Develop Reference

Plotting 3D Math Functions in Android

as part of my project, I need to plot 2D and 3D functions in android using android studio. I know how to plot 2D functions but I'm struggling with 3D functions.
What is the best way to plot 3D functions? What do I need and where do I start?
I'm not looking for code or external libraries that do all the work, I just need to know what I need to learn to be able to do it myself.
Thanks in advance.

I know how to plot 2D functions but I'm struggling with 3D functions.
What is the best way to plot 3D functions? What do I need and where do I start?
I'm not looking for code or external libraries that do all the work, I just need to know what I need to learn to be able to do it myself.
Since you already understand 2D and want to advance to 3D there's a simple and non-optimal method:
Decide on how much z depth you desire:
EG: Currently your limits for x and y in your drawing functions are 1920 and 1080 (or even 4096x4096), if you want to save memory and have things a bit low resolution use a size of 1920x1080x1000 - that's going to use 1000x more memory and has the potential to increase the drawing time of some calls by 1000 times - but that's the cost of 3D.
A more practical limit is matrices of 8192,8192,16384 but be aware that video games at that resolution need 4-6GB graphic cards to work half decently (more being a bit better) - so you'll be chewing up some main memory starting at that size.
It's easy enough to implement a smaller drawing space and simply increase your allocation and limit variables later, not only does that test that future increases will go smoothly but it allows everything to run faster while you're ironing the bugs out.
Add a 3rd dimension to the functions:
EG: Instead of a function that is simply line_draw(x,y) change it to line_draw(x,y,z), use the global variable z_limit (or whatever you decide to name it) to test that z doesn't exceed the limit.
You'll need to decide if objects at the maximum distance are a dot or not visible. While testing having all z's past the limit changed to the limit value (thus making them a visible dot) is useful. For the finished product once it goes past the limit that you are implementing it's best that it isn't visible.
Start by allocating the drawing buffer and implementing a single function first, there's no point (and possibly great frustration) changing everything and hoping it's just going to work - it should but if it doesn't you'll have a lot on your plate if there's a common fault in every function.
Once you have this 3D buffer filled with an image (start with just a few 3D lines, such as a full screen sized "X" and "+") you draw to your 2D screen X,Y by starting at the largest value of Z first (EG: z=1000). Once you finish that layer decrement z and continue, drawing each layer until you reach zero, the objects closest to you.
That's the simplest (and slowest) way to make certain that closest objects obscure the furthest objects.
Now does it look OK? You don't want distant objects the same size (or larger) than the closest objects, you want to make certain that you scale them.
The reason to choose numbers such as 8192 is because after writing your functions in C (or whichever language you choose) you'll want to optimize them with several versions each, written in assembly language, optimized for specific CPUs and GPU architectures. Without specifically optimized versions everything will be extremely slow.
I understand that you don't want to use a library but looking at several should give you an idea of the work involved and how you might implement your own. No need to copy, improve instead.
There are similar questions and answers that might fill in the blanks:
Reddit - "I want to create a 3D engine from scratch. Where do I start?"
Davrous - "Tutorial series: learning how to write a 3D soft engine from scratch in C#, TypeScript or JavaScript"
GameDev.StackExchange - "How to write my own 3-D graphics library for Windows? [closed]"

Tips regarding high performance drawing in Android

Background
I'm writing a graphing library for an android application (yes yes, I know there are plenty out there but none that offer the customizability we need).
I want the graphs to zoomable and pan-able.
Problem
I want the experience to be smooth, leave a small CPU footprint.
Solutions
Use View.onDraw(Canvas)
Use high resolution Bitmap
Use OpenGL
View.onDraw():
Benefits
Some what easy to implement
Drawbacks
Bad performance? (unless it uses OpenGL, does it?)
Bitmap:
Benefits
Really easy to implement
Great performance
Drawbacks
Have to use scaling which is ugly
OpenGL:
Benefits
Probably good performance depending on my implementation
Drawbacks
More work to implement
Final words
OpenGL would probably be the professional solution and would definitely offer more flexibility but it would require more work (how much is unclear).
One thing that is definitely easier in OpenGL is panning/zooming since I can just manipulate the matrix to get it right, the rest should be harder though I think.
I'm not afraid to get my hands dirty but I want to know I'm heading in the right direction before I start digging.
Have I missed any solutions? Are all my solutions sane?
Additional notes:
I can add that when a graph changes I want to animated the changes, this will perhaps be the most demanding task of all.

The problem with using Views is that you inherit from the overhead of the UI toolkit itself. While the toolkit is pretty well optimized, what it does it not necessarily what you want. The biggest drawback when you want to control your drawing is the invalidate/draw loop.
You can work around this "issue" by using a SurfaceView. A SurfaceView lets you render onto a window using your own rendering thread, thus bypassing the UI toolkit's overhead. And you can still use the Canvas 2D rendering API.
Canvas is however using a software rendering pipeline. Your performance will mostly depend on the speed of the CPU and the bandwidth available. In practice, it's rarely as fast as OpenGL. Android 3.0 offer a new hardware pipeline for Canvas but only when rendering through Views. You cannot at this time use the hardware pipeline to render directly onto a SurfaceView.
I would recommend you give SurfaceView a try first. If you write your code correctly (don't draw more than you need it, redraw only what has changed, etc.) you should be able to achieve the performance you seek. If that doesn't work, go with OpenGL.

