog是不參加正式會議的

不過在送廠壓片的前幾個月，我們每週至少開一次會

由Bruce Straley或Neil Druckmann主持，專注在遊戲的AI部分

幾乎每次開完會之後，調查系統都有需要更動的地方

前前後後總共經歷了好幾次大改

會讓敵人起疑的因素有兩種: 玩家和屍體

當敵人起疑了(起疑者)，他會抓最近的同伴來一起調查

離起疑點較近的人會成為調查者，另外一個人則是看守者

起疑者可能會視調查者，也有可能是看守者

我們總共有兩組不同的對話，適用於兩種不同的情況

(“那邊有異狀，我去看看” vs “那邊有異狀，你去看看”)

為了讓雙人調查看起來更自然

我使用了時域錯位的技巧，讓兩人的行動和威脅標示時間點錯開

否則兩個人的行為完全同步，看起來非常機械式、很不自然

如果調查者發現了屍體，他會通知全部的同伴開始搜索玩家

屍體也會被暫時標示，以讓玩家知道敵人為什麼進入警戒

在某些難度下，短時間內連續觸發調查，會讓敵人的感應力變敏銳

他們會更容易發現玩家，即使玩家躲在隱蔽草叢中也一樣

慘烈模式下，敵人永遠處於敏銳狀態

** = 對話動作 = **

這也是我負責的最後幾個功能之一

對話動作系統負責操控角色，在對話的時候做出一些小動作

像是轉頭看其他人和肢體動作

之前在The Last of Us

開發人員花好幾個月的時間，把整個遊戲所有的對話腳本手動加註上對話動作

我們可不想再做一次這種苦工

在這個開發階段，已經有部分對話腳本被手動加註好對話動作了

我們需要一個泛用型系統，可以幫沒有加註對話動作的腳本自動產生對話動作

而我就是負責製作這個對話動作系統

動畫師可以調整參數，改變轉頭速度、轉頭角度、注視時間、反覆時間等

** = 維持吉普車動量 = **

開發初期遇到的問題之一，就是馬達加斯加的吉普車駕駛關卡

當玩家開車撞到牆或者敵人的載具，玩家的車就會旋轉失速以致脫離車隊而關卡失敗

我使用的解決方法是，當玩家的車撞到牆或者敵方載具的時候

短暫地限制吉普車的最高角速度和線性速度的方向變量

這個簡單的方法相當有效，從此玩家就比較不容易旋轉失速而導致關卡失敗了

** = 載具死亡 = **

可駕駛的載具是首次在Uncharted 4登場

在這之前，所有的載具都是NPC駕駛、沿著固定軌道行進

我負責載具死亡的部分

摧毀載具有幾種方式:

解決駕駛、開槍射車、開車撞飛敵方機車、開車撞敵方吉普車導致旋轉失速

基於不同的死法，載具死亡系統會選擇載具和乘客的死亡動畫來播放

死亡動畫會漸漸混入物理引擎控制的ragdoll系統

所以死亡動畫會不著痕跡地轉換成物理模擬的翻車

當玩家開吉普車撞飛敵方機車的時候

我使用機車在XZ平面上投影的bounding box和碰撞點

來判斷要使用四個撞飛死亡動畫中的哪一個

至於衝撞使得敵方吉普車旋轉失速

我是拿敵方吉普車與預設行進方向之間的旋轉量差來比較旋轉失速判定閾值

載具播放死亡動畫的時候，有機會穿透牆壁

我使用球體投射，從預設位置投射向載具實際位置

如果投射結果是與牆壁碰撞，則把載具稍微往牆壁的法向量移動

不一次完全修正誤差，是為了避免太過劇烈的位移

我另外實作了一種特別的載具死亡類型，叫做載具死亡提示

這些死亡提示是動畫師和設計師在場景中擺置好的客製化死亡動畫

每個死亡提示在載具行進軌道上都有個進入範圍

當一個載具在死亡提示進入範圍中死亡，則會開始播放死亡提示的特殊死亡動畫

之所以開發這功能，一開始是為了2015年E3展的超帥氣吉普車死亡動畫

** = 混色用的貝爾矩陣 = **

我們想要消除攝影機切入看穿物體的瑕疵，特別是遊戲中的各種植物

於是我們決定要讓靠近攝影機的像素淡出

使用半透明像素並不是個好主意，因為非常消耗效能

我們使用的技巧，是所謂的混色(dithering)

https://en.wikipedia.org/wiki/Dither

使用混色技巧搭配貝爾矩陣(Bayer matrix)

利用一個預先決定的點陣模板來決定哪些像素可以捨棄而不渲染

https://en.wikipedia.org/wiki/Ordered_dithering

結果就是產生半透明的錯覺

一開始使用的貝爾矩陣是個8×8矩陣，取自上述的Wikipedia頁面

我認為這個矩陣太小，會造成不美觀的帶狀瑕疵

我想要使用16×16的貝爾矩陣，但是網路上都找不到相關資料

於是我試著用逆向工程找出8×8貝爾矩陣的遞迴特性

光用目測法，我想我應該可以直接解出16×16貝爾矩陣

但是我想要讓過程更有趣一點

我寫了一個工具，可以生成二的任何次方大小的貝爾矩陣

換到16×16貝爾具陣之後，可以明顯看到帶狀瑕疵的改善

** = 爆炸聲延遲 = **

這個部份我其實沒有什麼大貢獻，但是我還是覺得值得一提

在2015年E3展示中，Nate和Sully同時接收到高塔傳過來的爆炸聲和爆炸畫面

這是不合理的，因為高塔距離非常遠，爆炸聲應該會晚一點才被接收到

我在開展前幾週指出這點，美術團隊後來就在爆炸聲之前加上一小段延遲了

** = 繁體中文在地化 = **

直到送廠壓片前幾週我才開始在遊戲中改用繁體中文字幕，而我找到了許多錯誤

大部分的錯誤都是英文直譯中文，而變成四不像的用語

我認為我沒有足夠的時間可以單槍匹馬全破一次遊戲又同時抓出翻譯錯誤

於是我請幾個QA部門的人分章節、用繁體中文模式遊玩

然後我陸續瀏覽他們的遊玩錄製影片

結果這個方法相當有效率

我成功地把我找到的翻譯錯誤建檔，而在地化小組也有足夠的時間修正翻譯

** = 結束 = **

以上就是我對Uncharted 4開發上值得一提的貢獻

希望大家讀得愉快

This post is part of My Career Series.

Here is the Chinese translation of this post.

本文之中文翻譯在此

Now that Uncharted 4 is released, I am able to talk about what I worked on for the project. I mostly worked on AI for single-player buddies and multiplayer sidekicks, as well as some gameplay logic. I’m leaving out things that never went in to the final game and some minor things that are too verbose to elaborate on. So here it goes:

Before I start, I’d like to mention the post system we used for NPCs. I did not work on the core logic of the system; I helped writing some client code that makes use of this system.

Posts are discrete positions within navigable space, mostly generated from tools and some hand-placed by designers. Based on our needs, we created various post selectors that rate posts differently (e.g. stealth post selector, combat post selector), and we pick the highest-rated post to tell an NPC to go to.

The buddy follow system was derived from The Last of Us.

The basic idea is that buddies pick positions around the player to follow. These potential positions are fanned out from the player, and must satisfy the following linear path clearance tests: player to position, position to a forward-projected position, forward-projected position to the player.

Climbing is something present in Uncharted 4 that is not in The Last of Us. To incorporate climbing into the follow system, we added the climb follow post selector that picks climb posts for buddies to move to when the player is climbing.

It turned out to be trickier than we thought. Simply telling buddies to use regular follow logic when the player is not climbing, and telling them to use climb posts when the player is climbing, is not enough. If the player quickly switch between climbing and non-climbing states, buddies would oscillate pretty badly between the two states. So we added some hysteresis, where the buddies only switch states when the player has switched states and moved far enough while maintaining in that state. In general, hysteresis is a good idea to avoid behavioral flickering.

In some scenarios in the game, we wanted buddies to lead the way for the player. The lead system is ported over from The Last of Us and updated, where designers used splines to mark down the general paths we wanted buddies to follow while leading the player.

In case of multiple lead paths through a level, designers would place multiple splines and turned them on and off via script.

