R-Tree how to build the bounding boxes to contains road segments - gis

I am new to R-Tree. I want to build a R-Tree for a road network. The road network have road segments (which are lines with source id, segment id, target id). I understand the leaves of an R-Tree are bounding boxes (the rectangles). How can I decide how many segments to put into every bounding box. Another thing is that the road segments are usually connected to each other and I understand for R-Tree, it is better to minimize the overlaps, how to realize this? Thanks.

Just use the bounding box of the road, one road segment at a time.
The R-tree will take care of minimizing the overlap as well as distributing the individual road segments across the leaf nodes. You cannot avoid the overlap, unless your roads are disconnected...

Related

Dissolve polygons with road network gaps

I am using QGIS and have a shapefile of the blocks in a large city, where each polygon is a particular streetblock. The city is divided into various sectors, and each block has information on its sector. I can easily classify the blocks by this attribute to visually inspect the shape of these sectors:
The issue is that the gaps between the blocks is the road network. I would like to dissolve all blocks in the same sector into a contiguous polygon, but am unsure how to do this.
Does anyone know an easy way to "fill in" the gaps between the city blocks in order to make the dissolve work properly?
Dissolve into multipart features based on the sectors, then extract nodes and try the concave hull plugin? Not sure how well the plugin works, though. Never used it.

Isometric depth sorting issue with big objects

I'm currently building an as3 isometric game, but I'm having a lot of problem with depth sorting. I've searched for a solution, but didn't found anything that match my problem (rectangle objects).
Here is a screenshot of my game:
As you can see, depth sorting works well when it's between 1x1 tiles objects. I simply use their x and y coordinates (relative to the isometric map) to sort them.
The problem comes when I have bigger objects, like 2x2 or 1x4 or 4x1.
Any idea how should I handle depth sorting then?
I don't think it is possible to sort a scene based on a single x,y value for each object if some of them can be long enough that one end should be at a different depth than the other. For instance, consider how you'd handle the rendering if the brown chair in your picture was moved one square down-left (to the square between the blue chair and the long couch). It would be deeper in the scene than the red table behind the couch, but would need to be rendered on top of the couch, which would need to be on top of the table.
I think there are two simple solutions:
Design your
levels using only one sort of overlap for large objects. For
instance, you could specify that an object's depth is based on its
nearest corner, which would require you to avoid putting things in
front of its most distant bits (since it will render on top of them).
Or you could stick with your current code (which seems to use the
most distant corner for depth) and avoid putting anything behind the
nearer parts. You may still have trouble with characters and other
objects that move around though. You might be able to make the
troublesome tiles inaccessible if you're careful with your design,
but in some cases this may be too restrictive.
Break up your large objects into smaller ones
which would have their own depths. You will probably want to go right
down to 1x1 pieces, each of which will have an unambiguous depth. You
might choose keep the larger objects in the code as invisible
containers for the smaller pieces, or they could be eliminated
entirely, whichever makes it easier for you to load up and enable
interaction with the various bits.
Splitting larger objects in to 1x1 sized pieces can also be nice since you can make them modular. That is, you can build differently sized objects by putting together 1x1 pieces in different combinations. If you cut your 2x1 tables in your image in half vertically, for instance, and created a 1x1 middle tile that fit in between them, you could stretch the design out to 3x1 or 10x1, depending on how many times you repeat the middle tile. There's a lot of other ways to make tiled graphics look good with only a modest amount of art required.
Ultima Online emulators (specifically, POL, though there may be others) achieve this through the implementation and usage of the concept of a 'multi' -- a single object comprised of sections of cut-up larger graphics. These cut-up graphics are such that their sprites are vertically-split at the left- and right-corner points of iso grid boundaries.
Other considerations:
- render 'multi' pieces sorted screen-Y axis from top-to-bottom.
- the southern (i.e. screen bottom-left) component of a 'multi' becomes the anchoring tile position (in the case of your couch, its left-most piece).
- consider that each map location can also hold its own vertical stack of objects; offsetting each object's render by screen-Y simulates height/altitude, and these must be sorted bottom-to-top (e.g. lowest-altitude to highest altitude).
Good luck!

