Sine Language Lesson, Part 2

In Part 1 of this post I discussed some useful applications of the sine function without really delving into the details of how it works. Specifically, we focused on the equation y = sin(x). Here is a more useful variation of the sine function as demonstrated in the Ocean Waves demo:

y = A * sin(K*distance - F*time + S)

• A = amplitude
• K = angular frequency
• F = time frequency
• S = shift

Amplitude represents the height of the wave; it typically ranges from -1 to 1 but can be set to an arbitrary value (e.g. set A = 25 for the wave to range from -25 to 25). The angular frequency represents how quickly the wave travels vertically. The time frequency represents how quickly the wave travels horizontally; note that F*time can be omitted from the sine function to view a static snapshot of the wave at a point in time but is included in the Ocean Waves demo to provide the effect of a wave in motion. Finally, the shift parameter allows us to move the wave by a horizontal offset so it starts from a new position (e.g. setting S = -π/2 would map it to the cosine function).

The Point Light demo from Part 1 sets the light source position's Z-coordinate using a simple sine function and then calculates the X- and Y-coordinates as sine functions using the computed Z value as the distance parameter. The Ocean Waves demo combines multiple sine waves to achieve the illusion of irregularity (not all waves in the ocean are the same height and hit shore at the same regular time interval). For example, to apply the effects of y = sin(x) and y = 12 * sin(3x), we can simply write y = sin(x) + (12 * sin(3x)). Observe that the two functions are added together. Watch the web preview of Combining Sine Waves to see the concept in motion.

I hope this post encourages you to investigate some potential uses of sine/cosine functions, as well as return to Part 1 if you missed the demo programs. It seems some things we learned in high school actually did turn out to be useful!

Staying Motivated

I can't believe I started this blog more than six months ago. I remember thinking initially, after seeing many game development blogs trail off after just a couple months, that I would surely put out at least five posts every week. Ha! Let's just say I may have been a little ambitious. It's easy to push forward full steam when something is new, but the question of true dedication comes when the going isn't so easy.

I've seen forum posts regarding burnout on the game development dream and even noticed one of the blogs I followed (and had linked here) seems to have disappeared. So... how do you stay motivated when your enthusiasm wanes? I think part of it is remembering what you enjoyed about it (whether it is game development or another hobby) in the first place, and looking forward to what you will be able to do with practice. In my case I'm reading through a very dry, technical graphics book right now and sometimes it is flat-out boring; but I know that by reading it and working through the examples I will in time be a better game developer.

Quite honestly, I think everyone loses their enthusiasm at times. If you stay away from an activity too long it can be hard (though not impossible) to get back into it, and if you play with something too long it can start to feel like work. But the best approach is to just stick with it. Don't give up!

Check out Brenda Brathwaite's blog post for more inspirational thoughts on staying motivated. I'm proud to say that even though I'm not posting as frequently, I am still learning new graphics tricks (today was Direct3D meshes) and will not be disappearing any time soon!

Sine Language Lesson, Part 1

I've had this idea ruminating in my mind for some time now. Math is a big part of graphics development and I'm certainly no expert, but I wanted to show off some cool things that can be done with sine waves. This part introduces the concept and shows some fun demo programs you can play with; part two will delve into the inner workings of the demos, which have been adapted from Frank Luna's Introduction to 3D Game Programming with DirectX 9.0c: A Shader Approach.

You may remember from your high school Trigonometry class (don't worry if not, it was a long time ago for me too!) those two periodic functions, sine (pronounced "sign") and cosine ("co-sign"). They're essentially the same function and you could map one to the other with a slight shift. Cosine has some unique applications of its own, such as determining light intensity based on viewing angle, but the demos below will focus primarily on sine waves.

Credit: Wikimedia Commons

Notice a few interesting properties from the graph above. One is that a sine wave repeats itself every 2π (π ≈ 3.14159) or 360 degrees along the X-axis. Another is that it oscillates between the Y values -1 and 1. We write the function y = sin(x) to indicate the Y value as a function of X; see from the graph above that Y = 0 when X is any multiple of π and Y is either 1 or -1 (the peaks and valleys) when X is an odd multiple of π/2.

Point Light Demo - Download Program!

This demo shows how sine waves can be used to animate a light source. Use the specified keys to combine waves, creating a variety of unique horizontal and vertical motion paths.

Before learning this elegant method, my approach to animating an object that sways back and forth, or moves repeatedly up and down along a pole, was to use code like this in my update loop:

    static bool moveUp = true;
    if (moveUp) 
    { if (shipPos.y < 100) shipPos.y += value; else moveUp = false; }
    else 
    { if (shipPos.y > -100) shipPos.y -= value; else moveUp = true; }

With sine waves, this code reduces simply to shipPos.y = 100 * sin(x)! Notice that I multiplied by 100 to get the desired range instead of the standard oscillation from -1 to 1.

Ocean Waves Demo - Download Program!

This demo illustrates the effects of adding sine waves and two different wave types, circular and directional. Use the specified keys to play with parameters and change the wave patterns.

As with the Point Light demo, you will need to have DirectX (from Windows Update) installed in order to run the program.

These are just a couple applications of the sine function. Because of its periodic repetition, it could have many potential uses; some fellow GCG forum members cited their implementations of a 3D carousel and a wavy spaceship flight path as additional examples.

I hope you enjoy the demo programs of this post, though I admit I still need to learn better methods of input handling. Part two will describe wave alterations, based on the Ocean Waves demo, in greater detail. Until then, feel free to let us know: What's the coolest thing you've done with sine/cosine waves?