The player’s position is projected onto the spline, and a lead reference point is placed ahead by a distance adjustable by designers. When this lead reference point passes a spline control point marked as a wait point, the buddy would go to the next wait point. If the player backtracks, the buddy would only backtrack when the lead reference point gets too far away from the furthest wait point passed during last advancement. This, again, is hysteresis added to avoid behavioral flickering.

We also incorporated dynamic movement speed into the lead system. “Speed planes” are placed along the spline, based on the distance between the buddy and the player along the spline. There are three motion types NPCs can move in: walk, run, and sprint. Depending on which speed plane the player hits, the buddy picks an appropriate motion type to maintain distance away from the player. Designers can turn on and off speed planes as they see fit. Also, the buddy’s locomotion animation speed is slightly scaled up or down based on the player’s distance to minimize abrupt movement speed change when switching motion types.

In The Last of Us, the player is able to move past a buddy while both remain in cover. This is called cover share.

In The Last of Us, it makes sense for Joel to reach out to the cover wall over Ellie and Tess, who have smaller profile than Joel. But we thought that it wouldn’t look as good for Nate, Sam, Sully, and Elena, as they all have similar profiles. Plus, Uncharted 4 is much faster-paced, and having Nate reach out his arms while moving in cover would break the fluidity of the movement. So instead, we decided to simply make buddies hunker against the cover wall and have Nate steer slightly around them.

The logic we used is very simple. If the projected player position based on velocity lands within a rectangular boundary around the buddy’s cover post, the buddy aborts current in-cover behavior and quickly hunkers against the cover wall.

Medic sidekicks in multiplayer required a whole new behavior that is not present in single-player: reviving downed allies and mirroring the player’s cover behaviors.

Medics try to mimic the player’s cover behavior, and stay as close to the player as possible, so when the player is downed, they are close by to revive the player. If a nearby ally is downed, they would also revive the ally, given that the player is not already downed. If the player is equipped with the RevivePak mod for medics, they would try to throw RevivePaks at revive targets before running to the targets for revival (multiple active revivals reduce revival time); throwing RevivePaks reuses the grenade logic for trajectory clearance test and animation playback, except that grenades were swapped out with RevivePaks.

Crouch-moving in stealth grass is also something new in Uncharted 4. For it to work, we need to somehow mark the environment, so that the player gameplay logic knows whether the player is in stealth grass. Originally, we thought about making the background artists responsible of marking collision surfaces as stealth grass in Maya, but found out that necessary communication between artists and designers made iteration time too long. So we arrived at a different approach to mark down stealth grass regions. An extra stealth grass tag is added for designers in the editor, so they could mark the nav polys that they’d like the player to treat as stealth grass, with high precision. With this extra information, we can also rate stealth posts based on whether they are in stealth grass or not. This is useful for buddies moving with the player in stealth.

Since we don’t have listen mode in Uncharted 4 like The Last of Us, we needed to do something to make the player aware of imminent threats, so the player doesn’t feel overwhelmed by unknown enemy locations. Using the enemy perception data, we added the colored threat indicators that inform the player when an enemy is about to notice him/her as a distraction (white), to perceive a distraction (yellow), and to acquire full awareness (orange). We also made the threat indicator raise a buzzing background noise to build up tension and set off a loud stinger when an enemy becomes fully aware of the player, similar to The Last of Us.

This is the last major gameplay feature I took part in on before going gold. I don’t usually go to formal meetings at Naughty Dog, but for the last few months before gold, we had a at least one meeting per week driven by Bruce Straley or Neil Druckmann, focusing on the AI aspect of the game. Almost after every one of these meetings, there was something to be changed and iterated for the investigation system. We went through many iterations before arriving at what we shipped with the final game.

There are two things that create distractions and would cause enemies to investigate: player presence and dead bodies. When an enemy registers a distraction (distraction spotter), he would try to get a nearby ally to investigate with him as a pair. The closer one to the distraction becomes the investigator, and the other becomes the watcher. The distraction spotter can become an investigator or a watcher, and we set up different dialog sets for both scenarios (“There’s something over there. I’ll check it out.” versus “There’s something over there. You go check it out.”).

In order to make the start and end of investigation look more natural, we staggered the timing of enemy movement and the fading of threat indicators, so the investigation pair don’t perform the exact same action at the same time in a mechanical fashion.

If the distraction is a dead body, the investigator would be alerted of player presence and tell everyone else to start searching for the player, irreversibly leaving ambient/unaware state. The dead body discovered would also be highlighted, so the player gets a chance to know what gave him/her away.

Under certain difficulties, consecutive investigations would make enemies investigate more aggressively, having a better chance of spotting the player hidden in stealth grass. In crushing difficulty, enemies always investigate aggressively.

This is also among the last few things I helped out with for this project.

Dialog looks refers to the logic that makes characters react to conversations, such as looking at the other people and hand gestures. Previously in The Last of Us, people spent months annotating all in-game scripted dialogs with looks and gestures by hand. This was something we didn’t want to do again. We had some scripted dialogs that are already annotated by hand, but we needed a default system that handles dialogs that are not annotated. The animators are given parameters to adjust the head turn speed, max head turn angle, look duration, cool down time, etc.

One of the problems we had early on regarding the jeep driving section in the Madagascar city level, is that the player’s jeep can easily spin out and lose momentum after hitting a wall or an enemy vehicle, throwing the player far behind the convoy and failing the level.

My solution was to temporarily cap the angular velocity and change of linear velocity direction upon impact against walls and enemy vehicles. This easy solution turns out pretty effective, making it much harder for players to fail the level due to spin-outs.

Driveable vehicles are first introduced in Uncharted 4. Previously, only NPCs can drive vehicles, and those vehicles are constrained to spline rails. I helped handling vehicle deaths.

There are multiple ways to kill enemy vehicles: kill the driver, shoot the vehicle enough times, bump into an enemy bike with your jeep, and ram your jeep into an enemy jeep to cause a spin-out. Based on various causes of death, a death animation is picked to play for the dead vehicle and all its passengers. The animation blends into physics-controlled ragdolls, so the death animation smoothly transitions into physically simulated wreckage.

For bumped deaths of enemy bikes, we used the bike’s bounding box on the XZ plane and the contact position to determine which one of the four directional bump death animations to play.

As for jeep spin-outs, the jeep’s rotational deviation from desired driving direction is tested against a spin-out threshold.

When playing death animations, there’s a chance that the dead vehicle can penetrate walls. A sphere cast is used, from the vehicle’s ideal position along the rail if it weren’t dead, to where the vehicle’s body actually is. If a contact is generated from the sphere cast, the vehicle is shifted in the direction of the contact normal by a fraction of penetration amount, so the de-penetration happens gradually across multiple frames, avoiding positional pops.

We made a special type of vehicle death, called vehicle death hint. They are context-sensitive death animations that interact with environments. Animators and designers place these hints along the spline rail, and specify entry windows on the splines. If a vehicle is killed within an entry window, it starts playing the corresponding special death animation. This feature started off as a tool to implement the specific epic jeep kill in the 2015 E3 demo.

We wanted to eliminate geometry clipping the camera when the camera gets too close to environmental objects, mostly foliage. So we decided to fade out pixels in pixel shaders based on how close the pixels are to the camera. Using transparency was not an option, because transparency is not cheap, and there’s just too much foliage. Instead, we went with dithering, combining a pixel’s distance from the camera and a patterned Bayer matrix, some portion of the pixels are fully discarded, creating an illusion of transparency.

Our original Bayer matrix was an 8×8 matrix shown on this Wikipedia page. I thought it was too small and resulted in banding artifacts. I wanted to use a 16×16 Bayer matrix, but it was no where to be found on the internet. So I tried to reverse engineer the pattern of the 8×8 Bayer matrix and noticed a recursive pattern. I would have been able to just use pure inspection to write out a 16×16 matrix by hand, but I wanted to have more fun and wrote a tool that can generate Bayer matrices sized any powers of 2.

After switching to the 16×16 Bayer matrix, there was a noticeable improvement on banding artifacts.

This is a really minor contribution, but I’d still like to mention it. A couple weeks before the 2015 E3 demo, I pointed out that the tower explosion was seen and heard simultaneously and that didn’t make sense. Nate and Sully are very far away from the tower, they should have seen and explosion first and then heard it shortly after. The art team added a slight delay to the explosion sound into the final demo.

