I'm currently considering the implementation of a 2D data structure to allow me to store and draw objects in correct Z-Order (GDI+, entities are drawn in call order). The requirements are loosely:
Ability to add new objects to the top of any depth index
Ability to remove arbitrary object
(Ability to move object to the top of new depth index, accomplished by 2 points above)
Fast in-order and reverse-order traversal
As the main requirement is speed of traversal across the full data, the first thing that came to mind was an array like structure, eg. vector. It also easily allows for pushing new objects (removing objects not so great..). This works perfectly fine for our requirements, as it just so happens that the bulk of drawable entities don't change, and the ones that do sit at the top end of the order.
However it got me thinking of the implications for more dynamic requirements:
A vector will resize itself as required -> as the 'depth' vectors would need to be maintained contiguously in memory (top-level vector enforces it), this could lead to some pretty expensive vector resizes. Worst case all vectors need to be moved to new memory location, average case requiring all vectors up the chain to be moved.
Vectors will often hold a buffer at the end for adding new objects -> traversal could still easily force a cache miss while jumping between 'depth' vectors, rendering the top-level vector's contiguous memory less beneficial
Could someone confirm that these observations are indeed correct, making a vector a mostly very expensive structure for storing larger dynamic data sets?
From my thoughts above, I end up deducing that while traversing the whole dataset, specifically jumping between different vectors in the top-level vector, you might as well use any other data structure with inferior traversal complexity, or similar random access complexity (linked_list; map). Traversal would effectively be the same, as we might as well assume the cache misses will happen anyway, and we save ourselves a lot of bother by not keeping the depth vectors contiguously in memory.
Would that indeed be a good solution? If I'm not mistaken, on a 1D problem space, this would come down to what's more important traversal or addition/removal, vector or linked-list. On a 2D space I'm not so sure it is so black and white.
I'm wondering what sort of application requires good traversal across a 2D space, without compromising data addition/removal, and what sort of data structures are used there.
P.S. I just noticed I'm completely ignoring space-complexity, so might as well keep on ignoring it (unless you feel like adding more insight :D)
Your first assumption is somewhat incorrect.
Instead of thinking of vectors as the blob of memory itself, think of it as a pointer to automatically managed blob of memory and some metadata to keep track of it. A vector itself is a fixed size, the memory it keeps track of isn't. (See this example, note that the size of the vector object is constant: https://ideone.com/3mwjRz)
A vector of vectors can be thought of as an array of pointers. Resizing what the pointers point to doesn't mean you need to resize the array that contains them. The promise of items being contiguous still holds: the parent array has all of the pointers adjacent to each other and each pointer points to a contiguous chunk of memory. However, it's not guaranteed that the end of arr[0][N-1] is adjacent to the beginning of arr[1][0]. (To this end, your second point is correct.)
I guess that a Linked List would be more appropriate as you will always be traversing the whole list (vectors are good for random access). Linked lists inserts and removal are very cheap and the traversal isn't that different from a vector traversal. Maybe you should consider a Doubly Linked List as you want to traverse it in both ways.
Related
I have some vertex data. Positions, normals, texture coordinates. I probably loaded it from a .obj file or some other format. Maybe I'm drawing a cube. But each piece of vertex data has its own index. Can I render this mesh data using OpenGL/Direct3D?
In the most general sense, no. OpenGL and Direct3D only allow one index per vertex; the index fetches from each stream of vertex data. Therefore, every unique combination of components must have its own separate index.
So if you have a cube, where each face has its own normal, you will need to replicate the position and normal data a lot. You will need 24 positions and 24 normals, even though the cube will only have 8 unique positions and 6 unique normals.
Your best bet is to simply accept that your data will be larger. A great many model formats will use multiple indices; you will need to fixup this vertex data before you can render with it. Many mesh loading tools, such as Open Asset Importer, will perform this fixup for you.
It should also be noted that most meshes are not cubes. Most meshes are smooth across the vast majority of vertices, only occasionally having different normals/texture coordinates/etc. So while this often comes up for simple geometric shapes, real models rarely have substantial amounts of vertex duplication.
GL 3.x and D3D10
For D3D10/OpenGL 3.x-class hardware, it is possible to avoid performing fixup and use multiple indexed attributes directly. However, be advised that this will likely decrease rendering performance.
The following discussion will use the OpenGL terminology, but Direct3D v10 and above has equivalent functionality.
