It’s been a month since I made my first step into Singaporean soil.

First question that probably comes to your mind would be “How is it so far?”

My answer: …Okay laaaaa

You know, you’re gonna have to get used to my way of answering questions. I like to keep things simple and clear. And “Okay laaaa” is just the best way I can put it.

Fine fine, I’ll tell you how is it going so far in Singapore… seriously, I miss Malaysia a lot. There’s something that you can find in Malaysia, that you can’t in Singapore. I’m not sure what that something is, but when you’re in my shoes, you’ll be able to feel it.

Alright, I didn’t log in to wordpress just to talk about my deep deep fried feelings for Malaysia, nooooooo

I’m supposed to be ranting about some shit I just ran into for the past 3 weeks.

So, the other scholars have finally moved in, and I now no longer dominate the 8th floor of my hostel block. Oh, I miss the first 2 weeks here… Don’t you just love it when you don’t have to wait in line for that awesomely big shower cubicle? The other 2 cubicles are more of a squeeze… really ruin the excitement of showering…

You can tell, there’s a whole lot of biodiversity going on around here. There’s a bunch of Vietnamese, Indonesians, Malaysians and Indians (those from India itself, not the locals….)

I’m alright with most people. At least they’re easy to approach and talk to. But there’s just some people (and by some, I just refer to a couple of them) who are really egomaniacs…. They are so obsessed over their own pride… I have just nothing to say to them.

It’s not that I have issues with them or anything… actually, I do, but come on, work with me here

Another thing about them is their arrogance. If you want me to give you the top 2 type of people in my prestigious and oh-so-ridiculously-awesome List of My Most Hated Type of People, Arrogant Shits just follows Smokers.

All I can do is just smile when I’m in their clique. My wavelength and theirs just do not superimpose very well, if you know what I mean. I can talk so well with other people, except these bunch. If only they’re more… how do ya say… LESS of a shit than faecal matter?

Okay, enough of the ranting… here’s the good bit of the post. Wow, it’s amazing you’re still reading. Well, give your self a BIG clap for reading all that…

Seriously, I only allowed ONE clap, no more no less. If you did more than that, you’re doomed to a life of meatballs and goats… okay, I dunno what did I just say…

I was actually accepted into Choir! OMG! This is the first time I’m singing in public, but I’m still working on my ability to actually SING freely in public. Anyway, I’m in Bass. Somehow, knowing how my voice is just a slight bit higher than the average male’s voice, I’m amazed that I got into Base. I thought I would be in Tenor. Then again, Tenor’s quite high for me.

I’m also going to sing for a competition. You know it’s really easy to sing… IN THE BATHROOM where nobody cares…. When I play any instrumental songs for any song that I know how to sing, it totally wrecks havoc on my larynx. I can’t seem to sync up with the instrumental. Maybe cause I always try to transpose the song itself down to my vocal range… I dunno, but I’m gonna try.

It’s either I pass the audition or fail miserably with a possibility of embarrassment and humiliation. Well, it’s not that bad right? I’m sure there are people who have just the same predicament as me… Or maybe my brain just wants to think that way.

Well, that’s all for today. HOPEFULLY I can post again soon. Knowing how the stupid WIFI connection here can be very temperamental, it’s gonna be a challenge to even get to connect.

BYE!!!!

So, it’s already about 3 weeks I’ve been in Singapore. How am I finding it so far? 

Okay laaaaaa

That’s probably the best answer I can give you. I mean, it’s the safest answer anyway. I can’t say it’s totally awesome to be away from home – I’m missing home to be frank with you.

I can’t say it’s hopelessly horrible either. There are pros and cons in studying in Singapore, as a scholar. Education as a scholar over here is not entirely free though, even if many reviews and testimonies put it that way. The uniforms and food are quite pricey, if you do the price conversion back to malaysian currency. But I guess it’s normal for the people over here.

I know I haven’t been blogging for quite awhile. I think I’m restarting my blogging habits, just to vent my stress, despairs, anguish, and doubts for the world to see.

