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Rendering a "Slice" of a Sphere in Java - Efficiency

I'm attempting to render a hemisphere in java. However, I'm wanting to render the slice that is defined by 2 angles - Azimuth and Elevation. Since I'm defining a slice, I cannot (to my knowledge) use any built in primitives. If the azimuth range is defined 0-360 and the elevation range is defined as 0-70, this will be a hemisphere with an upside-down cone-shaped hole in the top.
When rendering this inside "cone", I have chosen to do it as triangles in 5 degree increments. This means that with a 360 degree cone, there are 73 different vertices (if I did the math correctly: 360/5degree slices with the origin or tip of the cone being shared with all sides, and all other vertices shared by adjacent triangle slices)
My question:
Is it more efficient to render these as a single polygon with with many vertices, or many triangles with only 3 vertices each. If I do a single polygon, will I still have to include all three points for each triangle, or if it is a shared vertex, would I only include it once? Sorry, my graphics rendering knowledge is limited. Also sorry for being so verbose; I'm hoping someone may spot something erroneous in my thought process which may clear things up either way.

First - Use Google to find an algorithm to create a sphere that is not a primitive.
Second - Somewhere down the chain - triangles will be used. Most likely by the underlying library. But for you - it depends upon whether or not you plan to chop up the created region. If you are not going to subdivide the region further I would just make it one polygon. Actually, after thinking about it for a second - you can always divide up the polygon afterwards too. So just make it one polygon.
I thought about it some more and decided to amend this answer. There are two ways you can create a polygon in openGL. You can either create it as a triangular mesh or as an outline polygon. So if you were asking "Should I use a triangular mesh or an outline polygon" I would say use the triangular mesh. It is a lot easier to break up the triangular mesh than a polygon outline since, to break the mesh, all you have to do is to just stop at one of the points, include the last two points in the new object, and continue on down the triangular mesh. An outline polygon requires you to go both left and right around the polygon to locate the two points where the break occurs. If that is clear. If not say so.
Update: 12:05pm
When making a polygon you can use a triangular mesh or a polygon outline. The outline is mainly good for 2D whereas the triangular mesh works in both 2D and 3D systems. If you have any kind of a polygon at all bigger than just three points then it is a good idea to put them all into an array. This allows you to use the built-in routines that take an array and simply go through it to build your polygon. By putting everything into an array you also make it easier on yourself to add new points or remove points or adjust points. All you do is to change the array entry and then call the same routine to draw everything again. (Which should be just a single call to a function.)

how to draw large grids for map editor?

I'm making a map editor for my 2d tile based RPG game, and I'm running into a roadblock. The problem is actually how to draw the grid lines efficiently for very large maps like, say 300x300 tiles.
Originally I called redrew the entire grid panel every time you moved the mouse or clicked(since it allows you to drag and also highlights the tile you are hovering over). This was horrible for large maps and was very slow.
So my solution was to create a bufferedImage for the grid of a specified size right when a new empty map was created, and redraw that image every time paint was called. This worked very well, except that for anything above 200x200ish java would run out of heap space in creating that bufferedImage. I can't really have a preloaded image because the user should be able to specify a new map to be any size. Also, I like the grid to be drawn over the tiles, otherwise the tiles cover up the lines and it looks messier. That means the grid has to be drawn again every time tiles are added right?
My question is, is there another way to draw a very large grid that will repaint each time you move the mouse?
The program Tiled can easily create maps of 1000x1000 or more, how is it done?? Thanks
EDIT:
I mean the actual grid LINES, not the grid content such as tiles. Right now when the grid is drawn it iterates through the 2D array and draws a line at every length of a tile.
EDIT:
I got it to work by painting only the visible portion of the screen. Turns out it's not that hard to find the coordinates of the view pane in a JScrollPane. :)

Ok so this is similair I guess to what im working on at the moment. I am currently writing a bit of simulation software with a 3D frontend in Ogre3D. I have a tile based map that can be easily 3000 x 3000 sometimes they may be even larger.
Now im not sure how you are going about drawing your grid, if you are just doing 2D/3D, but the main problem for me was how to apply different textures to each tile. If this isnt relevant then hopefully this may help anyway for future lol. The problem for me is that creating a seperate object for eacch tile is a no no, due to speed. If there are even 1024 x 1024 your looking at over 1 million tiles, each with attributes. This worked great on my first tests where I only had 10 x 10 maps but on larger maps it just ground to a halt.
What I am currently doing is rewriting it, the new approach is as follows. (You may be able to adapt this for what you are doing if it helps). The grid is now only 1 object, its a mesh in my case as im working in 3d. Each vertex holds a couple of values, one is the column and one is the row. I have a seperate texture which is the same size as my map, so for a map with 100 columns and 100 rows i create a texture 100 x 100 (this is created dynamically).
I then pass this texture and the vertices to my cg shader (this is where tyou may have to think of an equivalent way of doing things, but I think it should be doable). By looking up the colour at the pixel in this texture relating to the grid slot I want to texture I can find a colour value, these colour values relate to my texture atlas which holds all my possible textures for my map. All you then have to do is use that particular part of the texture atlas for that particular part of the mesh / grid.
I hope that makes some sort of sense, if not then id be happy to explain a bit more. I think even though im using CG shaders, you should be able to come up with an equivalent for non CG based stuff in java. The advantage of this is that you end up with one lookup texture, one object in memory and a buffer holding your vertices which is very quick for lookup.
Hope this helps.

