Background: I'm build a series of location-based apps that make heavy use of maps. These maps are annotated with locations fetched from a server, to which I pass regions of the map I need data for (defined as a lat/long and a latDelta/longDelta, much like MKCoordinateRegion, but with a different location of the reference coordinate). I'm writing a bunch of helper methods/classes to use when managing these regions. Compatibility with iOS 3.x is required (meaning MKMapRect is out).
Question: Am I setting myself up for failure by treating MKCoordinateRegions like rectangles? Specifically, I'm treating their geometry as if it was that of a rectangle, assuming they have basically the same properties as rectangles. I've implemented several methods that mirror CGRect's helper methods, such as MKCoordinateRegionUnion/Inset/Outset, etc, and they all pass my unit tests, but I'm starting to question if my underlying assumptions are correct. I know in fact that MKCoordinateRegion does not represent a geometric rectangle, but rather a region of a spherical surface bound by two sets of parallel planes, perpendicular to each other (bonus points if somebody can clue me in on a better term for that).
I'm not experiencing any anomalies yet, but since many apps will be reliant on my understanding of the geometry, I'd rather figure out now if I'm going down the wrong path. The fact that I slept through most of the classes in school dealing with 3d radial geometry doesn't give me much confidence that my intuition is correct.
If you are taking into account the equator, prime meridian and dateline edge cases, I think you will be ok.
Alternatively, you could develop your own MKMapRect like rects. Troy Brant has a great blog post about the how the rects are formed:
http://troybrant.net/blog/2010/01/mkmapview-and-zoom-levels-a-visual-guide/
While the blog post is mainly about zoom levels, all the information there can be used to build up your own map rect library.
As for areas bounded by great circles on the surface of a sphere, they are called spherical polygons. So I guess you could just call them spherical rectangles.
Related
I'm currently working on a visual odometry project. Currently I've implemented up to Essential Matrix decomposition stage. But the resulting translation vector is normalized and cannot be able to plot the movement.
Now how can I compute the displacement in some scale? I have seen some suggestions to use planner homography to compute the absolute translation. I didn't got the idea of doing it as, the outdoor environment is not simply planner. At least, by considering the ground as planner, how to obtain, the translation of it. I've seen a suggestion here. Is it possible to use this approach to get the displacement between two frames?
What you are referring to is called registration. This is a vast field. There are methods for linear transformation across the entire image, and per pixel methods ( the two ends of the spectrum). Naturally per pixel methods are far slower typically and have many local errors.
Typically two frames have very little transformation between them and simple Homography will do to find the general scaling between them. Especially if you are talking about aerial photos. If your case is very far from planar then you may want to use something closer to pixel-wise. For example using spline fitting: https://www.mathworks.com/matlabcentral/fileexchange/20057-b-spline-grid--image-and-point-based-registration
You cannot recover scale, generally speaking, unless you can recognize in the scene 1 or more objects of known physical size.
I'm currently working on an augmented reality application using a medical imaging program called 3DSlicer. My application runs as a module within the Slicer environment and is meant to provide the tools necessary to use an external tracking system to augment a camera feed displayed within Slicer.
Currently, everything is configured properly so that all that I have left to do is automate the calculation of the camera's extrinsic matrix, which I decided to do using OpenCV's solvePnP() function. Unfortunately this has been giving me some difficulty as I am not acquiring the correct results.
My tracking system is configured as follows:
The optical tracker is mounted in such a way that the entire scene can be viewed.
Tracked markers are rigidly attached to a pointer tool, the camera, and a model that we have acquired a virtual representation for.
The pointer tool's tip was registered using a pivot calibration. This means that any values recorded using the pointer indicate the position of the pointer's tip.
Both the model and the pointer have 3D virtual representations that augment a live video feed as seen below.
The pointer and camera (Referred to as C from hereon) markers each return a homogeneous transform that describes their position relative to the marker attached to the model (Referred to as M from hereon). The model's marker, being the origin, does not return any transformation.
I obtained two sets of points, one 2D and one 3D. The 2D points are the coordinates of a chessboard's corners in pixel coordinates while the 3D points are the corresponding world coordinates of those same corners relative to M. These were recorded using openCV's detectChessboardCorners() function for the 2 dimensional points and the pointer for the 3 dimensional. I then transformed the 3D points from M space to C space by multiplying them by C inverse. This was done as the solvePnP() function requires that 3D points be described relative to the world coordinate system of the camera, which in this case is C, not M.