Okay fine, maybe studying here isn’t that bad – it’s just a tad bit harder than STPM. Okay, I kid, it’s WAAAAAY HARDER than STPM.

If let’s say you learn “this” in STPM, you basically learn “this and a whole lot more shit” in Singapore A-levels. See the difference?

Although the syllabus are about the same, plus a little more bits and bobs here and there, the system here is more… in a way… diverse. A level subjects here are divided into 3 tiers, H1, H2 and H3.

For every subject, you are required to choose its tier, provided that it’s offered in the Junior College.

In the case of H1 and H2, the depth of the contents are about the same, but the breadth, or the amount of content in H1 is about half of that in H2. In a way, you cover less in H1 compared to H2.

Everyone is required to take at least 4 subjects, either 2 H2, 2 H1, or 3H2, 1 H1 or 4 H2, in the case of Anderson Junior College anyway.

H3 is a little different. It’s more specialised, as there are, sorta, university level contents in the syllabus. It’s definitely not something to be taken lightly, but the returns are greatly acknowledged, if I’m not wrong. If you pass your H3 with flying colours, you are definitely one big step ahead of everybody else.

But it isn’t that easy. H3 can only be offered in the 2nd year of Junior College, and it has its own eligibility criteria. At most, a typical student can take 1 H3 subject.

I dunno if I’ll be offering a H3 subject next year. Well, see how thing goes la.

Well, you know the moment when you suddenly have an idea in your head, and you got it on paper? Then the next day, you wanna start realising it. Then as time goes on, you just get very lazy. That’s exactly what’s happening to me. I think I have like 10+ game projects left to collect dust just because of my lack of commitment. I used to be so enthusiastic, until I come to realise that the coding is really frustrating.

This leaves me with one very good lesson – make a reusable game engine, so that I don’t have to code everything from scratch.

Another point though, I just realised that my games up to this point, are just proof-of-concepts. I make games just to prove to myself that something is do-able. Ever wondered why I spend so much time on Special effects than the main game design? Well, I’m really into it, that’s why. Things that please my eyes are probably the things I like to spend more time in.

I think I’m more of a Special Effects artist, although I’m never good in drawing. Seriously, I can’t draw, but I can always cheat in drawing stuff on screen.

Well, I should get started on simpler games now. I think I should put Mr Ball to rest, he’s been a great character. Looking back, he has seriously grown up to be a pretty awesome ball indeed. .. I’m sorry if that sounded a little wrong, it’s not intended to sound that way BTW…

Maybe in the future, when I have crew, maybe, just maybe, Mr Ball will become the new internet meme, or a ubiquitous character like Mario and Sonic. I dunno, maybe I’m being a little too ridiculous, but who knows.

And with that, ends the Mr Ball saga. I will stop making games on Mr Ball, but he’ll probably return as cameo appearances on my future games.

Today marks the end of my 6th year in SMK Taman SEA. I’ve always told myself to leave my mark in any memorable place I go to, and I dunno if I have successfully done so in my own school. I probably have one or two graffiti somewhere in the school, or maybe they’re already painted over.

Whether or not I left any marks, I will definitely miss going to school. There’s something about going to school that you just can’t quite put into words. Apart from the stuffy uniforms, secondary school life was one of the most influential period in my life.

And without the support of my family, teachers and friends, I probably wouldn’t have made it this far. I’ve gone too far to just give up just like that. There may be bigger hurdles and more slippery bananas later on to throw me off track, but I’ll stand my ground and hold my head up.

Seriously, I’m sure gonna miss Taman SEA. Actually, I have to thank my dad too. If it wasn’t for him, I wouldn’t have joined such a great school, cause I wasn’t posted to Taman SEA in the first place when I was about to start Form 1.

Thanks to all my friends and teachers. They’ve been great mentors and companions when I’m down.