The idea is to manually access the different vertex attributes from the vertex shader. Instead of sending the vertex attributes directly, the attributes that are passed are actually the indices for that particular vertex. The vertex shader then uses the indices to access the actual attribute through one or more buffer textures.
Attributes can be stored in multiple buffer textures or all within one. If the latter is used, then the shader will need an offset to add to each index in order to find the corresponding attribute's start index in the buffer.
Regular vertex attributes can be compressed in many ways. Buffer textures have fewer means of compression, allowing only a relatively limited number of vertex formats (via the image formats they support).
Please note again that any of these techniques may decrease overall vertex processing performance. Therefore, it should only be used in the most memory-limited of circumstances, after all other options for compression or optimization have been exhausted.
OpenGL ES 3.0 provides buffer textures as well. Higher OpenGL versions allow you to read buffer objects more directly via SSBOs rather than buffer textures, which might have better performance characteristics.
I found a way that allows you to reduce this sort of repetition that runs a bit contrary to some of the statements made in the other answer (but doesn't specifically fit the question asked here). It does however address my question which was thought to be a repeat of this question.
I just learned about Interpolation qualifiers. Specifically "flat". It's my understanding that putting the flat qualifier on your vertex shader output causes only the provoking vertex to pass it's values to the fragment shader.
This means for the situation described in this quote:
So if you have a cube, where each face has its own normal, you will need to replicate the position and normal data a lot. You will need 24 positions and 24 normals, even though the cube will only have 8 unique positions and 6 unique normals.
You can have 8 vertexes, 6 of which contain the unique normals and 2 of normal values are disregarded, so long as you carefully order your primitives indices such that the "provoking vertex" contains the normal data you want to apply to the entire face.
EDIT: My understanding of how it works:
I'm starting to use RWMutex in my Go project with map since now I have more than one routine running at the same time and while making all of the changes for that a doubt came to my mind.
The thing is that I know that we must use RLock when only reading to allow other routines to do the same task and Lock when writing to full-block the map. But what are we supposed to do when editing a previously created element in the map?
For example... Let's say I have a map[int]string where I do Lock, put inside "hello " and then Unlock. What if I want to add "world" to it? Should I do Lock or can I do RLock?
You should approach the problem from another angle.
A simple rule of thumb you seem to understand just fine is
You need to protect the map from concurrent accesses when at least one of them is a modification.
Now the real question is what constitutes a modification of a map.
To answer it properly, it helps to notice that values stored in maps are not addressable — by design.
This was engineered that way simply due to the fact maps internally have intricate implementation which
might move values they contain in memory
to provide (amortized) fast access time
when the map's structure changes due to insertions and/or deletions of its elements.
The fact map values are not addressable means you can not do
something like
m := make(map[int]string)
m[42] = "hello"
go mutate(&m[42]) // take a single element and go modifying it...
// ...while other parts of the program change _other_ values
m[123] = "blah blah"
The reason you are not allowed to do this is the
insertion operation m[123] = ... might trigger moving
the storage of the map's element around, and that might
involve moving the storage of the element keyed by 42
to some other place in memory — pulling the rug
from under the feet of the goroutine
running the mutate function.
So, in Go, maps really only support three operations:
Insert — or replace — an element;
Read an element;
Delete an element.
You cannot modify an element "in place" — you can only
go in three steps:
Read the element;
Modify the variable containing the (read) copy;
Replace the element by the modified copy.
As you can now see, the steps (1) and (3) are mere map accesses,
and so the answer to your question is (hopefully) apparent:
the step (1) shall be done under at least an read lock,
and the step (3) shall be done under a write (exclusive) lock.
In contrast, elements of other compound types —
arrays (and slices) and fields of struct types —
do not have the restriction maps have: provided the storage
of the "enclosing" variable is not relocated, it is fine to
change its different elements concurrently by different goroutines.
Since the only way to change the value associated with the key in the map is to reassign the changed value to the same key, that is a write / modification, so you have to obtain the write lock–simply using the read lock will not be sufficient.
Go doesn't allow taking the address of a map member:
// if I do this:
p := &mm["abc"]
// Syntax Error - cannot take the address of mm["abc"]
The rationale is that if Go allows taking this address, when the map backstore grows or shinks, the address can become invalid, confusing the user.