I didn’t switch to Traditional Chinese text and subtitles until two weeks before we were locking down for gold, and I found some translation errors. Most of the errors were literal translations from English to Traditional Chinese and just did’t work in the contexts. I did not think I would have time to play through the entire game myself and look out for translation errors simultaneously. So I asked multiple people from QA to play through different chapters of the game in Traditional Chinese, and I went over the recorded gameplay videos as they became available. This proved pretty efficient; I managed to log all the translation errors I found, and the localization team was able to correct them before the deadline.

These are pretty much the things I worked on for Uncharted 4 that are worth mentioning. I hope you enjoyed reading it.

]]>Here is the original English post.

本文之英文原文在此

註1：此文撰寫時間為Uncharted 4送廠壓片前

註2：為方便複製至PTT，本文排版採BBS格式，不習慣者請見諒

我開始參與Uncharted 4的製作，已經是快兩年前的事了

而現在，離發售日只剩下不到兩個月

這是我第一個以全職遊戲程式設計師身分參與開發的遊戲

(之前參與製作Planetary Annihilation時我仍只是個暑期實習生)

回頭一看才發現，自從十幾年前我夢想開發遊戲，真的走了很遠

我想要藉這個機會，把這一趟旅程跟大家分享，也為自己做個筆記

** = 當初我想要在電玩遊戲專賣店工作 = **

第一次接觸遊戲的時候是幼稚園，我爸買了一台元祖Game Boy給我

一開始我只有兩個遊戲：Super Mario Land和Tetris(俄羅斯方塊)

從這個時候開始，我就迷上電玩了

小學二年級的時候，我的兩位堂弟有了台超任

我常常跑過去找他們玩超任，但是只有兩個手把，所以我們必須輪流玩

經過一番拜託，我的父母也買了一台超任給我

我最喜歡的遊戲是Super Bomberman(超級轟炸超人)系列

甚至還回頭去蒐集Game Boy上所有的轟炸超人遊戲

小學四年級時，有位朋友把他的N64和Super Mario 64帶來我家玩

這是我第一次親手玩到3D遊戲，真的令我大開眼界

我們做了一筆”交易”，我比他稍微多買些遊戲

然後我們輪流擁有那台N64和遊戲，每幾個月交換一次

在這段期間，當有人問我未來想要做什麼

我會回答 “我想要在電玩遊戲專賣店工作，因為這樣就可以一整天都打電動”

這個想法，在我五年級的時候完全改變

當時的導師帶了一台PS1到學校，讓我們在放學等家長接送的時候可以玩

有天，導師在全班面前展現他的高超遊戲技巧，他說了:

“很會打電動的人很厲害，但你知道什麼人更厲害? 做遊戲的人更厲害!”

從這個時候起，我便決定我未來要製作遊戲

** = 我的程式設計史前時期 = **

當時，我完全不知道有什麼電玩遊戲開發的相關學習資源

我頂多就是用Macromedia Flash 3開發簡單的滑鼠互動動畫

這是我在學校的電腦課學到的

上國中的時候，我開始使用一款叫做TrueSpace的3D建模軟體

試著做一些簡單的人物模型，希望未來可以放到遊戲裡(最後當然沒成功)

我上高中後，加入了電子計算機研究社

希望可以藉此機會，學習遊戲開發的相關技術

上了第一堂社課，才發現我其實並不喜歡寫程式，比較喜歡美術

寫程式看起來好困難，而且又沒有美術那麼吸睛

所以，我與遊戲開發的程式領域脫節了一陣子

這段期間，我主要是在學習Photoshop和3ds Max

一位住在加拿大的朋友介紹了deviantART這個網站給我

我開始頻繁地產出畫作並上傳到deviantART上

這段期間，我也透過這個網站學會了許多口語式英文和網路用語

我注意到網站上有人上傳一些Flash遊戲

這重新點燃了我對使用Flash開發遊戲的興趣

我再次嘗試學習程式設計，一旦越過了一開始的學習陡坡，就沒那麼可怕了

同時，我開始使用Swift3D將3D模型輸出成Flash向量動畫格式，以開發遊戲

我完成度最高的作品是個兔子跳舞遊戲，叫做 “跳舞吧! R平方”

可惜的是，我並沒有完成它，而原始檔也遺失了

唯一剩下的就是當時上傳到deviantART的情人節桌布，包含四位主要角色

http://bit.ly/1RpBu8X

** = 我與Naughty Dog遊戲的第一次接觸 = **

有位朋友帶了從美國買的PS2來我家玩，也帶了Jak and Daxter這遊戲

台灣賣的PS2遊戲大部分是日本遊戲，這是我第一次看到美國的PS2遊戲

我在PS1時代只有稍微聽說過 “袋狼大進擊”

但不知道跟Jak and Daxter是同一個工作室製作的

過了不久，在高中二年級的時候，我禁不起同學午餐時間討論PS2的誘惑

也買了一台PS2

暑假期間，我們全家到美國加州去拜訪我父母的大學同學

我看到他們的小孩也有一台PS2，還有一堆我從來沒有看過的美國遊戲

出於好奇，我請他們帶我去當地的遊戲店逛逛，他們帶我去了一家GameStop

我看到架上有一款Jak X

封面上的 “綠頭髮男主角和一隻橘色像松鼠的跟班”

馬上就讓我想起當初看到的Jak and Daxter

我覺得這遊戲看起來很有趣，就買回去了

Jak X帶給我的電影般衝擊是前所未見的

此刻奠定了Naughty Dog在我心目中的地位

之後，我開始天馬行空胡思亂想，覺得要是我以後能在Naughty Dog工作就好了

我盯著Naughty Dog的官方網站

按下了那誘人的超連結: “想加入我們嗎?按這裡!”

然後跳出了一個問題: “你還是學生嗎?”

我選了 “是”，映入眼簾的是一條訊息:

“對不起，我們不收工讀生。但如果你畢業後想加入我們，上數學課就認真點!”

這是我人生的一大轉捩點，從此對數學課的態度完全改變

漸漸地，我開始覺得數學課其實很有趣、真的很有用，上課也更認真了

我努力學習了向量、矩陣、幾何、統計、排列組合與機率

在這裡有個有趣的小插曲:

我試著用ActionScript寫一個解二元一次聯立方程式的小程式

想要在數學作業上偷懶

結果，我沒有考慮到無解的狀況，讓程式處理了除以零的算式

於是得到NaN (not a number)的答案

當時我還以為電腦是在罵我嫩 (發音跟NaN相近)

高中的最後一個學期，國文老師出了一個作業

要我們寫一封給夢想中的公司(可虛構)的自我推薦信

我是班上唯一一個寫給外國公司的人，而那家公司，當然是Naughty Dog

當時還是有不少師長，會對從事遊戲開發皺眉

因為 “電玩遊戲會讓小孩子荒廢學業、帶壞小孩子”

不過，我的成績還算不錯，所以老師就沒有對我的作文多說什麼

接著，就要面對指考(大學聯考)了

**= 對Naughty Dog的遊戲上癮 = **

我的指考成績還算不錯，想要選的學校和科系都可以上

基於從事遊戲開發的決心，我告訴父母我決定要選擇資訊工程學系

不過我的爸爸給了我不同的建議，他說我應該要選電機工程學系

理由是: 他的本職是小兒科醫師，可是大學七年學的大都是其他科的知識

等到成為實習醫生之後，才開始鑽研小兒科

結果，現在他除了小兒科以外的病症，也可以處理各種的疑難雜症

結論就是，我不應該這麼早就把視野鎖定在我最有興趣的領域

應該放寬眼界，把相關領域的知識也學遍，更可以融會貫通

這個論點說服了我，於是我選了電機工程學系，開始學習電子硬體相關的知識

同時，我還有選修一些資訊工程的課，齊頭並進

有了低階硬體的知識，確實對我學習軟體工程和電腦架構大有助益

例如，學習了如何用邏輯閘建構記憶體，讓我了解記憶體的存取原理

學習邏輯閘等級的加法器和乘法器設計，讓我理解兩者架構和運算資源需求的不同

後來，我的妹妹到美國唸高中

我想起了當時玩Jak X的美好時光，就託她買Jak三部曲並寄回台灣

玩過了這三個遊戲，我見識到了一流的遊戲設計和敘事鋪陳

我對Naughty Dog更加尊敬，並且對他們的遊戲正式上癮

我再次去了Naughty Dog的網站

看到了剛發佈的PS3神祕專案預告，而這正是初代Uncharted

我並沒有特別喜歡射擊遊戲

但我告訴自己 “這可是Naughty Dog啊，這個遊戲一定很棒!”