Once all of this was done, I passed in the point sets into solvePnp(). The transformation I got was completely incorrect, though. I am honestly at a loss for what I did wrong. Adding to my confusion is the fact that OpenCV uses a different coordinate format from OpenGL, which is what 3DSlicer is based on. If anyone can provide some assistance in this matter I would be exceptionally grateful.
Also if anything is unclear, please don't hesitate to ask. This is a pretty big project so it was hard for me to distill everything to just the issue at hand. I'm wholly expecting that things might get a little confusing for anyone reading this.
Thank you!
UPDATE #1: It turns out I'm a giant idiot. I recorded colinear points only because I was too impatient to record the entire checkerboard. Of course this meant that there were nearly infinite solutions to the least squares regression as I only locked the solution to 2 dimensions! My values are much closer to my ground truth now, and in fact the rotational columns seem correct except that they're all completely out of order. I'm not sure what could cause that, but it seems that my rotation matrix was mirrored across the center column. In addition to that, my translation components are negative when they should be positive, although their magnitudes seem to be correct. So now I've basically got all the right values in all the wrong order.
Mirror/rotational ambiguity.
You basically need to reorient your coordinate frames by imposing the constraints that (1) the scene is in front of the camera and (2) the checkerboard axes are oriented as you expect them to be. This boils down to multiplying your calibrated transform for an appropriate ("hand-built") rotation and/or mirroring.
The basic problems is that the calibration target you are using - even when all the corners are seen, has at least a 180^ deg rotational ambiguity unless color information is used. If some corners are missed things can get even weirder.
You can often use prior info about the camera orientation w.r.t. the scene to resolve this kind of ambiguities, as I was suggesting above. However, in more dynamical situation, of if a further degree of automation is needed in situations in which the target may be only partially visible, you'd be much better off using a target in which each small chunk of corners can be individually identified. My favorite is Matsunaga and Kanatani's "2D barcode" one, which uses sequences of square lengths with unique crossratios. See the paper here.
My question maybe a bit too broad but i am going for the concept. How can i create surface as they did in "Cham Cham" app
https://itunes.apple.com/il/app/cham-cham/id760567889?mt=8.
I got most of the stuff done in the app but the surface change with user touch is quite different. You can change its altitude and it grows and shrinks. How this can be done using sprite kit what is the concept behind that can anyone there explain it a bit.
Thanks
Here comes the answer from Cham Cham developers :)
Let me split the explanation into different parts:
Note: As the project started quite a while ago, it is implemented using pure OpenGL. The SpiteKit implementation might differ, but you just need to map the idea over to it.
Defining the ground
The ground is represented by a set of points, which are interpolated over using Hermite Spline. Basically, the game uses a bunch of points defining the surface, and a set of points between each control one, like the below:
The red dots are control points, and eveyrthing in between is computed used the metioned Hermite interpolation. The green points in the middle have nothing to do with it, but make the whole thing look like boobs :)
You can choose an arbitrary amount of steps to make your boobs look as smooth as possible, but this is more to do with performance.
Controlling the shape
All you need to do is to allow the user to move the control points (or some of them, like in Cham Cham; you can define which range every point could move in etc). Recomputing the interpolated values will yield you an changed shape, which remains smooth at all times (given you have picked enough intermediate points).
Texturing the thing
Again, it is up to you how would you apply the texture. In Cham Cham, we use one big texture to hold the background image and recompute the texture coordinates at every shape change. You could try a more sophisticated algorithm, like squeezing the texture or whatever you found appropriate.
As for the surface texture (the one that covers the ground – grass, ice, sand etc) – you can just use the thing called Triangle Strips, with "bottom" vertices sitting at every interpolated point of the surface and "top" vertices raised over (by offsetting them against "bottom" ones in the direction of the normal to that point).
Rendering it
The easiest way is to utilize some tesselation library, like libtess. What it will do it covert you boundary line (composed of interpolated points) into a set of triangles. It will preserve texture coordinates, so that you can just feed these triangles to the renderer.
SpriteKit note
Unfortunately, I am not really familiar with SpriteKit engine, so cannot guarantee you will be able to copy the idea over one-to-one, but please feel free to comment on the challenging aspects of the implementation and I will try to help.
I am trying to find area of MKPolygonView object added to MapView. Apple documentation has method distanceFromLocation: to find distance between edges of MKPolygonView object. But I could not find anything to calculate area of the overlay.