But Go slice gets relocated when it outgrows its capacity, yet, Go allows us to take the address of a slice element:
a := make([]Test, 5)
a[0] = Test{1, "dsfds"}
a[1] = Test{2, "sdfd"}
a[2] = Test{3, "dsf"}
addr1 := reflect.ValueOf(&a[2]).Pointer()
fmt.Println("Address of a[2]: ", addr1)
a = append(a, Test{4, "ssdf"})
addrx := reflect.ValueOf(&a[2]).Pointer()
fmt.Println("Address of a[2] After Append:", addrx)
// Note after append, the first address is invalid
Address of a[2]: 833358258224
Address of a[2] After Append: 833358266416
Why is Go designed like this? What is special about taking address of slice element?
There is a major difference between slices and maps: Slices are backed by a backing array and maps are not.
If a map grows or shrinks a potential pointer to a map element may become a dangling pointer pointing into nowhere (uninitialised memory). The problem here is not "confusion of the user" but that it would break a major design element of Go: No dangling pointers.
If a slice runs out of capacity a new, larger backing array is created and the old backing array is copied into the new; and the old backing array remains existing. Thus any pointers obtained from the "ungrown" slice pointing into the old backing array are still valid pointers to valid memory.
If you have a slice still pointing to the old backing array (e.g. because you made a copy of the slice before growing the slice beyond its capacity) you still access the old backing array. This has less to do with pointers of slice elements, but slices being views into arrays and the arrays being copied during slice growth.
Note that there is no "reducing the backing array of a slice" during slice shrinkage.
A fundamental difference between map and slice is that a map is a dynamic data structure that moves the values that it contains as it grows. The specific implementation of Go map may even grow incrementally, a little bit during insert and delete operations until all values are moved to a bigger memory structure. So you may delete a value and suddenly another value may move. A slice on the other hand is just an interface/pointer to a subarray. A slice never grows. The append function may copy a slice into another slice with more capacity, but it leaves the old slice intact and is also a function instead of just an indexing operator.
In the words of the map implementor himself:
https://www.youtube.com/watch?v=Tl7mi9QmLns&feature=youtu.be&t=21m45s
"It interferes with this growing procedure, so if I take the address
of some entry in the bucket, and then I keep that entry around for a
long time and in the meantime the map grows, then all of a sudden that
pointer points to an old bucket and not a new bucket and that pointer
is now invalid, so it's hard to provide the ability to take the
address of a value in a map, without constraining how grow works...
C++ grows in a different way, so you can take the address of a bucket"
So, even though &m[x] could have been allowed and would be useful for short-lived operations (do a modification to the value and then not use that pointer again), and in fact the map internally does that, I think the language designers/implementors chose to be on the safe side with map, not allowing &m[x] in order to avoid subtle bugs with programs that might keep the pointer for a long time without realizing then it would point to different data than the programmer thought.
See also Why doesn't Go allow taking the address of map value? for related comments.
I've read a bunch of explanations about the difference between array pointers and map pointers and it all still seems a tad odd.
Consider this: https://go.dev/play/p/uzADxzdq2EP
I can get a pointer to the zeroth array object but after I add another object to the array the original pointer is still there but it no longer points to the zeroth object of the current array. It points to the original value. Sure, it's not pointing to a nil object, it's pointing to the same object, but it's no longer 'correct' for some version of correct.
I'm not sure what my point is here other than it's just...odd.
If we had an assignment:
Given a block of binary data, count the frequency of the bytes within it.
And you were supposed to do this in C, the answer would be trivial and reasonably fast even for larger binary blocks. How would one go about implementing this in a purely functional language, without side effects?
For example, if you wrote a function that accepted freqency counts for each byte and the rest of the list of bytes, and returned modified frequency counts, it would have to do awful lot of work for data set of 100M bytes.
Also, if you sorted the data and then somehow counted the amount of subsequent same-valued bytes, the sort itself would take a lot of time.
Is there a reasonable way to implement this?
The straightforward way to do it is indeed to pass in and return data structures mapping bytes to counts. This would probably be implemented as some kind of tree (since that's what you get out of the standard library containers, as far as I know). In pure functional programming when you're passed in a tree and you need to return a new tree with a difference in only one node, the returned tree ends up sharing almost all of its structure and data with the original tree.
There is some overhead in traversing the tree to get to the count, but since you're counting bytes the tree is only ever smaller than 256 elements, so the overhead is log(255), which is a constant. It doesn't get larger for large data sets - it doesn't change the big-oh complexity of the algorithm. That's actually true even if you use the greatest possible overhead of copying around a full 256-entry array of counts with no sharing.
