I am working on a project and need to find velocity and displacement in a single direction (that direction being straight up and down). I am using my Apple Watch and retrieving all of the Core Motion data from this. I understand that there is drift when integrating the acceleration which can create highly inaccurate displacements. Although through my research, I have read that if you constrain the motion to just one direction you can get better results.
If I would like to find velocity and displacement in only one direction will that truly give me better results? If so, how is this constraining actually done mathematically?
All the work I have done so far is to find the resultant direction of the acceleration from userAcceleration and while looking into the best way to integrate came across this displacement drift issue and wanted to find a path forward.
Related
I have a graph with vertices and edges (orthogonalEdgeStyle) and want to create new edges. After the creation the routing most times crosses existing vertices. Is there any possibility to route the new edges in a way that they not cross any vertex?
The best solution would be that other edges are also not crossed, but I think this is even more complex.
Any help is appreciated, if there is no build-in functionality (I found nothing), perhaps anybody has an idea where to start (overwrite function, algorithm)?
I'm also searching for a possibility to automatically create "bridges" if two edges are crossing.
In my LigGdx based game, I wish to move my Sprite in an elliptical path to reach the destination. I do not find any support in Universal tween engine. Sample of route example is shown below.
Questions :
Is there is any methods in UniversalTween Engine to have a elliptical path ?
Also let me know what is waypoints in UniversalTween Engine ?
Thanks in Advance !
The Universal Tween Engine now supports curves - Default is CatmullRom which would definitely be able to provide the smooth movement you want.
It's a little tricky to get your head around at first but not that bad once you get used to it.
Universal Tween Engine
Details of update that added curves
Well I have searched up this question for you and discovered you many people have already asked this question, and none of them got an answer, yet. So I will try to answer as best as I can. I believe that my method is not the best. But if your application is not time or performance sensitive, then this method may work.
Now this comes to a math problem. You know that the screen is make out of pixels and there is no point making it overly detailed because it isn't possible. So you can do this:
They grey line being your intended line, and the green line being your actual drawn line. If you move objects using the tween engine along the green path and switch path when hitting the red dots. You could mimic an elliptical movement. However, you need to use math and calculate your path. You could set the coordinates of your path as a constant for every screen size, or you could calculate it every time.
Overall, the more points you calculate, the more elliptical the movement will be.
Anyways if you look at this website, it teaches you how to tween.
You can use Tween.to(...); to help you tween to the points.
Hope this helped you
First time asking a question on the stack exchange, hopefully this is the right place.
I can't seem to develop a close enough approximation algorithm for my situation as I'm not exactly the best in terms of 3D math.
I have a 3d environment in which I can access the position and rotation of any object, including my camera, as well as run trace lines from any two points to get distances between a point and a point of collision. I also have my camera's field of view. I do not have any form of access to the world/view/projection matrices however.
I also have a collection of 2d images that are basically a set of screenshots of the 3d environment from the camera, each collection is from the same point and angle and the average set is taken at about an average of a 60 degree angle down from the horizon.
I have been able to get to the point of using "registration point entities" that can be placed in the 3d world that represent the corners of the 2d image, and then when a point is picked on the 2d image it is read as a coordinate with range 0-1, which is then interpolated between the 3d positions of the registration points. This seems to work well, but only if the image is a perfect top down angle. When the camera is tilted and another dimension of perspective is introduced, the results become more grossly inaccurate as there no compensation for this perspective.
I don't need to be able to calculate the height of a point, say a window on a sky scraper, but at least the coordinate at the base of the image plane, or which if I extend a line out from my image from a specified image space point I need at least the point that the line will intersect with the ground if there was nothing in the way.
All of the material I found about this says to just deproject the point using the world/view/projection matrices, which I find straightforward in itself except I don't have access to these matrices, just data I can collect at screenshot time and other algorithms use complex maths I simply don't grasp yet.
One end goal of this would be able to place markers in the 3d environment where a user clicks in the image, while not being able to run a simple deprojection from the user's view.
Any help would be appreciated, thanks.
Edit: Herp derp, while my implementation for doing so is a bit odd due to the limitations of my situation, the solution essentially boiled down to ananthonline's answer about simply recalculating the view/projection matrices.
Between position, rotation and FOV of the camera, could you not calculate the View/Projection matrices of the camera (songho.ca/opengl/gl_projectionmatrix.html) - thus allowing you to unproject known 3D points?
Ok, so I'll try to be as descriptive as possible.
I'm working on a project for a client that requires a jibjab-style masking feature of an uploaded image.
I would like to be able to generate a database-storable object that contains anchor/control positions of a bezier shape, so I can pull it out later and re-mask the object. This all is pretty easy to do, except for one catch : I need to create the bezier object from a user-drawn outline.
So far, here's how I imagine the process going:
on mouse down, create a new sprite, beginFill, and moveTo mouse position.
on mouse move, lineTo an XY coordinate.
on mouse up, endFill.
This all works just great. I could just store the info here, but I would be looking at a GIGANTIC object full of tons of pretty useless x/y coordinates, and no way to really make fine-tuning changes outside of putting handles on every pixel. (I may as well give the end user a pencil tool...)
Here's what I'm thinking as far as bezier curve calculation goes :
1: Figure out when I need to start a new curve, and track the xy of the pixel on this interval. I'm imagining this being just a pixel count, maybe just increment a count variable per mouse move and make a new one every x pixels. The issue here is some curves would be inaccurate, and others unnecessary, but I really just need a general area, not an exact representation, so it could work. I'd be happier with something a little smarter though.