Define if a contour is closed or not

I need a way to define if a contour represents a line or a closed shape. In Java, I have an object Shape which contains all the points which defines it again as separate objects. The object Point represents the coordinates of the point. I tried parsing the shapes with a recursion but for larger shapes, more then 150 points, the performance is very poor. I am attaching a picture of the shapes I want to parse to help better understand the question.
I am putting a image for better visualisation of the problem.
This is just showing all the shapes I got. I want to display just the two closed ones.
Thanks in advance.
Vassil Kossev

First idea: Use a suitable contour tracing algorithm to get an ordered contour. If your contour is closed you will get back to the first point eventually.
Second idea: Use a flood filling algorithm: if you get out of the bounding box of your object it is open, otherwise it is closed.
Third idea: use morphology. Remove lone pixels. Find all endpoints and branchpoints. Remove all branchpoints. Connected components with no endpoints are closed contours ("circles"), connected components with two endpoints are open contours ("lines"). Re-project connected components with no endpoints to the original image and keep only connected components that have common part with them. I think this could be implemented real-time, and the easiest to implement.

If you have contour lines of 1 pixel width, then you can count the number of neighbors for each point *. If every point of a given contour has 2 neighbors, then the contour is closed. If there are 2 points with only 1 neighbor each, then the contour is open.
If your contours are thicker, then you can apply a skeletonization algorithm to make them exactly 1 pixel thin. An interesting case is when you have side branches on a contour, but in this case there must be branching points with 3 neighbors, so similar situations can be handled easily.
* Counting neighbors is easy: use the original image! Choose one point of the contour randomly, check the neighboring 8 pixels, and count those which are part of the contour. Then repeat the neighbor-checking for these, and so on, until all pixels of the contour have been checked.

If the points are stored in order, you might be able to compare the first and last points. If they're spatially equal, the contour is closed.

Getting boundary information from a 3d array

Hey, I'm currently trying to extract information from a 3d array, where each entry represents a coordinate in order to draw something out of it. The problem is that the array is ridiculously large (and there are several of them) meaning I can't actually draw all of it.
What I'm trying to accomplish then, is just to draw a representation of the outside coordinates, a shell of the array if you'd like. This array is not full, can have large empty spaces with only a few pixels set, or have large clusters of pixel data grouped together. I do not know what kind of shape to expect (could be a simple cube, or a complex concave mesh), and am struggling to come up with an algorithm to effectively extract the border. This array effectively stores a set of points in a 3d space.
I thought of creating 6 2d meshes (one for each side of the 3d array), and getting the shallowest point they can find for each position, and then drawing them separetly. As I said however, this 3d shape could be concave, which creates problems with this approach. Imagine a cone with a circle on top (said circle bigger than the cone's base). While the top and side meshes would get the correct depth info out of the shape, the bottom mesh would connect the base to the circle through vertical lines, making me effectivelly loose the conical shape.
Then I thought of annalysing the array slice by slice, and creating 2 meshes from the slice data. I believe this should work for any type of shape, however I'm struggling to find an algorithm which accuratly gives me the border info for each slice. Once again, if you just try to create height maps from the slices, you will run into problems if they have any concavities. I also throught of some sort of edge tracking algorithm, but the array does not provide continuous data, and there is almost certainly not a continuous edge along each slice.
I tried looking into volume rendering, as used in medical imaging and such, as it deals with similar problems to the one I have, but couldn't really find anything that I could use.
If anyone has any experience with this sort of problem, or any valuable input, could you please point me in the right direction.
P.S. I would prefer to get a closed representation of the shell, thus my earlier 2d mesh approach. However, an approach that simply gives me the shell points, without any connection between them, that would still be extremely helpful.
Thank you,
Ze

I would start by reviewing your data structure. As you observed, the array does not maintain any obvious spatial relationships between points. An octree is a pretty good representation for data like you described. Depending upon the complexity of you point set, you may be able to find the crust using just the octree - assuming you have some connectivity between near points.
Alternatively, you may then turn to more rigorous algorithms like raycasting or marching cubes.

Guess, it's a bit late by now to be truly useful to you, but for reference I'd say this is a perfect scenario for volumetric modeling (as you guessed yourself). As long as you know the bounding box of your point cloud, you can map these coordinates to a voxel space and increase the density (value) of each voxel for each data point. Once you have your volume fully defined, you can then use the Marching cubes algorithm to produce a 3D surface mesh for a given threshold value (iso value). That resulting surface doesn't need to be continuous, but will wrap all voxels with values > isovalue inside. The 2D equivalent are heatmaps... You can refine the surface quality by adjusting the iso threshold (higher means tighter) and voxel resolution.
Since you're using Java, you might like to take a look at my toxiclibs volumeutils library, which also comes with sevaral examples (for Processing) showing the general approach...

