I'm having difficulty of knowing how to approach or how to tackle this problem. I've looked at some tutorials but they are meant for programmers that already know what they're doing. I followed a video on how to perform a form of pixel collision that applies to regular bounding boxes, where if the bounding boxes collide it checks if any non-transparent pixel in both intersecting boxes are overlapping. If they do, then a boolean will return a true value. Where and how could I start to implement the changing of the bounding box's axis in a rotating object to compliment the texture's appreance? I wouldn't prefer being pointed to an external tutorial because most of the ones I've read assumes the programmer knows everything the writer is talking about.
I've also looked at some source code that perfectly demonstrates what I'm looking for, but it seems I need a very in depth explanation to make any use of reading code as well.
First off, I don't really recommend doing this, as it's gonna be either computing- or resource-intensive (or both).
That said, one idea is to still do your aforementioned AABB method of straight-up pixel on pixel. This requires you to maintain your own pixel data in memory to only be used for collision, as opposed to relying strictly on the texture's data.
To be more specific, using this method you will have to generate what is essentially an "image", or 2 dimensional matrix of some kind, one that represents/follows your rotated image's pixels. But you will not be storing color information in it, as you would with a normal image. Instead, each "pixel" or entry in the structure shall be collision data: "block" or "not block". You could easily use a bitmask to represent this, with 1 meaning "block" and 0 meaning "not block", and you'd need one bit per pixel. (NOTE: Usually you don't need more than just a boolean "on" & "off" for this, but it's possible you may want different types of collision per pixel; if so, bitmasks won't work, instead encode whatever you need per pixel, regardless the overall idea remains the same)
Generating a bitmask (or other such structure) for your sprite will enable you to just use the AABB method; all you'd have to do is use the generated bitmask instead of the texture data directly, and everything else is the same as before. But how do we generate this? That's the true difficulty of this method, because you generating your own image is basically replicating the work of your graphics card when you tell it to do rotations.
You would essentially "draw" out the rotated image yourself. This could be done by stepping through your base texture image data pixel by pixel, and applying a rotational transformation matrix to each pixel to get it to the correct destination in your bitmask/buffer. Once you have the correct destination, you then would test the image data for "block" or "not block" (using transparency as you mentioned) and write a 1 or 0 there accordingly.
While you're generating, you should also keep track of local minima and maxima; that is, how far left, right, up, and down your rotated image goes, just to give it an actual true AABB to live inside for quick checks (i.e. "Do I even need to check per-pixel collision?")
To be fully accurate, you will probably need to know which interpolation/rounding algorithm you're using (bilinear, nearest neighbor, etc.), which can get ugly. Graphics systems often do very complicated things, so taking ALL of this into account just for collision is pretty extreme. At the end of the day, even applying this method, it may not truly be "pixel perfect" as far as "perfectly synchronized with the rendered image output", unless you really go far in replicating exactly what XNA / DirectX is doing.
Finally, when does this generation occur? The answer is every time anything rotates! Otherwise you'll be checking stale data. Obviously you could just keep one buffer per sprite and just keep changing that, to not hog so much memory. But this does mean potentially once per frame if you're rotating consistently. Which means multiple times per frame if multiple sprites are all rotating a lot. Might not be the most computationally friendly.
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Apologies for the lack of example code, I'm currently in the brainstorming phase of the problem and having trouble finding a proper solution.
As I have stated in my title, I want to find out what the intersection area of two polygon are.
To be more specific, I have two ARPlane's that may overlap each other on the x-z plane but be on different y-levels (imagine stairs with an overhang). I can get the area boundaries of these ARPlanes easily. My first idea to simplify the process is to remove the y-component so as to have them on the same plane and turn this into a 2D problem.
From here onward, I'm unsure of how to proceed. I could not find any methods that calculated the intersection areas of two polygons. I have a few solutions that look promising if I can get the planes aligned neatly (such that the +x direction points from the center of one of the planes to the other), but I cannot move them in any way so I must modify what the local "forward" for a plane is. Even then, I don't think the ARPlane has a direction vector in the first place as they are not GameObjects, so I am unsure if this is a viable option as a path to follow. ARPlane class for quick reference.
