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Custom 3D graphics engine... where to plot Z coordinate

I'm brainstorming a way to create a basic custom 3D engine by myself and it's all very new to me, as I've only practiced 2D graphics.
Assuming that we have calculations for a Z coordinate using the recommended formulas given here, how might I go about plotting the Z coordinate? I understand that by default, Java graphics draw on a 2D field, which means that the only coordinates I can draw to is either the X or Y coordinate... and that's where I'm stuck.
3D development is not taught in my college... so I really appreciate good feedback. The tutors here never practiced creating 3D engines, so I'm very frustrated because learning this concept is crucial.

In order to map 3D coordinates to a 2D plane (the screen) you'll need to understand the concept of the Frustum and how to utilize a Projection Matrix.
This article does an excellent job of explaining what it does and how to implement one. Writing your own engine for this seems to be a massive undertaking and assumes you understand the vector and matrix mathematics. If not, I would suggest doing some reading on linear algebra; it's fundamental to this kind of programming.
If you'd like to work with some already established technologies, look into OpenGL for Java.

I know how to make a 3d program in English but not in code.
If you would like to make one, please let me know. So I can see how active you are.
Oh my apologies. I didn't answer*. Let me elaborate on your predicament.
Z axis doesn't exist. It's an illusion. You need to produce a procedural code to establish this illusion.

Animate a cube turning via mathematics (Java)

For a school project i have made a program that can solve a rubiks cube (you know, that cube with all the colors). But now my teachers asked if i could do some research and try out 3d animation for one of the sides. But they want to see the mathematical way to do it. I have found a way to move the corners with the use of polar coordinates. But i do not know how i could render a cube in 3d and be able to animate it.
So my question is: how can i render things like a cube in 3d (or are there any good libraries for it) and how could i use these polar coordinates to animate it?
And is there a good tutorial out there for java 3d rendering?
i must say that i have absolutely no experience with 3d rendering, so it might be a bit difficult. But i really would like to try it out.
thanks in advance

Depending on whether you want to take an existing implementation or if you want to build code for 3D animations from scratch, you might try this tutorial. Graphics programming in this area can be quite involved; a full answer of the question is beyond the scope of this site. However, there are a few main areas.
Usage of vector math for transformation of objects (translation, rotation). This can be done directly or via projective geometry using 4-by-4 matrices. The latter is easier for concatenation of transformations.
Backface culling to remove faces of the object which cannot be seen by the camera.
Using a projection and a camera model to transform 3D coordinates to 2D coordinates.
Using a rasterizer to render the 3D vector information to the screen. Here Bresenham's algorithm might be a good start.

I would suggest you look at one of the 3D libraries. One that I've used a lot and found to be excellent is JMonkeyEngine (JME) which is designed for games but would work well for your needs. It also has an excellent tutorial that takes you from basic to very complex. In fact the first step in the tutorial is a revolving coloured cube!
JME takes a huge amount of the work out of 3D modelling. You build a scene in code with materials, lights etc. and JME does all the work to render it. You can even build your models in a tool such as Blender so you don't even need to do the modelling in code. But I will warn you that using modelling tools is definitely not for the faint hearted.

Processing/ Voronoi Diagram 3D - Simple Box

I searched a bunch of websites to find a working example of how to create a Voronoi based 3D Box.
The following link shows you guys for what i am looking for. Can someone help me out with this?
I created "Seedpoints" in a 3D Box and now what? ... couldn´t find a good and simple example on openprocessing either.
Thank you in advance.
Picture

I think Voro++ is doing exactly what you want. However, it is written in C++ but creating a small wrapper using swig for example will provide you a java binding.

You can start with 2D texture created by processing library Mesh (just use getEdges() function to draw border lines of regions) and use it with texture mapping on your 3D box.

Voronoi diagrams can be easily handled with pixel shaders depending on the format of your seed points This example is the best I've found so far but it relies upon points whose coordinates are computed inside the shader, at least to my understanding.

Java/Graphics: Plotting 3d coordinates?

