Triangulating Concave and Convex Polygons — Ear Clipping

The Problem

OpenGL and other low-level rendering APIs are limited to rendering convex polygons. This causes a complications to arise when trying to render concave primitives. In my case, I wanted to be able to render arbitrary 2D "ground,"  and not succumb to manually breaking apart the polygon into OpenGL-compatible primitives. Thus the search for a triangulation algorithm arose. All I could find were algorithm names without accompanying implementations or explanations, and long mathematical abstracts on computational geometry. Any implementations I did find seemed to be extremely over-engineered and over-complicated for easy comprehension and adaptation. I finally settled on writing my own implementation of the ear-clipping algorithm to facilitate triangulation.

What We Will Accomplish

139-vertex polygon

Triangulated

Setting Settings of Arbitrary Types in C++

It's been a while, but things are still slowly moving along. Working a 40-hour week doing web development leaves me with little time or energy to make game development progress!

I've begun a new iteration of my rendering engine, IronClad, now dubbed Zenderer. Over the past few weeks I've slowly been adding various modules and utilities to it, such as audio, file parsing, and asset management. Nothing is being rendered on the screen just yet, but that's next!

This post is primarily dedicated to creating a settings module that will accept arbitrary types, such as ints, floats, std::strings, and even bools. The final result will allow something like this:

// Optional file to parse immediately
CSettings Settings("SettingsFile.dat");
Settings.Init();

// Set settings
Settings["WINDOW_WIDTH"]    = 800;
Settings["WINDOW_HEIGHT"]   = 600;
Settings["WINDOW_NAME"]     = "Zenderer Window";
Settings["WINDOW_FS"]       = false;
Settings["SCROLL_SPEED"]    = 5.2;
Settings["FRAME_RATE"]      = 60;

// Retrieve settings
if((size_t)Settings["FRAME_RATE"] < 20)
{

    std::cerr << "[FATAL] Frame rate is too low for adequate gameplay.\n";

    exit(1);
}

// Change settings, regardless of type
Settings["WINDOW_FS"] = true;
Settings["WINDOW_NAME"] = 42.335f;

We will do this by creating an extremely dynamic COption class that accepts all different types for values and turns them into strings behind the scenes.

Yet Another Quad Tree Tutorial

There was nothing to show for Screenshot Saturday this week, but that doesn't mean there hasn't been any progress! I spent the weekend writing a quad-tree implementation and integrating it into the existing engine. It was not a very hard process, and there are already dozens of tutorials available online for this, but this guide may still come in handy for someone.

How Do Quad Trees Work

You may be familiar with a binary tree. Essentially there's a "root" structure (known as a "node") that branches out into two nodes (binary = two). Then, each of these nodes splits into two of their own. This continues as long as necessary. The nodes that aren't split are called "leaf" nodes.
Quad trees work exactly the same way, except the nodes are split into four parts rather than two. This is useful for video games because the screen is a rectangle, and can thus easily be split into smaller subsequent rectangles. Here's a screenshot of a stress-test quad tree in progress:

The small, 8x8 quads represent particles with physics. Each quad you see can contain a maximum of 32 (an arbitrary value) particles before it automatically splits into 4 nodes. The tree cannot go more than 6 levels deep, though, because that would eventually cause a stack overflow due to the recursion inherent to quad trees.

You can see this live, in-action by downloading a demo here (pardon the dependencies, I used my old wrapper classes to write this). Hold keys to generate particles, or use the mouse to set them in certain locations. Right-click the mouse to test for a collision with the large blue quad. The result will show up in the console window as a 1 (true) or 0 (false). You can notice that the operation is performed incredibly quickly, even with an insane amount of particles on the screen. That is the power of a quad tree.

Note: If you get DLL errors, you may need to install the VC++ redistributable from here.

Blurring The Line

This week, I've got some minor updates done. With midterms and projects across the board, it's been a pretty insane week, and not much progress has been made on the game visually. Behind the scenes, I've got some code-restructuring, and the beginnings of an enemy class. On the visual side of things, I've got a new game-play mechanic to show off!

While tweaking the time-trail algorithm, I realized that a particularly clever player could stand in a very bright area for an extended period of time to cast himself further into the future, then just skip throughout the level unnoticed by enemies while his past self slowly trudged through the layers of time. As I wondered about how to fix this, I realized that I had a couple of Gaussian blur shaders already implemented for when I was testing post-processing in my rendering engine. So I decided to test what it would be like if the player was faced with an increasing blur of the world around him as he traversed through time.