於是當我到美國拜訪我妹的時候，就順手買了一片Uncharted

我知道PS3沒有鎖區，所以等回到台灣之後，才買了PS3

Uncharted還蠻好玩的，而且技術上非常驚人，德瑞克的褲子沾水還會濕呢!

但是，Uncharted並沒有帶給我當初玩Jak三部曲時的感動

覺得這又是個畫面漂亮、打打殺殺的射擊遊戲而已

我對Naughty Dog的熱情稍微降了點溫

兩年後(大三)，我看到了Uncharted 2在E3展上的實機demo

我簡直不敢相信，德瑞克竟從正在崩塌的大樓中滑下並跳出，而且玩家還可以操控!

遊戲一發售，我馬上買了一片，並且不眠不休地將它玩完

真是個不可思議的遊戲:

壯麗的視覺表現、好玩的遊戲機制、刺激的故事演出、有趣又惹人愛的角色

我對Naughty Dog重拾了興趣

之後，我從大學畢業了

** = 出國 & 加入狗窩 = **

在服一年兵役前，我申請了一間叫作DigiPen的遊戲學校

我先前已寫過我在DigiPen的故事了，故容我在此快轉一下

(詳細故事請見 http://wp.me/p4mzke-Rb)

在DigiPen的第二個學期，Uncharted 3上市了

雖然故事上有些瑕疵，我還是玩得非常盡興

我對Naughty Dog的好感又增加了一些

不久之後，我看到了The Last of Us的首發預告

嚴肅的末世生存題材跟Uncharted的詼諧氣氛大相逕庭，還真是出乎我意料之外

我很讚賞Naughty Dog願意嘗試不同的遊戲風格

在2012年的Pax Prime遊戲展，我到了Naughty Dog的攤位

現場展示的是The Last of Us的實機遊玩

展示間的內部佈置，仿照喬爾和艾莉與獵人們戰鬥的旅館裝潢

這場展示令我印象深刻

喬爾與艾莉面對擁有人數優勢的敵人，在彈藥稀少的狀況下為生存而戰

讓玩家面對如此嚴苛的情境與壓力，是Naughty Dog遊戲中的首例

展示結束後，我拿到了一件艾莉T-shirt

也拿到了Neil Druckmann和Bruce Straley的簽名海報

The Last of Us發售當日，我立刻買了一片

能夠與遊戲角色產生情感上的連結，實在是一種稀有又美妙的經驗

艾莉給人的感覺，真的是活生生的夥伴，而不是某個用AI操控的跟班

喬爾與艾莉之間豐富的互動，給遊戲的故事注入了生命

他們一起戰鬥、互相關切、分享笑話、以及共同經歷情感轉折

如此扣人心弦的遊戲，實是非常罕見

再一次，我對Naughty Dog致上最高的欽佩與敬意

在DigPen學習的時候，我一直有個微薄的希望:

希望有朝一日可以加入Naughty Dog開發遊戲

我成功取得Uber Entertainment的實習機會，也參加了許多就業研討會

這時，我有著可以畢業即就業的自信

畢業前，我滿腦子都在規劃未來的出路:

先在學校附近(西雅圖地區)找個工作

希望可以是Wargaming, ArenaNet, 或Sucker Punch

工作了幾年之後，再試著去申請Naughty Dog

運氣好的話，搞不好真的可以加入Naughty Dog呢

誰知道命運的安排，將我的完美計畫稍微加速了一些

最終，我從DigiPen畢業，直接錄取Naughty Dog

(詳細故事請見 http://wp.me/p4mzke-TQ)

現在，我在Naughty Dog開發Uncharted 4

身為一個Naughty Dog粉絲

能夠參與開發奈森‧德瑞克的冒險終章，我感到非常榮幸

這真可謂為一趟祕境之旅呀!

Uncharted 4發售之後

我就會開始撰文介紹我自從加入Naughty Dog後，都做了些什麼

敬請期待

Here is the Chinese translation of this post.

本文之中文翻譯在此

*Note: This post was written before Uncharted 4 went gold, so it might contain tones or implications that Uncharted 4 hasn’t gone gold yet. Sorry for the confusion.*

I started working on Uncharted 4: A Thief’s End almost two years ago, and here we are, less than two months before release. This would be my first shipped title as a full-time game programmer (I shipped Planetary Annihilation during a summer internship). Looking back now, I realized that I’ve really come a long way since I first wanted to make games more than a decade ago. I would like to take this opportunity to write down this journey to share with you and as a note for myself.

My first contact with video games was when my dad got me an original Game Boy as a present while I was in kindergarten. My only two games were Super Mario Land and Tetris. That’s when I got hooked on video games. Later, I saw my cousins getting a Super Nintendo (SNES) when I was in 2nd grade. I went over and played with them pretty frequently, but we had to take turns as the SNES only has two controllers. After bugging my parents, I finally got my own SNES to play with. My favorite games were the Super Bomberman series. I even went and got all of the Bomberman games on the Game Boy.

In 4th grade, one of my friends brought over his Nintendo 64 (N64) and Super Mario 64; that was my first time playing a 3D game and it blew my mind. My friend and I made a deal where I would buy games slightly more frequently than he would, and we took turns owning the N64 and the games every couple months.

Around this time, when asked what I wanted to do in the future, I would say that I wanted to work at a game store so that “I could play video games all-day during work.” This all changed when, in 5th grade, my homeroom teacher brought a PlayStation (PS1) to school to let us play while we waited for our parents to pick us up after school. One day, as we watched in awe as he showed off how good he was at playing games, he said:

“You know what’s more impressive than being good at playing games? Making games.”

That, was when I decided that I wanted to make video games.

Back then, I knew of almost no resources on how to make video games. The best thing I was able to do was make very basic animations that reacted to mouse clicks in Macromedia Flash 3, which I learned in computer classes. In middle school, I picked up a 3D modeling software called TrueSpace and started experimenting with building simple character models, which I hoped would be someday used in a game (of course this didn’t happen).

When I started high school, I joined the Computer Research Club, in hopes of finally learning the technology behind making video games. On the first club lecture, I discovered that I did not like programming and preferred making game art; programming seemed daunting to me and not as visually attractive as art back then. So, I was detached from the programming aspect of game development for a while and focused on learning Photoshop and 3ds Max.

I was introduced to deviantART by a friend of mine in Canada. I started making and submitting art work to deviantART (both 2D & 3D) quite frequently; also, I picked up a lot of spoken English and internet slangs along the way. After noticing some Flash games uploaded to deviantART, my interest in making games with Flash re-kindled; I gave another try at programming, and once I got through the steep initial learning curve, it didn’t seem as daunting as it had before. I started using Swift3D to render 3D models into Flash vector format to put in games. My most complete project was a bunny dancing game called “R-Squared de Dance!” which, unfortunately, was never fully finished and was lost. I did submit to deviantART a Valentine’s Day wallpaper with all 4 characters, though.

One of my friends visited me and brought his PlayStation 2 (PS2) from the US, along with a copy of Jak and Daxter. The PS2 games sold in Taiwan were mostly Japanese titles; this was my first time seeing a PS2 title from the US. I only heard about Crash Bandicoot back in the PS1 days and didn’t know that it was developed by the same studio that made Jak and Daxter. Shortly after, during my sophomore year in high school, I got a PS2 because I couldn’t resist the temptation after hearing all of my friends talking about their PS2 games during lunch breaks.

During a summer break, my family went to visit some friends in California. I saw that their kids also had a PS2, with a whole collection of US games I’d never seen before. Intrigued, I asked them to bring me to a local game store. They brought me to a GameStop, and on the shelves I spotted a copy of Jak X: Combat Racing. That “weird-looking green-haired guy with an orange giant squirrel-like sidekick” instantly reminded me of my first sight of the original Jak and Daxter. I thought it looked interesting and decided to give it a try, so I picked up the game.