Anyway, life’s been really… stormy. Yea, that’s right, it’s been raining almost everyday. To think that I have only 2 more months in Malaysia, the gloomy skies is just a reflection on how sad I am to leave Malaysia. But if it’s to secure my future, then so be it. =D

So, recently I just started a new 2D Mr Ball project. Why not 3D? One reason: There’s one less axis to take care of. Trigonometry is so much more simpler since you don’t need to deal with the Z-coordinates. I mean, we’re all used to the usual X-Y Cartesian coordinates, so screw you, 3-Dimensions!

I know, 2D games are sooooo last decade, right? yea… but the feel in playing 2D games and 3D games are different, so it’s hard to compare both of them.

Well, there has been more graphical improvements in my 2D game. Additive blending is being abused, for one.

Normally, images are blended on top of each other on screen through “normal” blending, where the Alpha value determines how much of a particular image can be seen. Think of Alpha value as sort of a “transparency” value.

Additive blending basically does what its name implies: Add. The colours of an image is added to whatever colour below that image on screen. So, Additive blending makes visual effects look brighter and vibrant. Things like Fire and Magic Spells are drawn using this type of blending.

But screw blending. The one thing I’m really proud of is having curved polygon in my game. It’s not a totally new concept though. It’s used everywhere in real life. Even in modern games, it’s still being used, although it’s made to adapt to 3-Dimensional space.

Basically, how game developers imitate curvature in games is by drawing many many smaller lines which are tangents to a general curvature (think of a jagged curve).

I always love drawing lightning cause they’re just beautiful, but one thing I noticed in all my games is that all my lightnings are straight. Okay sure, they may have different orientation, but they’re still linear, so today I thought, why not make a curved lightning, and there I decided to make use of one of the many tactics employed in today’s modern games to draw curved polygons.

But seriously, you don’t have to read on if you don’t want to. I just want to make my blog look “updated”.

Well, since you want to move on, fine, go ahead. Read on…

This is how I want my lightning to arc – it starts from an origin, O, then it arcs downwards through a vertical distance of h towards a point, P, that is a certain distance, d, away horizontally from the origin.

Here’s a picture to illustrate all that gibberish

If you draw 2 lines from the ends of the arc in such a way as seen in the picture, you can see that you can form a Sector, with the 2 lines having the same length. Good so far. Before we can do anything with the arc, we need a way to describe its curvature.

And the curvature of the arc is really dependent on the radius of the curvature, no?

Now look at the picture on the right:

Since it’s one big Sector, we can say that

Angle QOP = Angle QPO = θ

We can find θ by using simple trigonometry.

Now we have θ, we can fine Angle OQP, which we will call φ. By observation, we know that

Now that we have φ, we can determine the value of r.

But since we know that

we can substitute that into the equation and use some trigo identity magic and get this:

And with that, you just need to dump in a bit of magic, and pray that it’ll present you with something awesome.

So, first thing I did when developing the curved lightning is to test out the equations above, and got this:

You cannot tell how wonderfully happy I was just to see a line like that. Yea, I’m easily impressed XD

So, happy with the line, it needs some width, so a bit more trigonometry has to be used to expand the line into a polygon:

Happy with the outline, I given it coordinates for the lightning texture I downloaded somewhere in the web.

Finally, the wireframe’s removed. (Actually, the wireframe never existed. I just made another lightning object just for this post to illustrate the many phases of planning and development)

Now repeat that a few more times, add a bit of glowy-things here and there, and some sparks for good measure, and omg, you get this:

Now I dare you to open any game and try to think of how developers actually draw certain things on to the screen. It’s very hard to pick out the tricks used to render images cause most of the time, the developers cleverly limits camera movements to avoid showing the artifacts to the player, but with a keen eye, any tricks can be revealed.

ASEAN scholarship is given by the Singapore Ministry of Education to students from ASEAN countries, excluding Singapore. Somehow, knowing how competitive is the scholarship intake, receiving it had never ever crossed my mind.

The first reaction I got from the email that I received a couple of weeks ago from the MOE is just a tsunami of contradicting emotions. I’m happy, and yet I’m sad. Part of me doesn’t want to leave, but the other part is just excited.

