This is Madness...This is Matrices!!

So I've been looking through the CG examples to get my head around some of it.  The 2D stuff was fairly simple, just take in the vertices and does whatever, then outputs no problem.  But then hit the 3D example program and was blasted in the face by more matrices than I knew what to do with.  

So I consulted the bible of CG (Nvidia Tutorials) and went down the rabbit hole.  Chapter 4 in the tutorial is where I needed to be.  To reinforce what I've learned I'm going to attempt and explain what exactly the chapter talks about.  It begins with some easy stuff about coordinate systems and the pipeline, then gets into the heart of the matter.

We begin at object/model space, which is the coordinate system for the object itself.  Each vertex in the 3D object can (of course) be placed somewhere in the object space, with a vector to store all the translation/rotation info.  Although not always shown, the w value is always there if you can't see it.  It is more handy to use the 4-value vector because it makes all the 4x4 matrices much easier later (I'll get to it!)


Speaking of which, to get the object in world space you must combine all the rotations and translations into a homogeneous 4x4 matrix.  Each object in the world have its own matrix to define where it is and its orientation etc.  This way everything is relevant to the other objects in the world.  These transformations can be concatenated to define the precise location of each object.  Now with everything there, we need to look at it.


Eye space is the next stage, and it involves where we will be looking at the world from.  In eye space, the camera or 'eye' will be at the origin and everything else will be relative to it in this coordinate system.  To transform the world into eye space, the view transform must be done.  This usually involves some sort of translation to offset all the other objects compared to the camera.  Once you figure out where you want the camera, you multiply its homogenous 4x4 matrix by the model one to get the modelview matrix.

Creating the modelview matrix.

Now that we have a camera which can see things, we must define what exactly it can see.  This next part is called the clip space, and will ultimately determine what shows up on the screen.  In CG shaders, the vertex shader will always take in vertices and output into clip space.  To get the clip space, the next step is to multiply the projection matrix by the modelview.

This results in the projmodelview matrix and is what makes up where the fragments are.  In OpenGL the clip space will divide by the w to get each of x, y, z between -1 and 1.  This means that the vectors are now normalized in the clip space.  The final fragments are then sent through to be rasterized by the GPU, which then is displayed on the screen.

Hopefully I got this more or less.  Now to do the hard part and actually figure how all this code works..

Of Airplanes and Dinosaurs

Today I'm going to go over our two new board games and review the game atoms, as well as explain a concept I wanted to add to them.  The WWII game we came up with is called Flight Path and involves 2-4 players trying to reach an aircraft carrier at the other end of the map.  The pick-up mechanic game is called Rescue Racers where the goal is to rescue civilians via helicopter from the dinosaur invasion.

In Flight Path each player controls a WWII era airplane which is in need of repairs.  The players can choose from the Saetta, Spitfire, Komet, and Mustang models, and their objective is to reach the Campania class escort carrier near the shore.  The players start spread out at one end of the map, while the carrier occupies two spaces at the opposite end.  The first two players to get there will be repaired and win the game.

Campania class escort carrier.

Each turn every player can move up to two spaces on the map.  A 90 degree turn will use up one of these two movements.  Players are limited to 90 degree turns and a max of two movements per turn.  Additionally, certain tiles will limit movement.  It takes both movements to get through one cloud tile on the map, while mountain tiles are impassable to all players and must be flown around.

The main mechanic of the game is managing your fuel resource.  Each player starts with, and can have a maximum of 6 fuel.  Each turn they use up one unit of fuel.  Scattered around the map are refuelling stations which will put a player to maximum fuel again.  These fuel-stations are one-time use and players will have to keep finding more to stay in the air.

Strategy in Flight Path results from choosing where to fly your plane in an attempt to cut other players off.  If a player can't manage to reach a fuel station and crash-lands, they must wait two full turns before they can begin moving again.  There are several different maps planned, some with choke points and others with limited fuel stations to keep the game intense.

A little interlude here for game atoms; I believe that progression is a big part of games, but maybe not quite a game atom.  It is on a higher level but encompasses a lot of the game atoms within itself.  All games involve a progression of start to finish, or setup to resolution.  It keeps the game going or keeps the player motivated, and can be thought of as a resource similar to time.  It could be linked to addiction in an MMO sense, as players have the strong urge to continually level up and progress to equip better weapons and armour.  More simply it can be thought of as: a game progresses until culmination when a winner is declared.

Warning: Progression in an MMO may reduce social skills progression by 100%.

 Games without progression would be endless.  It would be like Clue where you never find who did it, or Dungeons & Dragons where your character just sits around town all day.  Linear or open-ended, progression is the catalyst to which players strive to improve and continue.  Progression creates a sense of purpose and clarity of intent, a direction so to speak.  Without progression, why bother playing?


Moving on to the pick-up game; Rescue Racers features 2-4 players saving terrified people from scary dinosaurs.  The game map is similarly laid out in square tiles but this time the players are in helicopters and must rescue the people from rooftops in a city environment.  The game ends when all the humans are rescued, and the player with the most is declared the winner (and a hero!).

There goes the neighbourhood...

Each player rolls a die on their turn and MUST move the number of spaces they roll.  The player may make one change in direction during their move but ONLY one.  This means at most a player can fly in an L-shape in a single turn (I'll explain why this came about later).  Landing on a civilian means that you pick them up; at most a player can carry two civilians.  To score, the player must return their carried civilians back to their respective helipad at the edge of the map (where they started). Additionally, movement through skyscrapers and buildings is prohibited, and they must be avoided.

The competitive aspect comes from the ability to steal another player's civilians.  This happens when a player lands directly on another player's piece.  If they have room they steal the player's cargo and move two spaces directly in any direction from the opponent they landed on.  Some players may choose to go around rescuing while others may hang around their opponents helipads and attempt to steal all their passengers.

During play-testing our group came across a major flaw in the movement system.  Originally you could move to any space each step of your turn.  So if you wanted to move two spaces but rolled a six, you could bounce back and forth until you landed on it.  This created a phenomena where Tom and I kept rolling a 2, 4, or 6 and repeatedly stole each others passengers.  This combined with the bouncing two spaces mechanic created a situation where we stole back the passengers with a 50% success rate.

After a few turns of this it really became frustrating and the game quickly turned into a steal-fest; not very fun.  With this flaw in mind, we decided that the player could only change direction once per turn and after that the chance to steal from a player drastically dropped.  Oh it still happened, but it was a fair mechanic and we had a lot of fun with it.

While both these games feature a flying aspect, their goals and mechanics are quite differentiated.  Each has its own pace and a distinguishing flair to it, and both are a ton of fun.  On that note, I've got a couple more blogs to write so adieu for now!