Jak X brought me a cinematic gaming sensation I had never experienced before. That was when Naughty Dog made a mark on me. I started having crazy thoughts about how amazing it would be if I could work at Naughty Dog. So there I was, staring at Naughty Dog’s website, clicking the tempting hyperlink that read “Want to join us? Click here!” A question popped up: “Are you still a student?” After clicking “yes”, I landed on a page that basically told me that Naughty Dog did not have opening for interns and “If you want to join us after graduation, you should pay more attention in math classes.” This, was the pivotal moment that made me adjust my attitudes towards math classes. Math became my favorite subject in high school, and I put a lot of effort in mastering vectors, matrices, geometry, statistics, combinatorics, and probability.

Fun fact: I tried programming a solver for linear systems of two variables in ActionScript, so that I could use it to do my math homework. I did not handle divions-by-zero, and when the computer told me the answers were NaN’s, I thought it was mocking me for being a noob, which has similar pronunciation in Chinese to NaN.

In my last high school semester, our Chinese teacher asked us to write a mock-up letter addressed to our dream company, be it real or fictional, and describe “why they should hire you.” I was the only person writing a letter to a foreign company which, of course, was Naughty Dog. Back then in Taiwan, working for a game company was generally frowned upon by parents and teachers, as video games were “what made kids bad.” However, I did have good grades, so my teacher did not give me a hard time for wanting to work at a game company.

And there came the nation-wide joint college entrance exam.

I did pretty well in the exam, so I basically got to choose whichever college and whatever major I wanted. Determined to make games and becoming interested in programming again, I told my parents that I wanted to major in Computer Science. My dad, however, advised against that and suggested that I major in Electrical Engineering. He said that, as a pediatrician, he spent seven years in medical school learning everything besides pediatrics, and focused on pediatrics after becoming a medical intern; his argument was that I should not hop directly into focusing on what I was most interested in with tunnel vision, and should learn other related disciplines first, so that I could have a broader view.

My dad was pretty convincing, so I agreed; I chose Electrical Engineering and focused on hardware stuff, including electronics and integrated circuit design. Meanwhile, I still took some classes from the Computer Science department. Having a low-level understanding of hardware did make it easier for me to learn programming and computer architecture. For instance, I learned how to build computer memory from logic gates, and that helped me understand how memory access works. I also got to learn the gate-level design of full-adders and multipliers, hence their differences and why one is more computationally expensive than the other.

After my parents sent my sister to attend high school in the US, I remembered the fun I had with Jak X, so I asked my sister to send me copies of the Jak trilogy. As I went through the three games, witnessing the incredible work put into the game design and storytelling, I admired Naughty Dog even more and officially became addicted to their games. I went to Naughty Dog’s website once more, and saw the reveal trailer of their secret PlayStation 3 (PS3) project, later known to be Uncharted: Drake’s Fortune. I wasn’t very into shooters, “but it’s Naughty Dog, it’s got to be good.” So I picked up a copy of Uncharted when I visited my sister in the US during a summer break; knowing that the PS3 was not region-locked, I waited until I returned to Taiwan to get a PS3.

I played Uncharted. It was fun and technically impressive; I mean, look at the WATER on Drake’s pants! However, it didn’t give me the same charm as the Jak trilogy. To me, it felt like just another visually impressive action shooter with endless waves of enemies for target practice. So Naughty Dog dropped off my radar for a while.

Two years later (junior year), I saw the E3 live demo of Uncharted 2: Among Thieves. It completely blew me away. Did Drake just slide down and jump out of a COLLAPSING BUILDING, while IN-GAME? That sealed the deal. I got the game on release and powered through it; it was such an incredible game: stunning visuals, fun gameplay, awesome storytelling, and lovable characters. This was when I re-gained interest in Naughty Dog.

Then, I graduated from college.

Before I started my one-year mandatory military service, I applied for the undergrad program at a college focused on game development, called DigiPen Institute of Technology. I’ve already written about my story at DigiPen, so I’ll fast-forward a little bit. Uncharted 3: Drake’s Deception came out during my second semester at DigiPen. In spite of a few flaws in storytelling, I still thought the game was fantastic, just when I thought I couldn’t like Naughty Dog more.

Soon after, Naughty Dog released the reveal trailer for The Last of Us. This game completely caught me by surprise; a serious post-apocalyptic survival game is quite different from Uncharted’s lighthearted adventures. I thought it was a nice change of mood and appreciated that Naughty Dog was willing to try something different. At PAX Prime 2012, I went to Naughty Dog’s booth that showed a live demo of The Last of Us. The interior of the demo room was set up to look like the rundown hotel where Joel and Ellie fought the hunters. The demo itself was an impressive demonstration of hardcore gameplay, where Joel and Ellie fought for survival while out-numbered and out-gunned. Such harsh circumstances and pressure imposed on the player was a first among Naughty Dog games. After the demo, I got an Ellie T-shirt and lined up to get an autographed poster by Neil Druckmann and Bruce Straley.

I got a copy of the The Last of Us right upon release. Being able to emotionally connect to game characters is such a rare and beautiful experience. Ellie felt like a real companion, not just some emotionless sidekick controlled by AI. The rich interactions between Joel and Ellie made the story feel so alive; they fought together, they cared for each other, they shared jokes, and they experienced the same emotions together. Not many games had reached such level of compelling storytelling. I gave Naughty Dog my deepest admiration and respect, again.

When studying at DigiPen, I always had the slightest hope that some day I might end up working at Naughty Dog. After successfully landing an internship at Uber Entertainment and attending various career workshops at DigiPen, I was confident that I could get a job straight out of college. I had all these plans in my head: getting a job around the Seattle area where DigiPen is (perhaps Wargaming, ArenaNet, or Sucker Punch), working in the industry for a few years, applying for job at Naughty Dog, and then finally working there if I was lucky.

Little did I know that destiny would speed up this plan a little bit for me, where I came straight to Naughty Dog after graduating from DigiPen. You can read this story in detail here.

So here I am, working at my favorite studio, making Uncharted 4. As a huge Naughty Dog fan, I feel so honored to be working on the closing chapter of Nathan Drake’s adventure.

This has really been an uncharted journey.

After Uncharted 4 is released, I will write about what I have been working on since I started at Naughty Dog. Stay tuned.

]]>Here is the original English post.

本文之英文原文在此

註：為方便複製至PTT，本文排版採BBS格式，不習慣者請見諒

畢業滿一年了，最近看到跟我同屆的DigiPen同學陸陸續續開始工作 (我去年提早畢業)

突然讓我注意到，今年還沒延續之前每年寫一篇DigiPen推坑文的優良(?)傳統

那我就廢話不多說，以下開始本文囉

** = 找到&選擇DigiPen = **

我攻完電機學士學位之後，自然而然就跟著同學們一起準備申請美國的資工研究所

當時也沒有想太多，就只是跟著同學們的動作有樣學樣而已

著手蒐集研究所資料過了幾天後，一個埋藏在心裡深處的想法才慢慢浮現

仔細回想，才開始記得當初選擇電機這條路的原因，是為了要製作遊戲

大學四年胡亂度過了，竟然忘了最初的夢想

想當年，在高中的時候玩了PS2上的Jak & Daxter三部曲

還因此把Naughty Dog遊戲工作室當作我的第一志願呢

想到這點，突然覺得自己實在是太健忘了!

