Understanding the libGDX Projection Matrix

Question

Over the past few weeks I've been attempting to learn the libGDX library. I'm finding it hard, especially for my first endeavor toward game development, to comprehend the system of Camera/viewport relationships. One line of code that I've been told to use, and the API mentions, is:

    batch.setProjectionMatrix(camera.combined); 

Despite a good 4 hours of research, I'm still lacking a complete understanding of the functionality of this code. It is to my basic understanding that it "tells" the batch where the camera is looking. My lack of comprehension is depressing and angering, and I'd appreciate if anyone could assist me. Another issue with the code snippet is that I'm unsure of when it's necessary to implement (in the render method, create method, etc).

Answer 1

Consider taking a picture with a camera. E.g. using your smartphone camera taking a picture of a bench in the park. When you do that, then you'll see the bench in the park on the screen of your smartphone. This might seem very obvious, but let's look at what this involves.

The location of the bench on the picture is relative to where you were standing when taking the photo. In other words, it is relative to the camera. In a typical game, you don't place object relative to the object. Instead you place them in your game world. Translating between your game world and your camera, is done using a matrix (which is simply a mathematical way to transform coordinates). E.g. when you move the camera to the right, then the bench moves to the left on the photo. This is called the View matrix.

The exact location of the bench on the picture also depends on the distance between bench and the camera. At least, it does in 3D (2D is very similar, so keep reading). When it is further away it is smaller, when it is close to the camera it is bigger. This is called a perspective projection. You could also have an orthographic projection, in which case the size of the object does not change according to the distance to the camera. Either way, the location and size of the bench in the park is translated to the location and size in pixels on the screen. E.g. the bench is two meters wide in the park, while it is 380 pixels on the photo. This is called the projection matrix.

camera.combined represents the combined view and projection matrix. In other words: it describes where things in your game world should be rendered onto the screen.

Calling batch.setProjectionMatrix(cam.combined); instruct the batch to use that combined matrix. You should call that whenever the value changes. This is typically when resize is called and also whenever you move or otherwise alter the camera.

If you are uncertain then you can call that in the start of your render method.

Answer 2

The other answer is excellent, but I figure a different way of describing it might help it to click.

You generally deal with your game in "world space", a coordinate system that is analogous to the real world. In linear algebra, you can convert points in space from one coordinate system to another by multiplying the point's coordinates by a matrix that represents the relation between two coordinate systems.

The view matrix is multiplied by a point to convert it from world space to camera space (the camera's point of view). The projection matrix is used to convert a point from camera space to screen space (the flat 2D rectangle of your device's screen). When you call update() on a camera in Libgdx, it applies your latest changes to position, orientation, viewport size, field of view, etc. to its view and projection matrices so they can be used in shaders.

You rarely need to deal with stuff in camera space in 2D, so SpriteBatch doesn't need separate view and projection matrices. They can be combined into a single matrix that converts straight from world space to screen space, which is already done automatically in the Camera, hence the camera.combined matrix.

SpriteBatch has a default built-in shader that multiplies this projection matrix by all the vertices of your sprites so they will be properly mapped to the flat screen.

You should call setProjectionMatrix whenever you have moved the camera or resized the screen.

There is a third type of matrix called a model matrix that is used for 3D stuff. A model matrix describes the model's orientation, scale, and position in world space. So it is multiplied by coordinates in the model to move them from local space to world space.