My field consists of open grid spaces and filled grid spaces. My bot can move on only open spaces. It can only detect if there is a filled grid space in any of its 8 neighbouring grids (i.e. up, down, left, right , and diagnol spaces). That is, it cannot look beyond the 8 neighbouring spaces. What would be the best search technique in such a grid? My aim, lets say, is to find the no of objects in the grid ( an object is a connected set of filled spaces)
I've tried the following, all have been pretty bad:
keeping a list of spaces visited ( by taking initial position as 0,0 and storing relative positions of the spaces visited). That is, I preferably visit those locations which have not been visited.
Initially go to the bottommost and leftmost point, then start searching exhaustively for 5 bottom rows, then the next 5 bottom rows, and so on...
I'm not entirely sure I understand your aim, but the most common (non-optimized) algorithm for general grid path-finding, grid flood-fill, etc. is A* (pronounced "A - Star"). Its most widespread application is grid-based path-finding with "open" and "closed" nodes; much like your "open" and "filled" grid spaces.
Check out
http://en.wikipedia.org/wiki/A*_search_algorithm
Hope that helps!
You don't describe why you consider your solutions "pretty bad", but I assume you observe inefficient search behavior. An attempt you might want to try is to label each space with "value of information" that is, how many previously undiscovered neighboring spaces will you discover when you would visit that space. This is your "reward". Your "cost" is the distance to travel to that particular space. Then you will have to find a devise a search strategy that maximizes (reward - cost).
Sounds like a partially observable markov decision process. Maybe have a look at reinforcement learning. There's a free online version of a book by Sutton and Barto.
I think the problem is too hard for reinforcement learning producing a good result and it is too uncertain for classical approaches (using logic).
Related
I am a beginner C programmer.
I have been failing to find an algorythm that can solve the following problem:
On an array "board[x][y]" with two dimensions, which contains
following arranged elements:
Floor (white), Item (blue), Backpack (green) and Player (orange), the Player can move and can move Items by directly "touching" them, in a way that they move into the same direction and
stay attatched. "Touching" is defined by an Item being on either of
the four sides of the Player.
Graphic 1 describing predicted movement
If there is a Backpack attatched to the Player, the Backpack itself
acts as kind of a sticky attachment, moving all Items attached to that
Backpack, including other Backpacks.
Graphic 2 describing predicted movement
Is there an algorithm that can sucessfully move the resulting "structures" formable by the rules, only moving Items "attached"? If you can help me find a way or guide me on a path, I'd be very happy to learn about it.
Thank you in advance.
Store in a list the positions of the player and of the attached items and backpacks. When you perform a move, all elements in the list move. After the move, consider the player and backpacks in the list, and add the neighboring items or backpacks that are not already there.
[But see my second comment.]
I have a set of pages that look like this:
I have the content in grids with * Heights and Widths so the grid correctly scales when the entire window resizes. I would like the text to resize with the grid. Basically I would like the user to resize from this:
To this:
(preserving white space)
One way to do this would be to wrap the TextBlock in a ViewBox with margins on the right and bottom (for Grid.Row="3") to account for white space. But because I have several pages with different lengths and line counts I would have to set the margin specifically for each page otherwise the text sizes would differ on each page. Is there a better way to do this??
I don't think there is a better way to do this. There are different ways. But, I think it isn't just a matter of opinion that they would not be better.
Ways I can think of.
Render your text offscreen, rendertargetbitmap that so you've got a picture. Change your textblocks on screen to images and stretch them.
Or
Work out the size your text wants to be. Then do some calculation comes up with a different fontsize which is "better". This is a lot easier to write a description of than do.
In my opinion.
A viewbox is easier to implement. Way less error prone than calculations. Will give at least as good results as rendering to a picture.
I just want to add one more solution to the ones suggested by Andy, which is more of a scientific approach and takes a bit of practice to master.
Suppose you have to find a function F, which maps one or more variables to a desired single value. In your case that would be a function F, which takes aspect ratio of the window as input and outputs an appropriate font size.
How can you find such a function?
Well... you don't need to do any math yourself!