I’ve formed so many bonds here in my homeland; bonds which I really really want to preserve. Malaysia’s been really nice all this while, although, there are some questionable issues around here. Am I saying this like I’m about to leave Malaysia permanently? Sounds like it, lolx. But actually, I will never leave my home country forever.

As much as I like to travel, this is the place I was born, and this will be the place I will exhale my last breath. My family is here, heck, my friends are here too. And because of that, it pains me to think that I’m about to leave to Singapore for quite a while. It’s not that I don’t want to, but somehow, the bonds are just too strong. In the end, I still have to go.

What more, I love my school. It’s been months in Form 6, and there is still so much more I can do in school. You know, it’s not possible to turn back time and relive high school life all over again. Out of my 18 years of being on Earth, it’s my time in SMK Taman SEA that really changed and moulded me into what I am right now. Words can’t express my appreciation to all my friends, my teachers and my family.

I’m anticipating a very harsh life up ahead in Singapore. Rumours has it that the syllabus there is way more difficult than what I’m learning now. But come one, life is never a bed of roses. If life was that simple, what reason is there for me to live? Life without challenges would be a freaking boring place to be, no?

Seriously, there’s no turning back. I’ve signed all the documents and what not. I really hope that I’ll do well. Contrary to popular belief, I’m not really a studios person. I don’t spend hours on the books. I do have a life myself =D

Well, that’s that. No maths for today. I’m yet to derive something stupid and ridiculous, but hopefully, I can find something even more redundant for the next post. Maths can’t just be useful only, it should also be useless. … Sorry, I dunno what I’m saying.

Of course, when you think of pi π, you think of circles right? So, we can try and determine the value of π through the usage of circles. But, not so fast. It’s gonna a little bit more complicated from there.

We can’t just draw a circle and expect the value of π to pop out just like that. You must screw the fact that the Area of Circle is πr². Basically, one way or another, what we’re gonna do is deriving that formula.

Alright, now comes your visualization skills. Imagine a circle of radius r. Circumscribed in it is a regular polygon of n-sides.

Take for example, a square circumscribed in a circle (cyclic quadrilateral);

θ here would be the internal angle of the polygon. To calculate θ, it is given that

θ = (n-2)(180) / n

In other words,

θ = 180 – 360/n

As you can see, it is possible to subdivide the cyclic n-polygon into n-number of isosceles triangles.

Therefore, the area of the polygon is equal to the sum of the areas of all the triangles.

If we used a unit circle, then the equation can be reduced to:

Here’s a question, what if we circumscribe a polygon with a very very large number of sides? The value of the Area using the formula above will slowly approach the area of the unit circle, and the area of the unit circle, theoretically, is π, but we’re gonna prove that.

That means, we are asking, what happens when we take the following limit:

But first, we have some simplification to do.

If we use the radians, then we know that

θ = π – 2π/n

We substitute that into the Area equation.

Using the trigonometric identities and some number crunching, we end up with this

So, we take the limit to infinity for n:

Obviously, there will be a problem here, cause of that stupid little “n” that appears all by itself. We can’t multiply an infinity, so here’s a clever workaround, cause limits are so friendly to fractions:

If we evaluate this limit now, you will know that you’re gonna have to divide by zero, which is a big crime in the maths world, no?

To avoid being filed a lawsuit just because you attempted to divide by nothing, we can use L’Hospital’s Rule. It states that if you are taking the limit of a quotient between 2 functions, and somehow, you are unable to do it, the next thing you can do is to evaluate the limits of the quotient between the derivatives of the 2 functions.

Anyway, in other words,

Okay, so, going back to

You know what to do next right? Differentiate the numerator and denominator separately. Note that the product rule has to be applied on the numerator.

Simplifying:

As you know, when n gets infinitely large, anything divided by a large number will be very close to zero. So, taking that into account, you’ll have this:

Okay, so what can we do with this? If you have just this expression:

The larger the value of n you sub in, the closer the approximation you get to π

Just for fun, here’s a graph of

There’s an asymptote at y=π

So yea, instead of the oh-so-boring 22/7 and 3.147 approximations, you can add

into the list of approximations of π

It’s been a few months in Form 6 already, and how am I finding it? Pretty awesome, and pretty stressful too.