製作遊戲是我從小的夢想，竟然差點就跑去跟別人一起爬學術象牙塔去了

於是，我毅然停止搜尋美國的資工研究所

直接去Google搜尋 “Game School”

得到了多筆結果，DigiPen也包含在內

我開始研究各個學校的學程與課表

隨著我的研究，我越來越覺得想要學的東西實在是太多，兩年的碩士學程絕對不夠用

我最後看上了DigiPen的四年大學部學程

除了時間足夠以外，我也看中DigiPen為了學習遊戲開發提供的專屬環境

而且大學部一個年級中的人較多，比較容易找到適合的人，組成遊戲製作團隊

還好我的父母願意聽我解釋為什麼我想要攻讀第二個學士學位

再三確認過我的決心之後，他們同意了

“如果這真的是你想要的學習路徑，那我們也會全力支持你”

我真是感激不盡 T_T

** = DigiPen不是一所簡單的學校 = **

我永遠忘不了DigiPen的校長Claude Comair先生在開學典禮上說的一句話

“看看你左邊的人，看看你右邊的人

等到這屆學生畢業的時候，你會至少看不到其中一個人…

…而且你不一定是畢業的那個人”

據說他每年的開學典禮都會講這句話

而我和朋友們發現，此話並不假

四分之一的新鮮人會在第一學期結束前放棄並退學

只有大約一半的學生可以撐到畢業

(也有一些沒有畢業的人，是因為拿到工作offer而放棄學校)

上課、寫作業、考試，這些標準的大學要素是一定有的

然而除此之外，學生們必須利用課外時間，自行組成遊戲開發團隊

一年級的兩個學期必須各開發一個遊戲專案

之後則是每年開發一個遊戲

最後一年的遊戲學分，可以選擇業界實習來折抵

根據我的經驗

從學校學到的知識，最多只佔業界所需基本能力的20%

那剩下的80%要從哪來?

跟同學組成學習小組、自己進行研究與個人專案、

參加社團教學與研討會、找同學跟教授進行專題研究…等

我對於遊戲物理與遊戲引擎架構的重要知識

主要來自於參與學生社團的研討會，而不是從學校學來的

** = DigiPen的各種學程 = **

在我於DigiPen開始上課的時候，總共有五種不同學士學程

後來又陸陸續續新增了一些，包含兩個關於遊戲音樂與音效的學程

Bachelor of Science in Real-Time Simulation (RTIS)

– 基本上是一般資工學程，再加上遊戲相關技術課程

Bachelor of Science in Game Design (BSGD)

– 遊戲設計技巧，較專注在技術層面

Bachelor of Arts in Game Design (BAGD)

– 遊戲設計技巧，較專注在美術層面

Bachelor of Fine Arts (BFA)

– 遊戲美術

Bachelor of Science in Computer Engineering

– 電機工程，專注在遊戲硬體研究與開發

我選擇的是RTIS學程，所以對RTIS瞭解比較深入

** = 學習環境 = **

DigiPen的整個校區就是一棟三層樓的建築

一樓是餐廳、教室、一些較大的演講堂

還有一間雖然不大，卻有很多遊戲開發相關藏書的圖書室

學生也可以在圖書室借到各種遊戲軟體和硬體(當然是研究用)

二樓和三樓則是更多教室，還有整個學校最重要的空間：開放研究空間

開放研究空間是一個寬敞的區域，擺滿長桌和上百台電腦

學生可以使用這些電腦寫作業、做研究、還有開發遊戲專案

遊戲團隊通常會自己劃出團隊空間，以用來長期進行遊戲開發

我在DigiPen的前兩年，幾乎每一天(含周末)，都是早上9點到校，晚上11點左右離開

不是在上課，就是在我的團隊空間裡寫作業、做研究、和開發遊戲

** = 遊戲專案 = **

每個學期有特殊的”遊戲學分”，必須以開發遊戲專案來取得

每一個遊戲專案的開發循環，學校都會訂下里程碑(milesones)

共有 Engine Proof, Prototype, First Playable,

Alpha, Beta, 和 Gold

當一個milesone到期時

一群遊戲教授就會連續花幾天，逐一審視各團隊的成果發表簡報

仿照業界的專業遊戲技術與設計需求(TCRs & DCRs)評比

里程碑簡報是非常紮實的訓練

想我當初第一次上台的時候，緊張到全身發抖和冒汗，非常狼狽

等到我畢業前的最後一次簡報，不是我自誇，我的台風已經變得相當專業

我們學到了如何為遊戲專案訂下實際可行的計畫，而不是天馬行空地不斷擴大企劃

同時，我們也學會在milesone到期前，忍痛割去無法如期完成的部分計畫

為了讓學生提早體驗到業界的人力流轉之恆常性

學生可以自己隨時跳槽到別的開發團隊

開發團隊也可以隨時雇用新成員和開除舊成員

學生也可以自己成立一小組

當遊戲教授認定一個學生參與遊戲專案的時間不足，就會把該學生當掉

一個遊戲團隊的最終作品過度不完整，也會被全數當掉

通常一個學生團隊的成員組成，主要是RTIS的程式設計師、

一兩個BAGD或BAGD的遊戲設計師、幾個BFA美術、和一個製作人

各團隊的製作人，每週都要跟教授開會

學習製作人的技能以及討論遊戲專案進度

學生團隊可以與一位遊戲教授約”team-on-one”會談

這個會談為時4小時，大家坐下來吃吃喝喝、悠閒地討論遊戲專案

目的是要讓學生們從旁觀者的角度來回顧專案進度，以及審視團隊溝通問題

每個會談結束之後，我總是覺得我的思路被重新開機，又回復動力了

** = 社團 = **

有別於一般大學，DigiPen的社團主要都是與玩遊戲或者開發遊戲相關

例如：桌遊社、射擊遊戲社、格鬥遊戲社、

遊戲電腦圖學社、遊戲物理社、遊戲引擎架構研究社…等

其中有一個社團比較特別：遊戲測試社

一周有兩天，遊戲測試社會在開放研究空間的電腦上，安裝大家的作品

讓學生們來測試各個團隊的遊戲，並且給予寶貴的回饋

測試滿三個遊戲，可以獲得學校餐廳的餐點兌換券

** = 業界結合 = **

DigiPen與業界的結合非常緊密

大多數的教師都是在業界打滾多年的老手

還有部分的教師仍在業界工作，來學校兼差教學

學校的春假與秋假

每年都刻意跟 遊戲開發者大會(GDC) 和 電子娛樂大展(E3) 重疊

讓學生們和教師們可以自由前往參加

參加GDC是非常重要的大事

學生們可以藉此與業界人士建立聯繫，還可以找工作機會

如果我沒有去參加2013年的GDC

就不會撞到Naughty Dog的人力主管，我現在就不可能在Naughty Dog工作了

(詳細故事請見 http://wp.me/p4mzke-qa)

我先前有寫一些參加GDC的心得與撇步

有興趣者請見 http://wp.me/p4mzke-kP 和 http://wp.me/p4mzke-KM

** = 就業優先 = **

將學生送入遊戲業界是DigiPen的首要宗旨，比訓練業界所需的能力還優先

學生的就業機會比什麼都重要，這也是教職員們的共識

我去Naughty Dog公司現場面試當天，正好跟一個期中考撞期

教授覺得面試比期中考重要多了，所以就讓我改天再考，分數也不打折

我當天也錯過了一些課，但是教授們都不以為意

** = 就業服務中心 = **

DigiPen的眾多資源中，我覺得最重要的非就業服務中心莫屬

學生可以與就業服務中心約時間

會有專業人員協助準備找工作所需的素材

例如一起設計履歷表、個人網站和名片

我前後總共約談了至少20次，才把我的履歷表、個人網站和名片搞定

當我與Naughty Dog進行緊急電話面試的時候

就業服務中心也馬上提供一間空的會議室讓我可以順利進行

之後，他們還協助我撰寫一封得體的微軟offer拒絕信

幾乎每一個禮拜，就業服務中心都會舉辦”company day”

邀請業界人士，來對學生介紹自己的遊戲公司，和說明徵人條件

甚至有公司在活動結束之後，就直接在學校開始跟學生面試

就業服務中心隨時會舉辦不同的研討會

有時候會針對不同時機設計

例如GDC的前幾週，考慮到DigiPen學生大多很內向

有一年，就業服務中心邀請學校附近的業界人士

來和學生們進行一場”模擬社交活動”