Quick Random Update

So, Gamasutra is on Twitter too. You may recognize them, or at least you should if you have any business as a video game developer/designer. Gamasutra is one of the most popular game-oriented websites with full-featured articles and commentaries on the state of the industry, game reviews, yadda yadda yadda. So now you can check out not only the website, but also the Twitter feed. Oops, sorry if that last link didn't work; I suppose I should have linked it the proper way: @Gamasutra!

Enough hype, this post is mostly me checking in for a quick progress update. I blasted through reading about lighting, textures, blending, and stenciling in my Direct3D book and then found out the exercises required a fair deal of re-reading. Lesson learned, I have to work through chapter exercises before moving on to more difficult chapters! The same applies to the Game Design Concepts course I'm taking -- it's much easier to keep up with the readings than work through the exercises, some of which I have to skip. FYI, you can follow discussion for the course on Twitter too; just search for #GDCU!

The topic of my next post will be the power of sine waves. Yep, I'm talking about those tricky oscillating waves you learned about way back in high school. I've found some interesting applications and want to show off some of the cool stuff you can do with them. And now that I'm finally understanding the basics of HLSL (High Level Shader Language) shaders, the part that tripped me up big time in the last book I read, you can expect some posts on that stuff too.

Just curious, when was the last time you used something from high school you never thought you would need again? What's the trickiest math you've used in game development, and does calculus ever figure into the equation (pun... fully... intended!)?

The Problem with the Mythical Black Box

In programming, we occasionally make use of something known as a "black box." This Mythical Black Box is any library or chunk of code written by someone else that allows us to abstract a problem so we don't have to understand the details of solving it. For example, if we pass the values 3 and 4 to a "calculator black box", which might be a class library written by another developer, we would expect it to return the value 12 for multiplication. We don't care how it works internally, whether it computes 3+3+3+3 or 4+4+4; all we care is that it returns the correct value. A black box diagram for an encryption algorithm might look something like the following.

Password => { Encryption Black Box } => Encrypted Password

Jeff Atwood of Coding Horror has recently expressed seemingly contrasting views on this topic, both touting and refuting the benefits of abstraction. And for good reason, because it can be a good thing or a bad thing depending on whose library you choose. For one thing, you should never introduce code into your project if you aren't 100% certain it will fulfill its promise. Many developers (myself included) prefer the "roll your own" method for most tasks simply because you know you can trust your own code (not that it will be error-free, just that it won't be malicious). But sometimes it makes sense to use a well-tested library from another developer, such as the ever-popular JQuery library for Javascript development. In such cases I suggest ensuring you trust the developer (e.g. they're well known, such as Microsoft, and would be ridiculed if the library failed) or that you have full access to the source code. Many open source projects are reviewed by large numbers of people such that bugs are caught and fixed quickly.

Unfortunately, even if you take my suggestions your black box may someday fail. The whole reason I bring this up is that I faced this exact problem with my SkyCop demo. I developed it using the Common Files Framework presented in Engel's Beginning Direct3D Game Programming, 2nd Edition and provided in a specific version of the Microsoft DirectX SDK. When I ugraded to the most recent build of the SDK, my demo suddently stopped working and I started getting reports of others not being able to run it either. I ran into numerous problems trying to get it to work with the latest DirectX SDK and believe the Common Files Framework was removed altogether in the latest version. Having relied too heavily on that framework, I wasn't sure how to resolve the compilation errors and feared I would have to scrap the project altogether.

Fortunately, in his Introduction to 3D Game Programming with DirectX 9.0c: A Shader Approach, Frank Luna fully describes a working game framework instead of glossing over it and providing another black box. I was able to essentially rip out the core of my SkyCop demo, converting it to use the new framework, and am pleased to have an updated demo below that should work on any DirectX 9 (or newer) version, but let me know if you still have any trouble running it.

SkyCop v1.1 Demo Download

Black boxes can be a good thing when they're well-written by a trusted developer, but it's also a good idea to review the code (if possible) and at least have a basic understanding of how it works. In my case, as a learning newbie, I was happy to avoid the initial complexity and that later bit me from behind. One thing to keep in mind, though, is that black boxes come in many shapes and sizes. My black box was a game framework but the concept could also apply to a game engine, a single portion (Renderer, Physics, Sound, etc.) of a game engine, or some other game components I'm not even aware of yet.

Do you know what's going on under the hood of your game framework/engine? What black boxes are you relying on to develop your games?

June Monthly Checkup

Yep, another month has come and gone. Sadly I still don't have a finished game, but I do have some cool demos to show off in upcoming posts. I'm up to chapter thirteen (of twenty-two) in Luna's Introduction to 3D Game Programming with DirectX 9.0c: A Shader Approach and am learning a lot, but it takes a while to work through the chapter exercises. I'm also in the process of taking Ian Schreiber's free online game design course. My portfolio website is nearly completed; I just need to find a better host before posting the link here on GDJ.

So it's been yet another busy month of learning and experimenting, all while prepping for our big move to NC in August. After we get settled I plan to join the Triangle IGDA chapter so I can get serious about that whole networking thing.

Speedrunning

The Escapist recently caught my attention with this article on speedrunning. If you're not familiar with the concept, some people spend WAY MORE time trying to master games than you or I do. In fact, they spend countless hours and thousands of lives (digital lives of course) trying to master game levels, determining the most efficient paths to complete a level - or in some cases the entire game - in the shortest time possible. There are plenty of other worthy examples on YouTube; just search for "speed run" after the title of your favorite video game.

Would you have the patience to master this??? I doubt I would.