One other way is to turn the planes so that they're in alignment with world x axis. This looks promising over the other methods but as I previously stated, I cannot turn the actual ARPlanes. I must make a copy of them and turn the copies while keeping their relative rotations and positions the same.
So far these have been the methods I could come up with but could not develop fully due to unity restrictions. My question, then, is whether there is a way to get around the issues of these problems; failing that, whether there is an alternative solution to the issue that can be recommended.
Below is an example use case of the tool. As can be seen, some stair threads have an overhang that covers a portion of the previous thread's surface (second and third figure). Each stair thread will be scanned and then processed to find their usable surface. The area covered by the overhang is not a usable surface. This usable area is defined by the placements of a staircase thread (A), and the very next thread right above it (B); so then the usable area will be surface_area_of_A - xz_crossSection_of_AB
What I'm trying to do: I want to compress a 2D grey-scale map (2D array of float values between 0 and 1) into a DFT. I then want to be able to sample the value of points in continuous coordinates (i.e. arbitrary points in between the data points in the original 2D map).
What I've tried: So far I've looked at Exocortex and some similar libraries, but they seem to be missing functions for sampling a single point or performing lossy compression. Though the math is a bit above my level, I might be able to derive methods do do these things. Ideally someone can point me to a C# library that already has this functionality. I'm also concerned that libraries that use the row-column FFT algorithm don't produce sinusoid functions that can be easily sampled this way since they unwind the 2D array into a 1D array.
More detail on what I'm trying to do: The intended application for all this is an experiment in efficiently pre-computing, storing, and querying line of sight information. This is similar to the the way spherical harmonic light probes are used to approximate lighting on dynamic objects. A grid of visibility probes store compressed visibility data using a small number of float values each. From this grid, an observer position can calculate an interpolated probe, then use that probe to sample the estimated visibility of nearby positions. The results don't have to be perfectly accurate, this is intended as first pass that can cheaply identify objects that are almost certainly visible or obscured, and then maybe perform more expensive ray-casting on the few on-the-fence objects.
I want to slice a 3D model relative to an infinite plane(In WPF). I'm checking if edges intersect with the infinite plane. If true, I'll create a new point at the intersection position, so I'm getting a couple of points that I want to generate a cap on so that the model is closed after slicing. For example, if this is the cross section, the result would be as follows:
Note: The triangulation ain't important. I just need triangles.
I also need to detect the holes as follows(holes are marked in red):
If it is impossible to do it the way I think(It seems to be so), the how should I do it? How do developers cap an object after being sliced?
There is also too much confusion. For example, The first picture's result may be:
What am I missing??
EDIT:
After some research, I knew one thing that I am missing:
The input is now robust, and I need the exact same output. How do I accomplish that??
In the past, I have done this kind of thing using a BSP.
Sorry to be so vague, but its not a a trivial problem!
Basically you convert your triangle mesh into the BSP representation, add your clipping plane to the BSP, and then convert it back into triangles.
As code11 said already you have too few data to solve this, the points are not enough.
Instead of clipping edges to produce new points you should clip entire triangles, which would give you new edges. This way, instead of a bunch of points you'd have a bunch of connected edges.
In your example with holes, with this single modification you'd get a 3 polygons - which is almost what you need. Then you will need to compute only the correct triangulation.
Look for CSG term or Constructive Solid Geometry.
EDIT:
If the generic CSG is too slow for you and you have clipped edges already then I'd suggest to try an 'Ear Clipping' algorithm.
Here's some description with support for holes:
https://www.geometrictools.com/Documentation/TriangulationByEarClipping.pdf
You may try also a 'Sweep Line' approach:
http://sites-final.uclouvain.be/mema/Poly2Tri/
And similar question on SO, with many ideas:
Polygon Triangulation with Holes
I hope it helps.
Building off of what zwcloud said, your point representation is ambiguous. You simply don't have enough points to determine where any concavities/notches actually are.
However, if you can solve that by obtaining additional points (you need midpoints of segments I think), you just need to throw the points into a shrinkwrap algorithm. Then at least you will have a cap.