讓學生練習主動開口，與陌生的業界人士攀談和自我介紹

有時候，也會舉辦找工作所需素材的研討會

教學生如何設計履歷表、個人網站、名片

我從中吸收到了很多寶貴的經驗

例如怎麼針對不同公司調整履歷表，還有面試的時候要注意什麼

我最近聽說學校加開了一些”專業溝通”課程

內容包含履歷表製作、個人網站設計、社交常識、會議禮儀…等

非常務實的課

https://www.digipen.edu/coursecatalog/?c=SG#COM150

此外，就業服務中心也負責一年一度的就業博覽會

跟一般學校不同的是，學校不是讓各公司擺攤，讓學生跑攤

而是讓每個學生設立自己的攤位，展示自己的作品，讓公司的人跑攤

一場就業博覽會下來，拿到多個offer也不是什麼稀有的事

過去四年的RTIS學生畢業前就拿到offer的比例介於84%-90%之間

** = 結尾 = **

以上，我目前能夠想到的就這些了

我就附上最近剛畢業並開始工作的同屆朋友們的一些連結

讓有興趣的人可以follow他們，以此作結吧 (當然，已徵求他們同意)

Justin Cook

– Software Engineer at Respawn Entertainment

– Website: http://justinmrcook.net

– Twitter: @jmrcook

Joe Lubertazzi

– Software Engineer at Respawn Entertainment

– Website: http://joelubertazzi.com

– Twitter: @joelubertazzi

Davis Standley

– Game Designer at Respawn Entertainment

– Twitter: @Absyrdist

Justin Maio

– Game Programmer at Monolith

– Website: http://www.justinmaioai.com

Garrett Woodford

– Software Engineer on Xbox Team

– Website: http://www.garrettwoodford.net

– Twitter: @MCGWoody

Eric Lynum

– Associate UI Engineer at Bungie

– Website: http://ericlynum.weebly.com

Danny Frisbie

– Production Engineer at Bungie

– Twitter: @Danny_Frisbie

Samir Patel

– Producer at Bungie

– Twitter: @Arukemos

最後補上我的

Ming-Lun “Allen” Chou

– Game Programmer at Naughty Dog

– Website: http://AllenChou.net

– Twitter: @TheAllenChou

有沒有注意到我們的網站網址全部都是自己的名字?

這也是就業服務中心教的喔

Here is the Chinese translation of this post.

本文之中文翻譯在此

Disclaimer: This post is all about my personal experience with DigiPen and is in no way intended to represent anyone else’s experience or opinions.

I went to DigiPen Institute of Technology to learn how to make games in 2011, and graduated last year (2014). I graduated one year earlier than my fellow classmates in the same year, because I transferred in some credits I had already earned at my previous college in Taiwan.

I have written one post about my life at DigiPen every year on a game design forum in Taiwan. Also, many of my DigiPen friends just graduated and have started their jobs in the game industry. So I thought, why not write a dedicated post about my experience at DigiPen in English on my blog?

When I was almost done with my bachelor’s degree in Electrical Engineering at my first college in Taiwan, I blindly followed what most of my other peers did: looking for a master’s program in the US to advance further in academia. As I was combing through the overwhelming amount of resources on the internet over a few days, an idea deep in my mind struck me: I chose a program in Electrical Engineering because it had always been my dream to make games, and Electrical Engineering was the closest I could get in Taiwan (next to Computer Science). So why on earth was I blindly searching for a path confined within academia, just because everyone else was doing the same thing? After four years of college, I numbed my senses and got lost a little, forgetting my original dream. Hadn’t I played the Jak & Daxter trilogy and made Naughty Dog my dream company in high school? Stupid. Stupid. Stupid!

So I threw away all my research on master’s programs, and simply started Googling “game school”. Several results turned up, and DigiPen was among them. I did some research and comparison on different curriculums and programs. As I learned about the vast number of various game-related courses there were, I became more and more convinced that a 2-year master’s program would not be long enough for what I wanted to learn. I ultimately chose DigiPen, which provides several 4-year undergrad programs, a learning environment exclusively for making games, and a large number of students in each year, which is a big enough pool to look for people to form a game team.

This wasn’t an easy decision to share with my parents. One stereotype about Chinese parents is unfortunately true: many Chinese parents expect successful academic progression from their kids, so they encourage – sometimes even force – kids to pursue higher degrees in academia. As far as I know, going for a second bachelor’s degree after already having earned one was unheard of in my circle. Fortunately for me, my parents are very reasonable people. After confirming with me for probably the fifth time that I was determined to do this, they finally said: “If going to this game school is really what you want, then you have our full support.” And I am forever grateful for their generous support.

I will never forget the opening speech given by DigiPen’s president, Mr. Claude Comair, at the orientation.

“Look to your left. Look to your right. You won’t be seeing at least one of the people you just saw when you graduate…or not.”

This, as I learned later, is a very true statement, and he says it every year! Learning to make games at DigiPen is much more demanding than many people think. A quarter of freshmen can’t finish the first semester every year, and only about half of the students graduate on time; it’s worth mentioning, though, that some students choose to drop out because they have accepted job offers before finishing school.

Students are expected to attend classes and finish assignments just like regular college students do. However, on top of that, students need to use their own free time to work on game projects with a team. There are two game projects in the freshman year (one per semester), and one game project per year after that. Students can opt to intern at game companies instead of participating in student game projects in the final year.

Based on my experience, the things you learn from school, only account for 20% of the basic knowledge you need in the industry. What about the other 80%? You learn by forming study groups, conducting personal research and projects, attending club lectures, going to workshops, and last but not least, meeting with peers and professors. I learned about game physics and game engine architecture mostly through club lectures and research with peers.

When I started at DigiPen, there were 5 major undergrad programs, listed below. DigiPen has since added several new programs, including two sound & music programs for games.

**Bachelor of Science in Real-Time Interactive Simulation (RTIS)**

This is basically a standard Computer Science program, plus extra courses focusing on game technology. The name of the program was changed during my sophomore year to Bachelor of Science in Computer Science in Real-Time Interactive Simulation, shortened BSCSRTIS, which is still quite a mouthful.**Bachelor of Science in Game Design (BSGD)**

Game design techniques, focusing more on the technical side of game design, e.g. scripting, gameplay programming.**Bachelor of Art in Game Design (BAGD)**

Similar to BSGD, but focusing more on the art side of game design, e.g. level design.**Bachelor of Fine Arts (BFA)**

As the name suggests, game arts.**Bachelor of Science in Computer Engineering (BSCE)**

Electrical engineering. Hardware stuff.

I was an RTIS student, so I have a better understanding of the RTIS program.

DigiPen is a 3-story building. On the first floor, there’s a cafeteria, some classrooms, including several bigger lecture halls, and a library (although not very large) full of books about making games (programming, art, game design, game history, you name it). You can also borrow games and various gaming hardwares from the library (for research purposes of course). On the second and third floors, there are more classrooms and the most important space of the school: the open lab.

The open lab consists of a big open space with tables and hundreds of computers. Students can use these computers to work on their assignments and game projects. Most game teams would stake out team spaces and use them throughout a game project cycle. In my first two years at DigiPen, I went to school at 9 in the morning and left around 11 at night almost every day. When I wasn’t in a class, I would be sitting in my team space, working on assignments, game projects, or conducting research. Good times.

Game projects account for special “game credits”. Throughout each project cycle, students have real milestones (Engine Proof, Prototype, First Playable, Alpha, Beta, and Gold), just like the industry. Upon each milestone, DigiPen’s game professors gather and sit through milestone presentations by every single team, usually non-stop throughout a couple days. Presentations are scored, and projects are also rated based on completion of Technical Certification Requirements (TCRs) and Design Certification Requirements (DCRs), all based on common industry standards.

These are very solid practices for presentation skills. During my first milestone presentation, I was so nervous that I sweated and trembled ridiculously. During my last presentation, not to brag, I was as calm as a pro.

We also learned to scope our games, as well as making the hard decision of cutting features before milestones.

In order to let students get a better taste of the industry, students are allowed to jump from one team to another; on the other hand, teams can hire or fire students. Students also have the option to go solo. If the game professors decide that a student has spent too much time without a team or a solo project, they can fail the student for game credits. A game team can also fail game credits if their game ends up incomplete.

A typical student game team consists of programmers from the RTIS program, a couple game designers from the BSGD or BAGD programs, some artists from the BFA program, and a producer. Producers have weekly meetings with game professors to learn production skills and discuss progress on the game projects.

Game teams can schedule a “team-on-one” with one of the game professors. A team-on-one is a 4-hour session with a professor, where everyone sits down, eats snacks, and talks about the game project casually. This is sort of like a reality check for the game project and a good chance to fix communication problems within the team, utilizing various team exercises. After every session, I always felt like my mind had been refreshed and my motivation rebooted.