I'm coding a programm, that will produce 3d coordinates for a rocket and I would like to do a rudimentally graphic output for this.
it just has to be scaleable and rotationable, so that you can change the view manually.
the postions should be connected by lines and
it ould be nice to have spheres for earth and moon ( and perhaps addtional celestial objects).
I think, there should be some ready stuff for this kind of plott already available, but I couldn't find one.
So that's why I'm here to ask you, if you know such a thing.
and if there isn't I would kike to ask you how a bignner like me should start this?
I ust coded for console apllications, because there was no need for a real graphics output.
thank you in advance for any tip! :)
Andreas

I don't think there are sand-box ready things you can use to draw customizable 3d objects in Java, if you can live without strange things you can you just a graph library able to draw 3d graphs like for example jMathTools (link).. otherwise you should go into J3D with opengl and similar things.
I don't think they exist just because doing simple things is trivial if you work with OpenGL or similar APIs..
Doing what you need with OpenGL is not complex at all, just a GL_LINE_STRIP to draw the trajectory and some primitives if you need earth, moon and so on.. rotating and scaling come implicitly moving the camera of your viewport..
Take a look at: Java3D or JOGL

I can't believe nobody has mentioned this yet, but the NASA WorldWind project seems like exactly what you need: http://worldwind.arc.nasa.gov/java/ You can extend it with JOGL if needed, or you can use some of the vast modeling objects already available to mark trajectory and location in 3D coordinates, complete with zooming/rotating and the like. Having accurate Earth layers is nice as well =)

Use JOGL! It is easy to install, and if you know Java it should be easy. There are a few things in JOGL that require you to be decent in trigonometry. This tutorial might help you get started: http://www.youtube.com/watch?v=rT02jFYrXv0

Do I need to use OpenGL in my 2D Java sim game?

I have recently been developing a sim game in java, as many of my questions show, and it's come a long way! Graphically, it is somewhat lacking, and at current I'm using shapes for items, people, rooms etc.
I was looking at other similar projects, and noticed that one was using OpenGL. I have been reading CokeAndCode "space invaders 103 - refactoring and OpenGL", and I still don't know if it is something I need in my game or not.
Here is a video that I used for a previous question, but it still shows basically what I have so far (http://www.screenjelly.com/watch/Bd7d7pObyFo), although I have done a lot of refactoring and re coding over the last few weeks, but graphically, nothing has changed. As I understand it, I'm currently using java2D to do this.
I really don't know how I should continue graphically with this game. This is my first project I have done outside of learning for my own enjoyment, and so I'm still rather new to this.
Thanks in advance!

This could turn into a long subjective conversation quickly but I want to state the fact that you don't need openGL. Your application doesn't need to be the best looking one out there. Nethack still attracts people and between you and me : the graphics sucks.
Do you want to learn about 2D and 3D graphics and textures and so on ? Then try stuff... best way to learn. Then you can add this to your resume.
There are a lot of tutorial to do your first steps in OpenGL or some other graphic library. You can even try Qt Jambi. But once you start, you're in for a ride ;)

According to this, it's still largely possible to implement a working graphical game in Java2D with decent performance, as long as you make sure not to do a certain number of bad things.
It might help you to check and see how your approach is, compared to this.
I have no idea how far along Java has come with OpenGL support, so were I in your place I would probably just see how much refactoring of the Java2D code I could do, and figure out what to do from there.
Hope this helps, at least a bit.

One good side of using opengl (even for 2D graphics) is that you will get (if properly done) hardware graphics acceleration for your scenes.
Also, you can use orthogonal projection and keep one of the axis (Z) as zero to do your 2D graphics. It will be easy if you want to add a 3D effect (like lightning or something) if you use OpenGL.
However it all depends on how much you want to improve the graphics, since adding OpenGL might make things a little more complicated than plain Java2D.

How to continue graphically: use textures, more interesting animations (implement a simple physics engine and/or collision detection, that always looks nice).
When you go 3d (for example using opengl) you can add lighting effects to the equation, that usually does a lot to the aesthetics of the whole. For example if the moving circle was a sphere with a nice texture (marble or something), then you could make it really role over the board, and you could specify diffuse and specular reflection values to vary the lighting like for example here.
Camera movement can also beef up the graphics.