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How can I stop my textures from becoming low resolution in libGDX

I am using libGDX to make a small game, I made a little sprite (32x32) that is shown in the center of the screen. For some reason when I render the texture to the screen it loses its quality. Since the textures are so small I made the screen width and height 200 and 100 respectively. Any tips or answers would be much appreciated.

Your sprite (32x32) needs to be displayed on an area which is larger than 32x32, meaning that the image needs to be upscaled and interpolated (i.e. pixels between the 32 known ones need to be calculated). A common approach is smooth (often times linear) interpolation to fill in the additional pixels, which works well for photorealistic textures; it appears to have occurred here.
For pixel-art, you likely want "nearest-neighbor" interpolation instead. While the exact way to set it depends on the structure of your code, you may be able to do something like:
textureObject.setFilter(TextureFilter.Nearest, TextureFilter.Nearest);

LWJGL using texture as alpha mask

I am creating a 2D game with lwjgl and slick-util. For a special feature in my game I wanted to be able to give textures a certain opacity. I have managed to figure this out but the next step is giving a Texture as a paramter which will give me the ability to give certain textures certain opacities in certain spots.
Note: I have gotten it sort of working before, but the mask also seemed to remove my background image, which I do not want.
I cannot post images because I dont have enough reputation or something but anyway what I want to basically do is:
first render a background image.
then render another images on top with a mask on it, I do not want this mask to apply onto the background.
How would I go about doing this?

I think you use wrong blending mode. If you did not change default blending mode, then you need:
glEnable (GL_BLEND); // Enable blending.
glBlendFunc(GL_SRC_ALPHA, GL_ONE_MINUS_SRC_ALPHA); // Setup blending function.
I think in you case, texture does not blend with background, it simple replaces background.

Android - Turn off Smoothness for Drawing on a Canvas using Bitmaps and Matrices

I have some very small images (20 by 20 pixels) which I am drawing using matrices onto a canvas using Canvas.drawBitmap(Bitmap, Matrix, Paint). The problem is that I am scaling these up about 5-10 times larger when I am drawing them and it is automatically re-sampling these images with smoothness. What I want is nearest-neighbour style re-sampling (so it will look pixelated) not the smoothness. I cannot find a way to change this. Also creating another whole image that is larger to store a properly re-sampled picture is not an option since I am under memory constraints. Thanks for any help!

You need to set up the paint you pass to drawBitmap, like so:
paint.setFilterBitmap(false);

Generating Very Large Images at Runtime with OpenGL and libgdx

I am generating very large hex grids (up to 120k total hexes at 32px wide hexes results in over 12k wide images) and I'm trying to find an efficient way to bind these to OpenGL textures in libgdx. I was thinking of using multiple FBOs and breaking the grid up as necessary into tiles, but I'm not sure how to ensure continuity between the FBOs. I can't start with one massive FBO, because that is backed up by a texture so it would fail from trying to load it to video memory. I can't use a standard bitmap on the heap because I need the drawing functionality of an OpenGL surface.
So what I was thinking was I would need to overdraw on the FBOs and somehow pick up on the next FBO exactly where the previous left off. However I'm not sure how to go about this. I'm drawing the hex grid with a series of hexagonal meshes, FYI.
Of course, there's probably some other much simpler and more efficient way to do this that I'm not even thinking of, which is why I pose this question to you fine people!

You have to draw it in pieces. You need to be able to draw your hex grid from an arbitrary position. This means being able to compute which hexes to draw based on a rectangle overlaid over the map. This isn't a hard problem, and I wouldn't worry too much about drawing extra stuff off-screen. You should master this ability to view the hexmap from any position before moving on.
Once you've mastered that, it's really simple.
Draw the top-left corner and store the pixel data. Then move the area you're drawing over exactly one image width. Draw and store that. Move the area over one image width. Draw and store it. Keep doing that until you've covered the entire width.
Move down one image height and repeat the process. Once you've run out of width and height, you're done. Save your mega-huge image.
You don't need FBOs for this. You could draw it to the screen if you wanted. Though if you want maximum performance, I would suggest using FBOs, double buffering them, and using glReadPixels though a pixel buffer object. That should cut down a lot on latency.

Using a canvas much larger than the screen

I'm trying to draw a 2D contour plot of some data on Android and I'm wondering what the best approach would be to draw those. The whole datasets can be relatively large (2k * 2k points) and zooming and moving inside the plot should be very fast. Most of the time only a small part of the data will be drawn as the user has zoomed in on the data.
My idea now would be to draw the whole plot onto a large canvas, but clip it to the portion visible on the screen, so that only that part would be really drawn in the end. I find the 2D drawing API of Android somewhat confusing and I'm not sure if this is really a feasible approach and how I would then go about executing it.
So my questions are:
Is it a good idea to draw onto a canvas much larger than the screen and use clipping to display only the relevant part?
How would I create a larger canvas and how would I select which parts should be drawn?

You should start the other way around. Instead of creating a huge canvas you should detect what part of your plot you need to draw and draw only that.
So basically you need some navigation/scrolling and you need to keep the offset from the starting point in memory to calculate where you are. Using the offset you can easily zoom in and out because you just need to scale the plot to the screen.

Is it a good idea to draw onto a
canvas much larger than the screen and
use clipping to display only the
relevant part?
A better question might be, do you have any other options. Some might argue that this is a bad idea since your going to keep memory in use when it isn't relevant to whats happening on the UI. However, from my experiences with the Canvas, I think you'll find this should work out just fine. Now, if you are trying to keep "5 square miles" of canvas in memory your definitely going to have to find a better way to manage it.
How would I create a larger canvas and
how would I select which parts should
be drawn?
I would expect that you will be creating your own "scrolling" method when the user touches the screen via overriding the onTouchEvent method. Basically your going to need to keep track of a starting point X and Y and just track that value as you move the Canvas on screen. In order to move the Canvas there are a number of built in's like translate and scale that you can use to both move the Canvas in X and Y as well as scale it when the user zooms in or out.

I don't think that is a good idea to draw your 2D contour plot on a big bitmap because you need a vector type graphics to zoom in and out in order to keep it sharp. Only pictures are good to scale down but graphs will lose thin lines or come out deformed when scaled down in bitmaps.
The proper way is to do it all mathematically and to calculate which part of the graph should be drawn for required position and zoom. Using anti_alias paint for lines and text, the graph would always come out sharp and good...
When the user zooms out, some items should not be drawn as they could not fit into the screen or would clutter it. So the graph would be always optimised for the zoom level...