Unlike ordinary colleges, most of the clubs at DigiPen are either about playing games or making games: Board Game Club, Shooting Game Club, Fighting Game Club, Game Graphics Club, Game Physics Club, Game Engine Architecture Club, etc.

Among them is a special club called the Playtesting Club. They hold playtesting sessions twice a week in the afternoon, setting up games on the computers in the open lab. Game teams can participate by putting up their games and let other students play. Playtesting sessions are valuable time spent in getting precious feedback on your game from fellow classmates. By the way, you can get a voucher for a free entree from the cafeteria if you playtest three games. Why wouldn’t you participate?

DigiPen has a very tight relationship with the game industry. Many of the faculty are industry veterans; some are still in the industry and teaching at DigiPen part-time.

Spring breaks and fall breaks are always aligned with the Game Developer Conference (GDC) and the Electronic Entertainment Expo (E3), so students and faculty are free to attend these important industry events.

I cannot stress enough the importance of attending GDC. You can make professional connections there, and it is a great place for job hunting. My current job at Naughty Dog would not have been possible had I not run into Naughty Dog’s recruiter at GDC in 2013. I also wrote down some GDC social tips; if you’re interested, you can check them out here and here.

If there’s one thing at DigiPen that is more important than preparing students for the industry, it is putting them into the industry. This is a general consensus among faculty. A student’s opportunity to break into the industry takes top priority.

For instance, my on-site interview with Naughty Dog coincided with a midterm. My professor thought the interview was much more important than her midterm, so she let me go to the interview and take the midterm another day without penalty. I also missed some other classes that day, and all professors were totally fine with it.

In my opinion, the Career Services Center is one of the best resources DigiPen provides.

You can schedule a meeting with a dedicated professional at the center. During the meeting, you can discuss how to write your resume, design your website and business cards, practice interviews, and so much more. I went to over 20 meetings before I finalized my resume, personal website, and business cards.

When I had my phone interviews with Naughty Dog, they kindly let me borrow a meeting room. They also helped me draft a very professional-looking turn-down letter to a Microsoft offer I received.

Almost every week, the Career Services Center would invite a game company over to the school’s biggest lecture hall for a “company day”. They would talk about the company and what they look for in job applicants. Sometimes, companies even hold interviews right on-campus!

The school holds various workshops, some designed for current events. For instance, most DigiPen students are quite shy; in one of my years at DigiPen, a few weeks before GDC, where people get socialized and make connections with people from the industry, they invited some people from the industry and held a miniature mixer to let students practice having conversations with professional game developers. Every now and then, they also hold workshops focusing on self-presentation, helping students understand how to appear more professional with their social skills, resumes, websites, business cards. I really learned a lot of great tips from these workshops, including how to tailor resumes to specific companies, and what to look out during interviews.

I recently learned that the school has started officially offering classes dedicated to professional communication taught by Sonia Michaels, including everything from resumes to business cards to professional networking and, of course, conference behavior.

The Career Services Center is also responsible for DigiPen’s annual career fair, which is famous for being quite different from regular colleges. Instead of having students walking around company booths, students set up booths and recruiters walk around to hunt for prospective hires. It is not uncommon for a student to end up with multiple job offers after the career fair.

The placement rate of the RTIS program in the past four years ranges from 84% to 90%, i.e. at least 8 out of 10 RTIS students graduated with a job offer already in hand in the past four years.

These are the things I have to say about DigiPen off the top of my head.

I’ll end with a list of my friends from DigiPen who recently graduated and got jobs, in case you would like to follow them.

- Justin Cook (Website / Twitter)

– Software Engineer at Respawn Entertainment - Joe Lubertazzi (Website / Twitter)

– Software Engineer at Respawn Entertainment - Davis Standley (Twitter)

– Game Designer at Respawn Entertainment - Justin Maio (Website)

– Game Programmer at Monolith - John Hughes

– Feel Engineer at thatgamecompany - Garrett Woodford (Website / Twitter)

– Software Engineer on Xbox Team - Eric Lynum (Website)

– Associate UI Engineer at Bungie - Danny Frisbie (Twitter)

– Production Engineer at Bungie - Samir Patel (Twitter)

– Producer at Bungie

Source files are on GitHub

Previously, I talked about numeric springing and provided some examples.

I have been saving up miscellaneous topics I would like to discuss about numeric springing, and now I have enough to write another post. Here are the topics:

- Using The Semi-Implicit Euler Method
- Numeric Springing vs. Tweening
- Half-Life Parameterization

Recall the differential equation for a damped spring:

And the equations for simulating such system obtained by the implicit Euler method:

where:

I presented the equations obtained by the implicit Euler method, because they are **always stable**. We can obtain a different set of equations that can also be used to simulate a damped spring system by the semi-implicit Euler method:

The equations obtained by the semi-implicit Euler method involve much less arithmetic operations, compared to the equations obtained by the implicit Euler method. There is a catch: the equations obtained by the semi-implicit Euler method **can be unstable** under certain configurations and the simulation will blow up over time. This can happen when you have a large and . However, the and on most use cases are far from the breaking values. You would almost never use an overdamped spring, so is usually kept under 1. Even if is set to 1 (critically damped spring), can be safely set up to (5Hz), which is a very fast oscillation you probably would never use on anything.

So, if your choice of and result in a stable simulation with the equations obtained by the semi-implicit Euler method, you can use them instead of the equations obtained by the implicit Euler method, making your simulation more efficient.

Here’s a sample implementation:

/* x - value (input/output) v - velocity (input/output) xt - target value (input) zeta - damping ratio (input) omega - angular frequency (input) h - time step (input) */ void SpringSemiImplicitEuler ( float &x, float &v, float xt, float zeta, float omega, float h ) { v += -2.0f * h * zeta * omega * v + h * omega * omega * (xt - x); x += h * v; }

Numeric springing and tweening (usually used with the famous Robert Penner’s easing equations) might seem very similar at first, as they are both techniques to procedurally animate a numeric value towards a target value; however, they are actually fundamentally different. Tweening requires a pre-determined duration; numeric springing, on the other hand, does not have such requirement: numeric springing provides a simulation that goes on indefinitely. If you were to interrupt a procedural numeric animation and give it a new target value, numeric springing would handle this gracefully and the animation would still look very natural and smooth; it is a non-trivial task to interrupt a tweened animation, set up a new tween animation towards the new target value, and prevent the animation from looking visually jarring.

Don’t get me wrong. I’m not saying numeric springing is absolutely superior over tweening. They both have their uses. If your target value can change dynamically and you still want your animation to look nice, use numeric springing. If your animation has a fixed duration with no interruption, then tweening seems to be a better choice; in addition, there are a lot of different easing equations you can choose from that look visually interesting and not necessarily have a springy feel (e.g. sine, circ, bounce, slow-mo).

Previously, I proposed a parameterization for numeric springing that consisted of 3 parameters: the **oscillation frequency** in Hz, and the **fraction of oscillation magnitude reduced** over a **specific duration** due to damping.

I have received various feedback from forum comments, private messages, friends, and colleagues. The most suggested alternative parameterization was the half-life parameterization, i.e. you specify the duration when the oscillation magnitude is reduced by 50%. So here I’ll show you how to derive to plug into numeric springing simulations, based on a given half-life.

I’ll use (lambda) to denote half-life. And yes, it is the same symbol from both Chemistry and the game.

As previously discussed, the curve representing the oscillation magnitude decreases exponentially with this curve:

By definition, half-life is the duration of reduction by 50%:

So we have:

Once we decide the desired , we lock in and compute :

And here’s a sample implementation:

void SpringByHalfLife ( float &x, float &v, float xt, float omega, float h, float lambda ) { const float zeta = -ln(0.5f) / (omega * lambda); Spring(x, v, xt, zeta, omega, h); }

Here’s a graph showing and (2Hz). You can see that the oscillation magnitude is reduced by 50% every half second, i.e. 25% every second.

I’ve discussed how to implement numeric springing using the faster but less stable semi-implicit Euler method, the difference between numeric springing versus tweening, and the half-life parameterization of numeric springing.

I hope this post has given you a better understanding of various aspects and applications of numeric springing.

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