The holes are a bit more tricky. Perhaps you can get away with just looking at the excluded points from the output of the shrinkwrap calculation and trying to find additional shapes in that, heuristically favoring points located near the centroid of your newly created polygon.
Additional thought: If you can limit yourself to convex polygons with only one similarly convex hole, the problem will be much easier to solve.
I'm wanting to do some placement of objects like trees and the like based on noise for the terrain of a game/tech demo.
I've used value noise previously and I believe I understand perlin noise well enough. Simplex noise, however, escapes me quite well (just a tad over my head at present).
I have an implementation in C# of simplex noise, however, it's almost completely stolen from here. It works beautifully, but I just don't understand it well enough to modify it for my own purposes.
It is quite fast, but it also gives rather smooth results. I'm actually wanting something that is a little more jagged, like simple linear interpolation would give when I was doing value noise. My issue here is that due to the amount of calls I'd be doing for these object placements and using fractal Brownian motion, the speed of the algorithm becomes quite important.
Any suggestions on how to get more 'jagged' results like linear interpolation gives with value noise using a faster algorithm than value noise is?
if you are using a complex noise function to do a simple task like the placement of trees, your using completely the wrong type of maths function. It is a very specific function which is great for making textures and 3d shapes and irregular curves. Placing treas on 2d certainly doesn't need irregular curves! Unless you want to place trees along in lines that are irregular and curved!
unless you mean you want to place trees in areas of the noise which are a certain level, for example where the noise is larger than 0.98, which will give you nicely randomised zones that you can use as a central point saying some trees will be there.
it will be a lot faster and a lot easier to vary, if you just use any normal noise function, just program your placement code around the noise function. I mean a predictable pseudo-random noise function which is the same every time you use it.
use integers 0 to 10 and 20 to 30, multiplied by your level number, to select 10 X and 10 Y points on the same pseudo-random noise curve. this will give you 10 random spots on your map from where to do stuff using almost no calculations.
Once you have the central point where trees will be, use another 10 random points from the function to say how many trees will be there, another 10 to say how far apart they will be, for the distribution around the tree seed quite exceptional.
The other option, if you want to change the curve http://webstaff.itn.liu.se/~stegu/simplexnoise/simplexnoise.pdf is to read this paper and look at the polynomial function /whatever gradient function could be used in your code, looking the comments for the gradient function, commented out and do X equals Y, which should give you a straight interpolation curve.
if you vote this answer up, I should have enough points in order to comment on this forum:]
I realise this is a very old question, but I felt that the previous answer was entirely wrong, so I wanted to clarify how you should use a noise function to determine the placement of things like trees / rocks / bushes.
Basically, if you want to globally place items across a terrain, you're going to need some function which tells you where those are likely to occur. For instance, you might say "trees need to be on slopes of 45 degrees or less, and below 2000 meters". This gives you a map of possible places for trees. But now you need to choose random, but clustered locations for them.
The best way of doing this is to multiply your map of zeroes and ones by a fractal function (i.e. a Simplex noise function or one generated through subdivision and displacement - see https://fractal-landscapes.co.uk/maths).
This then gives you a probability density function, where the value at a point represents the relative probability of placing a tree at that location. Now you store the partial sum of that function for every location on the map. To place a new tree:
Choose a random number between 0 and the maximum of the summed function.
Do a binary search to find the location on the map in this range.
Place the tree there.
Rinse and repeat.
This allows you to place objects where they belong, according to their natural ranges and so on.
I am working on a project where the game world is irregularly shaped (Think of the shape of a lake). this shape has a grid with coordinates placed over it. The game world is only on the inside of the shape. (Once again, think Lake)
How can I efficiently represent the game world? I know that many worlds are basically square, and work well in a 2 or 3 dimension array. I feel like if I use an array that is square, then I am basically wasting space, and increasing the amount of time that I need to iterate through the array. However, I am not sure how a jagged array would work here either.
Example shape of gameworld
X
XX
XX X XX
XXX XXX
XXXXXXX
XXXXXXXX
XXXXX XX
XX X
X
Edit:
The game world will most likely need each valid location stepped through. So I would a method that makes it easy to do so.
