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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.

Shape Detection in Java using OpenCV

I need to detect shapes and their colours on a taken image. These shapes are: a heart, a rectangle, a star and a circle. Each shape has one of 5 predefined colours. Colour recognition works fine, but shape recognition is a real problem.
After hours and hours of googling, trying and tweaking code, the best I have come up with is the following procedure:
First, read the image and convert it to grayscale.
Then, apply blur to reduce the noise from the background.
Medianblur seems to work best here. Normal blur has little effect, and Gaussian blur rounds the edges of the shapes which gives trouble.
Next, apply threshhold.
AdaptiveThreshold doesn't give the results I expected; the result vary widely with each image. I now apply two thresholds: One uses Otsu's algorithm to filter the light shapes, and the other uses the Binary Inverted value for the darker shapes.
Finally, find contours on the two threshholds and merge them in one list.
By the amount of points found in each contour, I decide which shape is found.
I have tried adding Canny, sharpening the image, different threshholds, Convex Hull, Houghes, etc. I probably tried every possible value for each method as well. For now, I can get things working with the above procedure on a few images, but then it fails again on a new image. Either it detects too much points in a contour, or it doesn't detect the shape at all.
I am really stuck and dont know what else to try. One thing I still have to work out is using masks, but I can't find much information on that and don't know if it would make any difference at all.
Any advice is more than welcome. If you would like to see my code, please ask. You can find sample images here: http://tinypic.com/a/34tbr/1

What is algorithm to detect a shape on some image? [duplicate]

I want to detect a circle, rectangle shaped object in an image and read the information from that object. Is there any api in java which will be helpful to me?
Ex: Detect a round shaped coin in a white background and obtain information about that that coin like ( value of a coin, etc.)
Thanks.

Here's an answer to a similar question for C++.
For Java, you can use the OpenCV wrappers. However, once you understand the essence of the approach you should be able to solve your problem using whichever framework is available.

Circles are perfect targets for the Hough transform. Check this out Detect circles with HT and OpenCV
Rectangles are a bit harder since the Hough Transform is not rotation invariant. You can go into edge detection and fast fitting (Fast line and rectangle detection by clustering and grouping)

Java advanced image manipulation

I am having a problem with manipulating images in java 7. I have researched the problem I am having for three weeks and have failed to find a solution,
I am trying to set an image over an area, basically setting the corner posistions.
I am using a BufferedImage.
This is for a 3D game where I am writing the 3D conversion code. I have managed to create a 3d world, and populate it with cubes, filling in the sides with graphics.fillPolygon():
What I would like to do is draw an image that fills a polygon's shape.
Any help I will be grateful for (even if it is formating this post better).

You can use transformations on your graphics. Here is a little tutorial on it. With that you can transform already drawn stuff. If you want to transform multiple images in different ways, you can draw them on different canvases and transform then separately. Then you can merge the images together...
But I would recommend using a 3D engine (JOGL, jMonkeyEngine, or others) for that (unless you want to learn about the geometric calculations with this task). It is also much faster to use OpenGL than drawing the stuff by yourself and doing the calculations in code (most probably meaning: on the CPU and not the GPU).

Have you tried using the drawImage? instead of .fillPolygon?

how to detect shapes in an image?

I want to detect a circle, rectangle shaped object in an image and read the information from that object. Is there any api in java which will be helpful to me?
Ex: Detect a round shaped coin in a white background and obtain information about that that coin like ( value of a coin, etc.)
Thanks.

Here's an answer to a similar question for C++.
For Java, you can use the OpenCV wrappers. However, once you understand the essence of the approach you should be able to solve your problem using whichever framework is available.

Circles are perfect targets for the Hough transform. Check this out Detect circles with HT and OpenCV
Rectangles are a bit harder since the Hough Transform is not rotation invariant. You can go into edge detection and fast fitting (Fast line and rectangle detection by clustering and grouping)