Simple particle system on Android using OpenGL ES 1.0

I'm trying to put a particle system together in Android, using OpenGL. I want a few thousand particles, most of which will probably be offscreen at any given time. They're fairly simple particles visually, and my world is 2D, but they will be moving, changing colour (not size - they're 2x2), and I need to be able to add and remove then.
I currently have an array which I iterate through, handling velocity changes, managing lifecyling (killing old ones, adding new ones), and plotting them, using glDrawArrays. What OpenGl is pointing at, though, for this call, is a single vertex; I glTranslatex it to the relevant co-ords for each particle I want to plot, one at a time, set the colour with glColor4x then glDrawArrays it. It works, but it's a bit slow and only works for a few hundred particles. I'm handling the clipping myself.
I've written a system to support static particles which I have loaded into a vertex/colourarray and plot using glDrawArrays, but this approach only seems suitable for particles which will never change relative location (ie I move all of them using glTranslate), colour and where I don't need to add/remove particles. A few tests on my phone (HTC Desire) suggest that trying to alter the contents of those arrays (which are ByteBuffers, pointed to by OpenGL) is extremely slow.
Perhaps there's some way of manually writing the screen myself with the CPU. If I'm just plotting 1x1/2x2 dots on the screen, and I'm purely interested in writing and not doing any blending/antialiasing, is this an option? Would it be quicker than whatever OpenGl is doing?
(200 or so particles on a 1ghz machine with megs of ram. This is way slower than I was getting 20 years ago on a 7mhz machine with <500k of ram! I appreciate I'm using Java here, but surely there must be a better solution. Do I have to use the NDK to get the power of C++, or is what I'm after possible)

I've been hoping somebody might answer this definitively, as I'll be needing particles on Android myself. (I'm working in C++, though -- Currently using glDrawArrays(), but haven't pushed particles to the limit yet.)
I found this thread on gamedev.stackexchange.com (not Android-specific), and nobody can agree on the best approach there, but you might want to try a few things out and see for yourself.
I was going to suggest glDrawArrays(GL_POINTS, ...) with glPointSize(), but the guy asking the question there seemed unhappy with it.
Let us know if you find a good solution!

Android drawBitmap Performance For Lots of Bitmaps?

I'm in the process of writing an Android game and I seem to be having performance issues with drawing to the Canvas. My game has multiple levels, and each has (obviously) a different number of objects in it.
The strange thing is that in one level, which contains 45 images, runs flawlessly (almost 60 fps). However, another level, which contains 81 images, barely runs at all (11 fps); it is pretty much unplayable. Does this seem odd to anybody besides me?
All of the images that I use are .png's and the only difference between the aforementioned levels is the number of images.
What's going on here? Can the Canvas simply not draw this many images each game loop? How would you guys recommend that I improve this performance?
Thanks in advance.

Seems strange to me as well. I am also developing a game, lots of levels, I can easily have a 100 game objects on screen, have not seen a similar problem.
Used properly, drawbitmap should be very fast indeed; it is little more than a copy command. I don't even draw circles natively; I have Bitmaps of pre-rendered circles.
However, the performance of Bitmaps in Android is very sensitive to how you do it. Creating Bitmaps can be very expensive, as Android can by default auto-scale the pngs which is CPU intensive. All this stuff needs to be done exactly once, outside of your rendering loop.
I suspect that you are looking in the wrong place. If you create and use the same sorts of images in the same sorts of ways, then doubling the number of screen images should not reduce performance by a a factor of over 4. At most it should be linear (a factor of 2).
My first suspicion would be that most of your CPU time is spent in collision detection. Unlike drawing bitmaps, this usually goes up as the square of the number of interacting objects, because every object has to be tested for collision against every other object. You doubled the number of game objects but your performance went down to a quarter, ie according to the square of the number of objects. If this is the case, don't despair; there are ways of doing collision detection which do not grow as the square of the number of objects.
In the mean time, I would do basic testing. What happens if you don't actually draw half the objects? Does the game run much faster? If not, its nothing to do with drawing.

I think this lecture will help you. Go to the 45 minute . There is a graph comparing the Canvas method and the OpenGl method. I think it is the answer.

I encountered a similar problem with performance - ie, level 1 ran great and level 2 didn't
Turned it wasn't the rendering that was a fault (at least not specifically). It was something else specific to the level logic that was causing a bottleneck.
Point is ... Traceview is your best friend.
The method profiling showed where the CPU was spending its time and why the glitch in the framerate was happening. (incidentally, the rendering cost was also higher in Level 2 but wasn't the bottleneck)

Can I increase performances using glscissor

I'm working on a 2D game for android using OpenGL ES 1.1 and I would like to know if this idea is good/bad/useless.
I have a screen divided in 3 sections, so I used scissors to avoid object overlapping from one view to the other.
I roughly understand the low level implementation of scissor and since my draws take a big part of the computation, I'm looking for ideas to speed it up.
My current idea is as follows:
If I put a glscissor around each object before I draw it, would I increase the speed of my application.
The idea is if I put a GLScissor, (center+/-sizetexture), then the OpenGL pipeline will have less tests to do (since it can discard 90~99% of the surface thanks to the glscissors.
So to all opengl experts, is this good, bad or will have no impact ? And why?

It shouldn't have any impact, IMHO. I'm not an expert, but my thinking is as follows:
Scissor test saves on your GPU's fill rate (the amount of fragments/pixels a hardware can put in the framebuffer per second),
if you put a glScissor around each object, the test won't actually cut off anything - the same number of pixels will be rendered, so no fill rate will be saved.
If you want to have your rendering optimized, a good place to start is to make sure you're doing optimal batching and reduce the number of draw calls or complex state switches (texture switches).
Of course the correct approach to optimizations is to try to diagnose why is your rendering slow, so the above is just my guess which may or may not help in your particular situation.