Does Apple have any documented method for finding area?
Concerning the comments on the question post, the Earth is not a perfect sphere either. In fact, it's not a perfect anything, so "correct" answers aren't possible. What matters is how accurate of an approximation you need. Also, are you interested in a mean sea level type measurement, or do you want the actual contours of the ground (for example if your polygon is put over a mountain, then the same exact size polygon is put over some plains, should the result you calculate be the same or different)?
Depending on how big your polygon is, and which measurement you're looking for, a 2D approximation can be pretty accurate (the smaller the polygon, the closer you'll get). Something to keep in mind, if you want your area in something like square feet, the distance between two longitudinal lines is not constant (63 deg west and 62 deg west are closer (in feet) somewhere in Alaska than they are at the equator). You might have to do a unit conversion to handle this depending on how big your polygon is (or if your polygon could be placed anywhere). If you can't do the 2D approximation, I'm not even sure how you'd do that.
When I did this, I did the 2D approx, and I had to do the unit conversion. If that's the way you go, I can try to dig up some of my old notes and the links I used to get you started.
I'd like to build an app using the new GLKit framework, and I'm in need of some design advice. I'd like to create an app that will present up to a couple thousand "bricks" (objects with very simple geometry). Most will have identical texture, but up to a couple hundred will have unique texture. I'd like the bricks to appear every few seconds, move into place and then stay put (in world coords). I'd like to simulate a camera whose position and orientation are controlled by user gestures.
The advice I need is about how to organize the code. I'd like my model to be a collection of bricks that have a lot more than graphical data associated with them:
Does it make sense to associate a view-like object with each handle geometry, texture, etc.?
Should every brick have it's own vertex buffer?
Should each have it's own GLKBaseEffect?
I'm looking for help organizing what object should do what during setup, then rendering.
I hope I can stay close to the typical MVC pattern, with my GLKViewController observing model state changes, controlling eye coordinates based on gestures, and so on.
Would be much obliged if you could give some advice or steer me toward a good example. Thanks in advance!
With respect to the models, I think an approach analogous to the relationship between UIImage and UIImageView is appropriate. So every type of brick has a single vertex buffer,GLKBaseEffect, texture and whatever else. Each brick may then appear multiple times just as multiple UIImageViews may use the same UIImage. In terms of keeping multiple reference frames, it's actually a really good idea to build a hierarchy essentially equivalent to UIView, each containing some transform relative to the parent and one sort being able to display a model.
From the GLKit documentation, I think the best way to keep the sort of camera you want (and indeed the object locations) is to store it directly as a GLKMatrix4 or a GLKQuaternion — so you don't derive the matrix or quaternion (plus location) from some other description of the camera, rather the matrix or quaternion directly is the storage for the camera.
Both of those classes have methods built in to apply rotations, and GLKMatrix4 can directly handle translations. So you can directly map the relevant gestures to those functions.
The only slightly non-obvious thing I can think of when dealing with the camera in that way is that you want to send the inverse to OpenGL rather than the thing itself. Supposing you use a matrix, the reasoning is that if you wanted to draw an object at that location you'd load the matrix directly then draw the object. When you draw an object at the same location as the camera you want it to end up being drawn at the origin. So the matrix you have to load for the camera is the inverse of the matrix you'd load to draw at that location because you want the two multiplied together to be the identity matrix.
I'm not sure how complicated the models for your bricks are but you could hit a performance bottleneck if they're simple and all moving completely independently. The general rule when dealing with OpenGL is that the more geometry you can submit at once, the faster everything goes. So, for example, an entirely static world like that in most games is much easier to draw efficiently than one where everything can move independently. If you're drawing six-sided cubes and moving them all independently then you may see worse performance than you might expect.
If you have any bricks that move in concert then it is more efficient to draw them as a single piece of geometry. If you have any bricks that definitely aren't visible then don't even try to draw them. As of iOS 5, GL_EXT_occlusion_query_boolean is available, which is a way to pass some geometry to OpenGL and ask if any of it is visible. You can use that in realtime scenes by building a hierarchical structure describing your data (which you'll already have if you've directly followed the UIView analogy), calculating or storing some bounding geometry for each view and doing the draw only if the occlusion query suggests that at least some of the bounding geometry would be visible. By following that sort of logic you can often discard large swathes of your geometry long before submitting it.