There's computational overhead and complexity associated with sparse representations, so unless the bounding area is much larger than your actual world, it's probably most efficient to simply accept the 'wasted' space. You're essentially trading off additional memory usage for faster access to world contents. More importantly, the 'wasted-space' implementation is easier to understand and maintain, which is always preferable until the point where a more complex implementation is required. If you don't have good evidence that it's required, then it's much better to keep it simple.
You could use a quadtree to minimize the amount of wasted space in your representation. Quad trees are good for partitioning 2-dimensional space with varying granularity - in your case, the finest granularity is a game square. If you had a whole 20x20 area without any game squares, the quad tree representation would allow you to use only one node to represent that whole area, instead of 400 as in the array representation.
Use whatever structure you've come up with---you can always change it later. If you're comfortable with using an array, use it. Stop worrying about the data structure you're going to use and start coding.
As you code, build abstractions away from this underlying array, like wrapping it in a semantic model; then, if you realize (through profiling) that it's waste of space or slow for the operations you need, you can swap it out without causing problems. Don't try to optimize until you know what you need.
Use a data structure like a list or map, and only insert the valid game world coordinates. That way the only thing you are saving are valid locations, and you don't waste memory saving the non-game world locations since you can deduce those from lack of presence in your data structure.
The easiest thing is to just use the array, and just mark the non-gamespace positions with some special marker. A jagged array might work too, but I don't use those much.
You could present the world as an (undirected) graph of land (or water) patches. Each patch then has a regular form and the world is the combination of these patches. Every patch is a node in the graph and has has graph edges to all its neighbours.
That is probably also the most natural representation of any general world (but it might not be the most efficient one). From an efficiency point of view, it will probably beat an array or list for a highly irregular map but not for one that fits well into a rectangle (or other regular shape) with few deviations.
An example of a highly irregular map:
x
x x
x x x
x x
x xxx
x
x
x
x
There’s virtually no way this can be efficiently fitted (both in space ratio and access time) into a regular shape. The following, on the other hand, fits very well into a regular shape by applying basic geometric transformations (it’s a parallelogram with small bits missing):
xxxxxx x
xxxxxxxxx
xxxxxxxxx
xx xxxx
One other option that could allow you to still access game world locations in O(1) time and not waste too much space would be a hashtable, where the keys would be the coordinates.
Another way would be to store an edge list - a line vector along each straight edge. Easy to check for inclusion this way and a quad tree or even a simple location hash on each vertice can speed lookup of info. We did this with a height component per edge to model the walls of a baseball stadium and it worked beautifully.
There is a big issue that nobody here addressed: the huge difference between storing it on disk and storing it in memory.
Assuming you are talking about a game world as you said, this means it's going to be very large. You're not going to store the whole thing in memory in once, but instead you will store the immediate vicinity in memory and update it as the player walks around.
This vicinity area should be as simple, easy and quick to access as possible. It should definitely be an array (or a set of arrays which are swapped out as the player moves). It will be referenced often and by many subsystems of your game engine: graphics and physics will handle loading the models, drawing them, keeping the player on top of the terrain, collisions, etc.; sound will need to know what ground type the player is currently standing on, to play the appropriate footstep sound; and so on. Rather than broadcast and duplicate this data among all the subsystems, if you just keep it in global arrays they can access it at will and at 100% speed and efficiency. This can really simplify things (but be aware of the consequences of global variables!).
However, on disk you definitely want to compress it. Some of the given answers provide good suggestions; you can serialize a data structure such as a hash table, or a list of only filled-in locations. You could certainly store an octree as well. In any case, you don't want to store blank locations on disk; according to your statistic, that would mean 66% of the space is wasted. Sure there is a time to forget about optimization and make it Just Work, but you don't want to distribute a 66%-empty file to end users. Also keep in mind that disks are not perfect random-access machines (except for SSDs); mechanical hard drives should still be around another several years at least, and they work best sequentially. See if you can organize your data structure so that the read operations are sequential, as you stream more vicinity terrain while the player moves, and you'll probably find it to be a noticeable difference. Don't take my word for it though, I haven't actually tested this sort of thing, it just makes sense right?