The awesome part of being in Form 6 would be my friends. Anywhere you go, it’s really important to have friends, no? Would you rather stay as a lonely, bitter old-man or a lively, friendly and happy young-man? Yea I know, the question’s a bit biased, and you’re bound to choose the latter, right? Am I not right? Oh dear…

Anyway, what about the stressful part of school life, you asked? Actually, school life itself is stressful, isn’t it? Work everyday. At first, before I wanted to join Form 6, I told myself not to get myself involved in too many extra-curricular activities, then again, now I’m the organising chairman for a Cultural Week at the end of the year. Great…

What’s worse is that the exams are pretty near, and I have not done any revision as of yet. I seem to be getting lazier and lazier everyday. This is soooo not good. It’s gonna take me one hell of a result to push me from Procrastination-BeeLee to HardWorking-BeeLee.

But, screw that. I shall start my rant. Here goes.

Did I mention how much I hate arrogant people? I think I did right? Yes, I did. They’re like next in line following smokers in my list of the most despicable people. I just find these people annoying.

And there are also people that I know who talks just a little bit too much. If they talk to you, you would feel like they’re belittling you, doubting your skills and all, and thinks that you can’t do much work. I can get a little worked up over this, but what can I do?

There are also strangely more blowhards nowadays. You know, those people who keep bragging how good they are in certain things, till they actually say they can do so much better than you? I mean, what do I care? As long as I can get my job done, does it matter if I’m good or bad at it? So what if I take a little more time to do? Will it kill a cat? No, I don’t think so. You think the world’s gonna run out of oil just because I want to spend just a little bit more time on my work? That’s like trying to say a candle’s gonna extinguish cause a watermelon fell on a cow.

Yea, I’m digressing a little too much, but you get the point right? Braggarts are so annoying. Well, I’m a braggart occasionally too, but not to the extreme extent like these people. You can’t even work in peace without them trying to correct you and say their way is so much better. Eat shit man, let me do my work my own way. At least it has my originality.

Oh, and for some people, it’s hard to tell whether they’re joking, or they’re being serious, cause of the way they express their opinion on some matter. Jokes might sound really serious, and this can be really awkward sometimes. But, this isn’t much of an issue for me, cause I’m able to laugh it off in the end, but for a small bunch of people I know, they just sound a little too serious in their joke. Well, to say the least, failed delivery.

Yea, that’s that. =D

This was one of the busiest holidays for me. Almost everyday I’ve been going out, from having a BBQ out in a park

to riding a boat upstream on the Pahang River.

And not to mention the good food during Raya in my aunt’s open house. Nothing like a good ol’ lemang during raya eh?

Right after the bbq on thursday, I went to Midvalley mall to have a look at the IT Fair, and watch Smurfs with my buddies.

Yea, so you can conclude that I didn’t really have any time for homework eh? Yea…… I feel so guilty now.

Before I end this post, it’s really not right to see a post without some numbers in it. So, here’s something very simple to ponder about.

If you’re in Malaysia studying Form 4 Biology, you should have already come across the term Capture, Mark, Release, and Recapture method to determine the population size in ecology. How it works is, you go to a place, you capture a specific number of stuff (M), mark them and then release them to do their stuff in nature. Give them a short period, then you return to the same spot and capture a specific number of stuff again (C). You count the number of marked stuff that you recaptured (R).

So far,
M=Number of animals captured and marked on first visit
C=Number of animals captured on second visit
R=Number of marked animals captured on second visit.

We need one more
N=Population size

Basically, the formula is a play on Probabilities. It is assumed that during that short period of time between the first and second captures, there was no change in the population size (ie, the population is “closed”). And also, it is assumed that the chances of capturing any individual in the second capture is the same regardless of whether that have been captured before.

So, the proportion of the captured marked individuals (R / M) should equal the proportion of the total population that is caught (C / N)

R/M = C/N

Therefore, N=MC/R

And that’s how they came up with the formula.