Effective data structure for overlapping spatial areas

I'm writing a game where a large number of objects will have "area effects" over a region of a tiled 2D map.
Required features:
Several of these area effects may overlap and affect the same tile
It must be possible to very efficiently access the list of effects for any given tile
The area effects can have arbitrary shapes but will usually be of the form "up to X tiles distance from the object causing the effect" where X is a small integer, typically 1-10
The area effects will change frequently, e.g. as objects are moved to different locations on the map
Maps could be potentially large (e.g. 1000*1000 tiles)
What data structure would work best for this?
Providing you really do have a lot of area effects happening simultaneously, and that they will have arbitrary shapes, I'd do it this way:
when a new effect is created, it is
stored in a global list of effects
(not necessarily a global variable,
just something that applies to the
whole game or the current game-map)
it calculates which tiles
it affects, and stores a list of those tiles against the effect
each of those tiles is
notified of the new effect, and
stores a reference back to it in a
per-tile list (in C++ I'd use a
std::vector for this, something with
contiguous storage, not a linked
list)
ending an effect is handled by iterating through
the interested tiles and removing references to it, before destroying it
moving it, or changing its shape, is handled by removing
the references as above, performing the change calculations,
then re-attaching references in the tiles now affected
you should also have a debug-only invariant check that iterates through
your entire map and verifies that the list of tiles in the effect
exactly matches the tiles in the map that reference it.
Usually it depends on density of your map.
If you know that every tile (or major part of tiles) contains at least one effect you should use regular grid – simple 2D array of tiles.
If your map is feebly filled and there are a lot of empty tiles it make sense to use some spatial indexes like quad-tree or R-tree or BSP-trees.
Usually BSP-Trees (or quadtrees or octrees).
Some brute force solutions that don't rely on fancy computer science:
1000 x 1000 isn't too large - just a meg. Computers have Gigs. You could have an 2d array. Each bit in the bytes could be a 'type of area'. The 'effected area' that's bigger could be another bit. If you have a reasonable amount of different types of areas you can still use a multi-byte bit mask. If that gets ridiculous you can make the array elements pointers to lists of overlapping area type objects. But then you lose efficiency.
You could also implement a sparse array - using a hashtable key'd off of the coords (e.g., key = 1000*x+y) - but this is many times slower.
If course if you don't mind coding the fancy computer science ways, they usually work much better!
If you have a known maximum range of each area effect, you could use a data structure of your choosing and store the actual sources, only, that's optimized for normal 2D Collision Testing.
Then, when checking for effects on a tile, simply check (collision detection style, optimized for your data structure) for all effect sources within the maximum range and then applying a defined test function (for example, if the area is a circle, check if the distance is less than a constant; if it's a square, check if the x and y distances are each within a constant).
If you have a small (<10) amount of effect "field" shapes, you can even do a unique collision detection for each effect field type, within their pre-computed maximum range.