If you want to optimise this, you can take advantage of the fact that the "intermediate" frequency counts are never needed except as part of the computation of the next set of counts. That means you can use various techniques for getting the implementation to use destructive updates even while you're still semantically writing functional code. An STref in Haskell is basically letting you do this manually.
Theoretically the compiler could notice that you're replacing a never-needed-again value with a new one, so it could do the update in place for you. I don't know whether or not any actual production ready compilers are currently able to make this optimisation.
Let's say I have circular objects. Each object has a diameter of 64 pixels.
The cells of my quad tree are let's say 96x96 pixels.
Everything will be fine and working well when I check collision from the cell a circle is residing in + all it's neighbor cells.
BUT what if I have one circle that has a diameter of 512 pixels? It would cover many cells and thus this would be a problem when checking only the neighbor cells. But I can't re-size my quad-tree-grid every time a much larger object is inserted into the tree...
Instead och putting objects into a single cell put them in all cells they collide with. That way you can just test each cell individually. Use pointers to the object so you dont create copies. Also you only need to do this with leavenodes, so no need to combine data contained in higher nodes with lower ones.
This an interesting problem. Maybe you can extend the node or the cell with a tree height information? If you have an object bigger then the smallest cell nest it with the tree height. That's what map's application like google or bing maps does.
Here a link to a similar solution: http://www.gamedev.net/topic/588426-2d-quadtree-collision---variety-in-size. I was confusing the screen with the quadtree. You can check collision with a simple recusion.
Oversearching
During the search, and starting with the largest objects first...
Test Object.Position.X against QuadTreeNode.Centre.X, and also
test Object.Position.Y against QuadTreeNode.Centre.Y;
... Then, by taking the Absolute value of the difference, treat the object as lying within a specific child node whenever the absolute value is NOT more than the radius of the object...
... that is, when some portion of the object intrudes into that quad : )
The same can be done with AABB (Axis Aligned Bounding Boxes)
The only real caveat here is that VERY large objects that cover most of the screen, will force a search of the entire tree. In these cases, a different approach may be called for.
Of course, this only takes care of the object that everything else is being tested against. To ensure that all the other large objects in the world are properly identified, you will need to alter your quadtree slightly...
Use Multiple Appearances
In this variation on the QuadTree we ONLY place objects in the leaf nodes of the QuadTree, as pointers. Larger objects may appear in multiple leaf nodes.
Since some objects have multiple appearances in the tree, we need a way to avoid them once they've already been tested against.
So...
A simple Boolean WasHit flag can avoid testing the same object multiple times in a hit-test pass... and a 'cleanup' can be run on all 'hit' objects so that they are ready for the next test.
Whilst this makes sense, it is wasteful if performing all-vs-all hit-tests
So... Getting a little cleverer, we can avoid having any cleanup at all by using a Pointer 'ptrLastObjectTestedAgainst' inside of each object in the scene. This avoids re-testing the same objects on this run (the pointer is set after the first encounter)
It does not require resetting when testing a new object against the scene (the new object has a different pointer value than the last one). This avoids the need to reset the pointer as you would with a simple Bool flag.
I've used the latter approach in scenes with vastly different object sizes and it worked well.
Elastic QuadTrees
I've also used an 'elastic' QuadTree. Basically, you set a limit on how many items can IDEALLY fit in each QuadTreeNode - But, unlike a standard QuadTree, you allow the code to override this limit in specific cases.
The overriding rule here is that an object may NOT be placed into a Node that cannot hold it ENTIRELY... with the top node catching any objects that are larger than the screen.
Thus, small objects will continue to 'fall through' to form a regular QuadTree but large objects will not always fall all the way through to the leaf node - but will instead expand the node that last fitted them.
Think of the non-leaf nodes as 'sieving' the objects as they fall down the tree
This turns out to be a very efficient choice for many scenarios : )
Conclusion
Remember that these standard algorithms are useful general tools, but they are not a substitute for thinking about your specific problem. Do not fall into the trap of using a specific algorithm or library 'just because it is well known' ... your application is unique, and it may benefit from a slightly different approach.
Therefore, don't just learn to apply algorithms ... learn from those algorithms, and apply the principles themselves in novel and fitting ways. These are NOT the only tools, nor are they necessarily the best fit for your application.
Hope some of those ideas helped.