Imagine a cone with a circle on top
(said circle bigger than the cone's
base). While the top and side meshes
would get the correct depth info out
of the shape, the bottom mesh would
connect the base to the circle through
vertical lines, making me effectivelly
loose the conical shape.
Even an example as simple as this would be impossible to reconstruct manually, let alone algorithmically. The possibility of your data representing a cylinder with a cone shaped hole is as likely as the vertices representing a cone with a disk attached to the top.
I do not know what kind of shape to
expect (could be a simple cube...
Again, without further information on how the data was generated, 8 vertices arranged in the form of a cube might as well represent 2 crossed squares. If you knew that the data was generated by, for example, a rotating 3d scanner of some sort then that would at least be a start.

Connect the dots - connect the line between contour points

I have a gray scale image of 64x64. I found the dots of the contour by a simple algorithm:
find brightest spot (Example: 100)
divide by 2 (100/2 = 50)
define a band around the result (50-5=45 to 50+5=55)
mark all dots that have value in the band (between 45 to 55)
The question now is, how do I decide of the order of connecting the dots?
(All references will be accepted, links, thoughts, etc')

Your algorithm allows the entire image, save for one pixel, to be "the contour". I'm not sure that's exactly what you want; usually a contour is a border between two different regions. The problem with your method is that you can get huge blobs of pixels that have no particularly obvious traversal order. If you have a contour that is a single pixel thick, then the traversal order is much more obvious: clockwise or counterclockwise.
Consider the following image.
........
..%%%%..
.%%%%...
...%%%%.
....%...
........
Here, I've marked everything "dark" (<50, perhaps) as % and everything bright as .. Now you can pick any pixel that is on the border between the two regions (I'll pick the dark side; you can draw the contour on the light side also, or with a little more work, directly between the light and dark sides.)
........
..%%%%..
.*%%%...
...%%%%.
....%...
........
Now you try to travel along the outer edge of the dark region, one pixel at a time. First, you look in the direction of something bright (directly left, for example). Then you rotate around--counterclockwise, let's say--until you hit a dark pixel.
........
..%%%%..
1*5%%...
234%%%%.
....%...
........
Once you hit position 5, you see that it's dark. So, you mark it as part of the contour and then try find the next piece on the contour by sweeping around starting from the pixel you just came from
........
..%%%%..
.0*%%...
.123%%%.
....%...
........
Here 0 is where you came from--and you're not going back there--and then you try pixels 1 and 2 (both light, which is not okay), until you hit pixel 3, which is dark.
In this way, you can walk around the contour pixel by pixel--both identifying the contour and getting the order of pixels--until you collide with the same pixel you started with and will leave from it so that you hit the same pixel that you did the first time you left it. Then the contour is closed. In our example, where we're making an 8-connected contour (i.e. we look at 8 neighbors, not 4), we'd get the following (where # denotes a contour point).
........
..####..
.##%#...
...#%##.
....#...
........
(You have to have this two-in-a-row criterion or if you have a dark region a single pixel wide, you'll walk up it but then not be able to walk back down along it.)
At this point, you've covered one entire boundary. But there might be others. Keep looking for dark pixels next to light ones until you have drawn a contour on top of all of them. Now you've converted your two-level picture (dark & bright pixels) into a set of contours.
If the contours end up too noisy, consider blurring the image first. That will smooth the contours out. (Alternatively, you can find the contours first and then average the coordinates with a moving window.)

In general, a given set of points can be connected in multiple ways to make different shapes.
For example, consider a set of 5 points consisting of the corners of a square and its center. These points can be connected to form a square with one side "dented in" to the center. But which side? There is no unique answer.
Other shapes can be much more complicated, with no obvious way to connect the dots.
If you are allowed to reduce your set of points to a convex hull, then it would be much easier.

I have also tried to create an algorithm that will connect contour dots into the smooth curve. See my open-source project http://outliner.codeplex.com.
The idea is the same as proposed by FUZxxl but I do not understand his worries about complexity: the time of processing is proportional to the total length of all contour strokes.

I don't know if collecting those points will get you far. (I can come up with situations in which it's almost impossible to tell which order they should come in.)
How about going to the brightest point.
Go to the brightness point of, say, 360 points surrounding this point at a distance of, say, 5 pixels.
Continue from there, but make sure you don't go back where you came from :)

Maybe try:
Start at a
Find the nearest point b
Connect a with b
and so on.
Probably not good, as complexity is something like O(n²). You may simplify this by looking only for points near the start, as aioobe suggest. This algorithm is good, if the points are just like 2-3px away from each other, but may create very strange grids.

See also Flood fill
and the lovely applet under SO
mapping-a-branching-tile-path .