Culling interior triangles

I have an array of thousands of quads; 4-sided 3D polygons. All I know are the coordinates of the quad corners.
A subset of these quads define the closed outer shell of a 3D shape. The remaining quads are on the inside of this closed solid.
How do I figure out which quads are part of the shell and which quads are part of the interior? This is not performance critical code.
Edit: Further constraints on the shape of the shell
There are no holes inside the shape, it is a single surface.
It contains both convex and concave portions.
I have a few points which are known to be on the inside of the shell.
This might be hard to implement if your shape self intersects, but if you can find one quad that you know is on the surface (possibly one furthest away from the centroid) then map out concentric circles of quads around it. Then find a continuous ring of quads outside that and so on, until you end up at the "opposite" side. If your quads intersect, or are internally connected, then that's more difficult. I'd try breaking apart those which intersect, then find all the possible smooth surfaces, and pick the one with the greatest internal volume.
How about this?
Calculate the normal vector of a quad (call this the 'current' quad).
Do an intersection test with that vector and all the remaining quads.
If it intersects another quad in the positive portion of the vector you know the current quad is an internal quad. Repeat for all the remaining quads.
This assumes the quads 'face' outward.
Consider that all of the quads live inside a large sealed box. Pick one quad. Do raytracing; treat that quad as a light source, and treat all other quads as reflective and fuzzy, where a hit to a quad will send light in all directions from that surface, but not around corners.
If no light rays hit the external box after all nodes have had a chance to be hit, treat that quad as internal.
If it's convex, or internal quads didn't share edges with external quads, there are easier ways.
It can be done quite easily if the shape is convex. When the shape is concave it is much harder.
In the convex case find the centroid by computing the average of all of the points. This gives a point that is in the interior for which the following property holds:
If you project four rays from the
centroid to each corner of a quad you
define a pyramid cut into two parts,
one part contains space interior to
the shape and the other part defines
space that might be exterior to the
shape.
These two volumes give you a decision process to check if a quad is on the boundary or not. If any point from another quad occurs in the outside volume then the quad is not on the boundary and can be discarded as an interior quad.
Edit: Just seen your clarification above. In the harder case that the shape is concave then you need one of two things;
A description (parameterisation) of the shape that you can use to choose quads with, or
Some other property such as all of the boundary quads being contiguous
Further edit: Just realised that what you are describing would be a concave hull for the points. Try looking at some of the results in this search page.
You may be able to make your problem easier by reducing the number of quads that you have to deal with.
You know that some of the quads form a closed shell. Therefore, those quads are connected at their edges. If three mutually adjacent edges of a quad (that is, the edges form a closed loop) overlap the edge of another quad, then these quads might be part of the shell (these mutually adjacent edges serve as the boundary of a 2D region; let's call that region the "connected face" of the quad). Make a list of these "shell candidates". Now, look through this list and throw out any candidate who has an edge that does not overlap with another candidate (that is, the edge overlaps an edge of a quad that is not in the list). Repeat this culling process until you are no longer able to remove any quads. What you have left should be your shell. Create a "non-shell quads" list containing all of the quads not in the "shell" list.
Draw a bounding box (or sphere, ellipse, etc) around this shell. Now, look through your list of non-shell quads, and throw out any quads that lie outside of the bounding region. These are definitely not in the interior.
Take the remaining non-shell quads. These may or may not be in the interior of the shape. For each of these quads, draw lines perpendicular to the quad from the center of each face that end on the surface of the bounding shape. Trace each line and count how many times the line crosses through the "connected face" of a quad in your shell list. If this number is odd, then that vertex lies in the interior of the shape. If it is even, the vertex is on the exterior. You can determine whether a quad is inside or outside based on whether its vertices are inside or outside.

Obfuscating Geocode results to protect privacy?

I have an app that finds other users within a 20 mile radius on a google map and associates an icon with each of them. However, I do not want their exact points to be given but rather an approximation. I've wrestled with a few ideas on how to do this:
Only Geocode the Zip Code, make graphic icons for 1-99, use the icon to represent how many results are within the zip code, and use the info window to show hyperlinks to the individual results. The only problem is, I'd like each individual icon to be shown because it just looks a lot better.
Add/Subtract a random number to the lat/lng values stored with each user and add a translucent circle around the icon.
What do you guys suggest?
It depends on the level of privacy you want (the 1st option protects privacy better), but I'd be tempted to go with randomly moving the indicators because it's a more natural representation (people on a map, not groups of people on a map) without too much of a compromise in terms of usefulness.
That depends on how hard you think someone will try to defeat your system.
If you plan to track these positions over time, you give away more information over time than you do in a snapshot. For instance, if you choose a fixed-offset from the center of the circle, it may be possible to find this offset by mapping the path over time to the street map. On the other hand if you continually change the offset, the position may be discoverable by averaging.
Here's one possible scheme based on hysteresis. Leave the visible circle in place until the user exits an invisible bounding circle with a random radius. Then compute a new visible circle with a different random offset, and also set up a new invisible circle with a different random radius. This should generate a visible-circle movement that is almost impossible to reverse engineer, but also avoids lots of jittery movement.