Here are a couple of screenshots showing the differences:

A small delay, ~1 second

A much larger one, ~10 seconds

The idea is that the player will not be able to accurately see what's going on in the level as the blur increases, and thus will be deterred from traveling a large amount into the future.

Algorithm Details

For the time-trail algorithm, I created a method called CWorld::CalculateLightInfluence(). It, aptly named, calculates the sum of the three most-influential light sources. It used to rely on distance, but that only makes sense if all of the lights have the same attributes, so now the actual influence is calculated and compared for all of the lights. The calculation is as follows:

distance * 200.f / (Constant Attenuation + Linear Attenuation * distance + Quadratic Attenuation * distance²) * brightness

This is almost the same as the algorithm I use in my lighting shader, except it's done on a single light rather than every pixel of the entire screen, heh. I can easily tweak the 200.f constant if I want lights to have more or less of a cumulative influence. So, this value is summed, capped at a range of [0, 5), and returned to the world for further processing.

Back in CWorld::Update(), this value is then used to create time-trail instances. After this, the blurring algorithm is performed. It determines the total time between the current time and the time-trail active at the moment. This represents the amount of time ahead the player is. This value is divided by 10000, because the Gaussian Blur shader only works well with really small radius values. It's clamped to [0, 1/300]. The larger the value, the closer it is to the limit, and thus the blur increases!

I want to tweak this to be a progressive algorithm, rather than just a linear increase. In the near future, I'll make a spread-sheet and maybe apply a increase based on a stretched out x² graph, like maybe x²/8

More Menu Magic

Some small, but beautiful updates this week!
The GUI keeps on improving, with new menus and transitions! I've added an options menu with functioning toggles, a credits menu with full recognition, a transition sound effect, a critical audio bug fix, and some updates to the player-trail algorithm!

Check out the screenshots below:

Making a Menu

I've been a bit quiet the past few weeks on here, but I've been actively participating in Screenshot Saturday on /r/gamedev. You can see last weeks here, and the one prior here.

This week, I've worked on creating a flexible, slick UI system for making menus. It proved to be pretty complex, and I used a seriously ass-backwards technique to get it accomplished.
You can think of a button as an physical entity, right? You need to be able to check collision, move it around for transitions, and swap textures easily. So I created a CButton class with a CEntity inside. At first, I just had a button texture rendered to the screen as a mesh, and the text rendered on top without being a part of the scene. This worked okay, but I wouldn't be able to add shader effects to the text portion of the buttons, which would look weird. So I had to have them both be a part of the scene.

Animating 2D Sprites in OpenGL

In working on my latest game, Praecursor, it came time to develop a system for easily animating sprites on the screen. I found a very nice sprite for a hero on OpenGameArt, and wanted to integrate his various animations into player actions. In the process, I created a CAnimation class that would extend the CRigidBody class, making it eligible to act just like a physical entity and be rendered on the screen with relative ease. The entire process was fairly challenging, requiring a custom file format parser and a new fragment shader. The following is a tutorial-like thought process that went into the development of animate-able sprites.

Layout

The CAnimation class is supposed to act exactly like a regular physical entity, but should support loading of custom .icanim files and have various functions related to animation. These include toggling animation, setting an automatic animation rate, quick-swapping sprite sheets, and manually switching sprites.

Quick-swapping seems like a pointless functionality of an animation class; after all, why not just create a separate instance and load it with the new sprite sheet? Well, I didn't think about this until I started trying to swap-out animations for running, jumping, and standing with the main player instance. When I would just have a list of animations and do m_Player = m_allAnimations[JUMP], the player would lose his physics properties, such as gravity or jump force. I tried a few workarounds, but none of them turned out like expected, so I decided to add a SwapSpriteSheet() method to the CAnimation class. This will attach a new texture to the material and give the shader new parameters based on width and heights.

In the future, I think I will change the class to incorporate animation boundaries, so I don't need to load a separate image for each animate-able action. I would be able to do something like SetAnimationIndex(0, JUMP), and the animation would only loop through sprites [0:JUMP], then if I wanted to just play the standing animation, I could do SetAnimationIndex(JUMP + 1, STAND), assuming the standing animation comes after the jumping one in the sprite sheet. This would likely all but eliminate the need for the swapping method.