First, you need some data to begin with:
1. Resize the window randomly
2. Calculate aspect ration (X)
3. Pick an appropriate font size that looks good enough (Y)
4. Repeat the measurement 7 to 10 times (sorry data scientists)
5. Enter the data in Excel - one column for X and another one for Y
6. Insert a scatter chart
7. Choose the best trendline for your data, but avoid the polynomial one
8. Display the trendline equation and use the expression in your code
Now I should mention the pros and cons of this regression technique.
Pros:
1. It can solve a wide range of tricky problems:
"I use this 3rd party control, but when the text is too long it overlaps the title bar. How to trim it so it doesn't go beyond the top border?. Deadline is coming!"
2. Even if it doesn't solve the problem perfectly, the results are often acceptable
3. It takes minutes to try out unlike spending a day refreshing your math skills
Cons:
1. The biggest problem is that to keep it simple, you often lower the number of
variables by assuming some of them to be constant. In this post I've assumed that
the font family won't change for example, neither the font weight.
2. If any of the assumptions does not hold the final result could be even worse
This technique is fragile, but powerful. Use it as your last weapon and never leave magic expression like
fontSize = (int)(0.76 + 1.2 * aspectRation) without documenting how it came to be.
I'm performing some geographical computations in a grid with squares (i.e. regions). I'm using Delphi, but the logic could probably be applied to C++ too. Let me first explain what I want to do.
The following image is a portion of my grid, which is represented by a two-dimensional array Square that denotes the centre point in each square, and the "movement through the layers":
The green square has an X and Y coordinate of 2, so that is Square[2,2]. The actual coordinates are stored in Square[2,2].Latitude and Square[2,2].Longitude as wel as extra information in e.g. Square[2,2].Info that I use for computations.
Now comes the purpose: I need to do some computations on the surrounding areas. How many of the surrounding areas can be called "neighbours", depends on how many "layers" I have defined. In the image above, I used two of these "layers". That means that when starting from the green cell, I go around it once (blue arrows) and then again in the second layer (red arrows).
Now comes the problem: if I would have started in Square[1,1] (green square) instead of Square[2,2] as in the image below, the second layer (in red) would try to access data on the left side and at the bottom that does not exist (i.e. in the "-1" column and row). See the image below. This problem occurs at all borders of course.
I probably can make exceptions with IF-statements for every scenario, but I was wondering if there are common programming "tricks" that can handle such situations where you try to access data does not exist.
For example, I imagine it would be very handy if I can follow the pattern of the arrows depicted in the first image to access all the neighbouring squares every single time, even if there are non-existing squares. So, looking at the first image, after Square[3,0] you'd go to something like Square[3,-1] etc. and then eventually come back into the "feasible" zone in Square[0,3].
To visit neighborhood, you can use some kind of BFS (breadth-first search).
But for sparse structure (like the last picture shows) it is worth to use some data structure to organize cells in a good way. Perhaps kd-tree is suitable - you add all existing cells in the tree and make range search around given cell to get other cells in its vicinity.
Also look at another spatial data structures (see list at the bottom of kd-tree page).
I'm working on a view that's implementing a multi-column text layout using CoreText (using CTFramesetter).
CoreText usually fills each frame completely, so when I call CTFramesetterCreateFrame with three rects that make up my columns, I get a layout that's similar to the following image:
So the left column is filled completely, the middle column partially and the right column is empty. But instead, I'd like the text to distribute over the three columns so that they take up the least vertical space possible, like in this image:
How to achieve this with CoreText?
I don't mind going low-level here, even drawing each CTRun by hand is an option if necessary.
One idea I came up with would be to create a large frame with the width of a column and then figure out which CTLine to draw in which column. But this has a few limitations:
It would only work if all columns had the same width.
It does not work with clipping paths.
Unfortunately, I'll need to use clipping paths (as in kCTFrameClippingPathsAttributeName) so this idea is out. I could live the fixed column width limitation, though.
Another idea would be to reduce the height until the last frame overflows but that's a pretty brute-force way that surely wastes resources.