Source: http://en.wikipedia.org/wiki/Mark_and_recapture

Alrights, let’s imagine we know nothing about x². We have no freaking idea what pattern does x² shows. Just throw it away from your brain.

Done? Okay.

Now, you know odd numbers right?

1,3,5,7,9,11,…

They are numbers that are indivisible by 2. So, what we have above here is an arithmetic series of odd numbers.

Kinda boring right? So now, we will form another pattern:

Start from 0.
Take that 0, add it to the first term in the odd number series, 1, and you get 1.
Now, take that result, 1, and add it to the 2nd term in the series, 3, and you get 4.
Take that and add it with the 3rd element, 5, and you get 9.

Repeat this a few times, and you get this rather odd pattern forming:
0,1,4,9,16,25,36

Looks familiar? It shouldn’t, cause I told you to forget about x² for now.

Right, so we need a way to describe that random, unknown pattern. Hmm… here’s a way:

We have to make a couple of functions to encapsulate the sets of numbers we got.

Let A={1,3,5,7,9,11,…}
So, A is a set of odd numbers from 1.

And Let S={0,1,4,9,16,25,36,…}
So, S is a set of numbers produced from the repeated addition operation with successive terms from N.

Lastly, let’s have X={0,1,2,3,4,5,6,…}
We will find out how set S relates to set X, which is our goal.

Suppose that we have functions f and g, such that

To make it easier, let’s assume that:
f(x) = (x+1)-th term of S
eg: f(0) = 0, f(2) = 4

and g(x) = (x+1)-th term of A
eg: g(0) = 1, g(3) = 7

Before we talk about the addition process, let’s describe how set A relates to set X first.

You know that the numbers in set A are increasing by the same amount each time, ie, linearly.
And since elements of set A are represented by g(x),
g(x) can be assumed as a polynomiol of degree 1, ie, linear.

Of course, now we need to solve for m and c, which shouldn’t be much of a challenge right? We can use the values stated above, g(0) = 1, and g(3) = 7
m(0) + c = 1
c=1

m(3) + c = 7
3m + 1 = 7
m=2

So,

Good, we tackled g(x). What about f(x)? Now, f(x) is a little harder, but it’s our last hurdle to describe the pattern of set S.
Alright, here goes:

We know that from the addition process,

In case you’re scratching your head over how I got that, basically it means, for the x-term in set S, it is the sum of the previous, ie (x-1)th, term in S and the corresponding term in set A.

From there, it’s obvious that it’s a recursive function, we by you can substitute in f(x) again and again repeatedly into the equation.

Since f(x-1) = f(x-2) + g(x-2),

Substituting again:

Seriously, this recursive substitution has to stop somewhere, otherwise we will go nowhere, eh? So, imagine we did this so many times until we reach this point:

Condensing everything, we have this:

By definition, we know that f(1) refers to the 2nd term of set S, which is 1, or f(1)=1
and we also know that g(x)=2x+1, hence we have

Expanding everything out:

We assume x as a constant in this equation. To continue dealing with the summation signs, we need to break it down a little.
Consider this:

where k=constant

What that expression means is, take (x-1) number of constant k’s and add all of them together. For example, take x=4, and k=2

In other words, we can rewrite the expression as:

Now, what about the summation of variable i as shown:

Basically, i is the variable for the summation. What this means is, take the sum of (x-1) number of values of i’s, each successive of the previous, starting from i=1. Again, another example, take x=4,

As you can see, this is the same as taking the sum of an arithmetic series with common difference of 1 and initial term of 1.
The formula for finding the sum of an arithmetic series is:

Of course, n=x-1, a=1, d=1. After plugging, chugging and simplifying, you get

After a while of digression, we can finally go back to our original equation:

From there, we make the necessary adjustments and crank this out:

After much simplification, we get this:

Awh, such a cute little equation, no?
You know what that means? We showed that the pattern in Set S are actually perfect squares. So, from there, we now know what is x².

We’ve gone through all that trouble just to prove a stupid and ridiculous quadratic term. Well, Maths is never always fun and simple, but it is always exciting.