(BTW, due to compability requirements the use of TextKit classes like NSTextStorage isn't possible; the resulting view is intended to be used on Mac and iOS, but it needs to work on iOS < 7)
Since there doesn't seem to be a non-expensive way to solve this, here's how I've done it:
I did go with the "reduce the height until the last frame overflows" approach. To reduce the height, I simply have another clipping path (kCTFrameClippingPathsAttributeName) which is a rectangle that fills the bottom of the view to the required height.
The probably most expensive but simple way would have been to increase the rectangle height until finally the text doesn't fit inside the last frame any more.
Instead I've implemented a binary search for that. For my demo app, I usually find the correct height after 8-10 recursions which still is expensive but at least it's pixel-perfect and doesn't rely on any other information other than "did the last frame overflow".
So, to start off, I'm not very good at computer graphics. I'm trying to implement a GUI toolkit where one of the features is being able to apply 3D transformations to 2D "layers". (a layer only has one Z coordinate, as pre-transform, it's a two dimensional axis aligned rectangle)
Now, this is pretty straightforward, until you come to 3D transformations that would push the layer back, requiring splitting the layer into several polygons in order to render it correctly, as illustrated here. And because we can have transparency, layers may not get completely occluded, while still requiring getting split.
So here is an illustration depicting the issue and the desired outcome. In this scenario, the blue layer (call it B) is on top of the red layer (R), while having the same Z position (but B was added after R). In this scenario, if we rotate B, its top two points will get a Z index lower than 0 while the bottom points will get an index higher than 0 (with the anchor point being the only point/line left as 0).
Can somebody suggest a good way of doing this on the CPU? I've struggled to find a suitable algorithm implementation (in C++ or C) that would be appropriate to this scenario.
Edit: To clarify myself, at this stage in the pipeline, there is no rendering yet. We just need to produce a set of polygons for each layer that would then represent the layer's transformed and occluded geometry. Then, if required, rendering (either software or hardware) is done if required, which is not always the case (for example, when doing hit testing).
Edit 2: I looked at binary space partitioning as an option of achieving this but I have only been able to find one implementation (in GL2PS), which I'm not sure how to use. I do have a vague understanding of how BSPs work, but I'm not sure how they can be used for occlusion culling.
Edit 3: I'm not trying to do colour and transparency blending at this stage. Just pure geometry. Transparency can be handled by the renderer, and overdraw is okay. In this case, the blue polygon can just be drawn under the red one, but with more complicated cases, depth sorting or even splitting up the polygons may be required (example of a scary case like that below). Although the viewport is fixed, because all layers can be transformed in 3D, creating a shape shown below is possible.
So what I'm really looking for is an algorithm that would geometrically split layer B into two blue shapes, one of which would be drawn "above" and one of which would be drawn below R. The part "below" would get overdraw, yes, but it's not a major issue. So B just need to be split into two polygons so it would appear to cut through R when those polygons are drawn in order. No need to worry about blending.
Edit 4: For the purpose of this, we cannot render anything at all. This all has to be done purely geometrically (producing 2D polygons). This is what I was originally getting at.
Edit 5: I should note that the overall number of quads per subscene is around 30 (average). Definitely won't go above 100. Unless the layers are 3D transformed (which is where this problem arises), they are just radix sorted by Z positions before being drawn. Layers with the same Z position are drawn in order in which they were added (first in, first out).
Sorry if I didn't make it clear in the original question.
If you "aren't good with computer graphics", Doing it on CPU (software rendering) will be extremely difficult for you, if polygons can be transparent.
The easiest way to do it is to use GPU rendering (OpenGL/Direct3D) with Depth Peeling technique.
Cpu solutions:
Soltuion #1 (extremely difficult):
(I forgot the name of this algorithm).
You need to split polygon B into two, - for example, using polygon A as clip plane, then render result using painter's algorithm.
To do that you'll need to change your rendering routines so they'll no longer use quads, but textured polygons, plus you'll have to write/debug clipping routines that'll split triangles present in scene in such way that they'll no longer break paitner's algorithm.
Big Problem: If you have many polygons, this solution can potentially split scene into infinite number of triangles. Also, writing texture rendering code yourself isn't much fun, so it is advised to use OpenGL/Direct3D.
This can be extremely difficult to get right. I think this method was discussed in "Computer Graphics Using OpenGL 2nd edition" by "Francis S. Hill" - somewhere in one of their excercises.
Also check wikipedia article on Hidden Surface Removal.
Solution #2 (simpler):
You need to implement multi-layered z-buffer that stores up to N transparent pixels and their depth.
Solution #3 (computationally expensive):
Just use ray-tracing. You'll get perfect rendering result (no limitations of depth peeling and cpu solution #2), but it'll be computationally expensive, so you'll need to optimize rendering routines a lot.
Bottom line:
If you're performing software rendering, use Solution #2 or #3. If you're rendering on hardware, use technique similar to depth-peeling, or implement raytracing on hardware.
--edit-1--
required knowledge for implementing #1 and #2 is "line-plane intersection". If you understand how to split line (in 3d space) into two using a plane, you can implement raytracing or clipping easily.
Required knowledge for #2 is "textured 3d triangle rendering" (algorithm). It is a fairly complex topic.
In order to implement GPU solution, you need to be able to find few OpenGL tutorials that deal with shaders.
--edit-2--
Transparency is relevant, because in order to get transparency right, you need to draw polygons from back to front (from farthest to closest) using painter's algorithms. Sorting polygons properly is impossible in certain situation, so they must be split, or you should use one of the listed techniques, otherwise in certain situations there will be artifacts/incorrectly rendered images.
If there's no transparency, you can implement standard zbuffer or draw using hardware OpenGL, which is a very trivial task.
--edit-3--
I should note that the overall number of quads per subscene is around 30 (average). Definitely won't go above 100.
If you will split polygons, it can easily go way above 100.
It might be possible to position polygons in such way that each polygon will split all others polygon.
Now, 2^29 is 536870912, however, it is not possible to split one surface with a plane in such way that during each split number of polygons would double. If one polygon is split 29 timse, you'll get 30 polygons in the best-case scenario, and probably several thousands in the worst case if splitting planes aren't parallel.
Here's rough algorithm outline that should work:
Prepare list of all triangles in scene.
Remove back-facing triangles.
Find all triangles that intersect each other in 3d space, and split them using line of intersection.
compute screen-space coordinates for all vertices of all triangles.
Sort by depth for painter's algorithm.
Prepare extra list for new primitives.
Find triangles that overlap in 2D (post projection) screen space.
For all overlapping triangles check their rendering order. Basically a triangle that is going to be rendered "below" another triangles should have no part that is above another triangle.
8.1. To do that, use camera origin point and triangle edges to split original triangles into several sub-regions, then check if regions conform to established sort order (prepared for painter's algorithm). Regions are created by splitting existing pair of triangles using 6 clip planes created by camera origin points and triangle edges.
8.2. If all regions conform to rendering order, leave triangles be. If they don't, remove triangles from list, and add them to the "new primitives" list.
IF there are any primitives in new primitives list, merge the list with triangle list, and go to #5.
By looking at that algorithm, you can easily understand why everybody uses Z-buffer nowadays.
Come to think about it, that's a good training exercise for universities that specialize in CG. The kind of exercise that might make your students hate you.
I am going to come out say give the simpler solution, which may not fit your problem. Why not just change your artwork to prevent this problem from occuring.
In problem 1, just divide the polys in Maya or whatever beforehand. For the 3 lines problem, again, divide your polys at the intersections to prevent fighting. Pre-computed solutions will always run faster than on the fly ones - especially on limited hardware. From profesional experience, I can say that it also does scale, well it scales ok. It just requires some tweaking from the art side and technical reviews to make sure nothing is created "ilegally." You may end up getting more polys doing it this way than rendering on the fly, but at least you won't have to do a ton of math on CPUs that may not be up to the task.
If you do not have control over the artwork pipeline, this won't work as writing some sort of a converter would take longer than getting a BSP sub-division routine up and running. Still, KISS is often the best solution.