2: take each new x/y, store it as an anchor, and figure out where a control would go to make the line curve between this and the last anchor. this is where I get really hung up. I'm sure someone has done this in flash, but no amount of googling can seem to help me out with the way to get this done. I've done a lot of sketching and what little math I can wrap my brain around, but can't seem to figure out a way of converting pixels to beziers.
Is this possible? All I really need is something that will get close to the same shape. I'm thinking about maybe only placing anchors when the angle of the next pixel is beyond 180 degrees in relation to the current line or something, and just grabbing the edge of the arc between these changes, but no matter how hard I try, I can't seem to figure out how to get this working!
Thanks for your help, I'll be sure to post my progress here as I go, I think this could be really useful in many applications, as long as it's actually feasible...
Jesse
It sounds like a lot of work to turn pixels into Bezier curves. You could try using something like the Linear least squares algorithm. http://en.wikipedia.org/wiki/Linear_least_squares
A different tact, could you have your users draw vector graphics instead? That way you can just store the shapes in the database.
Another cool method of converting raster to vector would be something like this iterative program: http://rogeralsing.com/2008/12/07/genetic-programming-evolution-of-mona-lisa/
Good luck
In my answer to this question I discuss using autotrace to convert bitmaps to beziers. I recommend passing your user drawing through this program on the server. Autotrace does a fantastic job of tracing and simplifying so there is no need to try and reinvent the wheel here.
Thanks for the answers, although I guess I probably should be more specific about the application, I'm really only needing an outline for a mask, so converting images to vectors or polygons, despite how cool that is, doesn't really fix my issue. The linear least squares algorithm is mega cool, I think this might be closer to what I'm looking for.
I have a basic workaround going right now, I'm just counting mouse moves, then every X (playing with it to get most desirable curve) moves, I grab the xy position. then, I take every other stored xy, and turn it into an anchor, the remaining xys are turned into controls. This is producing somewhat desirable results, but has some minor issues, in that the speed at which the mask is drawn effects the number of handles, and it's really just getting a general area, not a precise fit.
Interestingly, users seem to draw slower for more precise shapes, so this solution works a lot better than I had imagined, but it's not as nice as it could be. This will work for the client, so although there's no reason to pursue it further, I like learning new things, and will spend some off the clock time looking into linear least equations and seeing if I can drum up a class that will do these computations for me. If anyone runs across some AS3 code for this type of thing, or would like some of mine, let me know, this is an interesting puzzle.
Does anyone have any good references for equations which can be implemented relatively easily for how to compute the transfer of angular momentum between two rigid bodies?
I've been searching for this sort of thing for a while, and I haven't found any particularly comprehensible explanations of the problem.
To be precise, the question comes about as this; two rigid bodies are moving on a frictionless (well, nearly) surface; think of it as air hockey. The two rigid bodies come into contact, and then move away. Now, without considering angular momentum, the equations are relatively simple; the problem becomes, what happens with the transfer of angular momentum between the bodies?
As an example, assume the two bodies have no angular momentum whatsoever; they're not rotating. When they interact at an oblique angle (vector of travel does not align with the line of their centers of mass), obviously a certain amount of their momentum gets transferred into angular momentum (i.e. they each get a certain amount of spin), but how much and what are the equations for such?
This can probably be solved by using a many-body rigid system to calculate, but I want to get a much more optimized calculation going, so I can calculate this stuff in real-time. Does anyone have any ideas on the equations, or pointers to open-source implementations of these calculations for inclusion in a project? To be precise, I need this to be a rather well-optimized calculation, because of the number of interactions that need to be simulated within a single "tick" of the simulation.
Edit: Okay, it looks like there's not a lot of precise information about this topic out there. And I find the "Physics for Programmers" type of books to be a bit too... dumbed down to really get; I don't want code implementation of an algorithm; I want to figure out (or at least have sketched out for me) the algorithm. Only in that way can I properly optimize it for my needs. Does anyone have any mathematic references on this sort of topic?
If you're interested in rotating non-spherical bodies then http://www.myphysicslab.com/collision.html shows how to do it. The asymmetry of the bodies means that the normal contact force during the collision can create a torque about their respective CGs, and thus cause the bodies to start spinning.
In the case of a billiard ball or air hockey puck, things are a bit more subtle. Since the body is spherical/circular, the normal force is always right through the CG, so there's no torque. However, the normal force is not the only force. There's also a friction force that is tangential to the contact normal which will create a torque about the CG. The magnitude of the friction force is proportional to the normal force and the coefficient of friction, and opposite the direction of relative motion. Its direction is opposing the relative motion of the objects at their contact point.
Well, my favorite physics book is Halliday and Resnick. I never ever feel like that book is dumbing down anything for me (the dumb is inside the skull, not on the page...).
If you set up a thought problem, you can start to get a feeling for how this would play out.
Imagine that your two rigid air hockey pucks are frictionless on the bottom but have a maximal coefficient of friction around the edges. Clearly, if the two pucks head towards each other with identical kinetic energy, they will collide perfectly elastically and head back in opposite directions.
However, if their centers are offset by 2*radius - epsilon, they'll just barely touch at one point on the perimeter. If they had an incredibly high coefficient of friction around the edge, you can imagine that all of their energy would be transferred into rotation. There would have to be a separation after the impact, of course, or they'd immediately stop their own rotations as they stuck together.
So, if you're just looking for something plausible and interesting looking (ala game physics), I'd say that you could normalize the coefficient of friction to account for the tiny contact area between the two bodies (pick something that looks interesting) and use the sin of the angle between the path of the bodies and the impact point. Straight on, you'd get a bounce, 45 degrees would give you bounce and spin, 90 degrees offset would give you maximal spin and least bounce.
Obviously, none of the above is an accurate simulation. It should be a simple enough framework to cause interesting behaviors to happen, though.
EDIT: Okay, I came up with another interesting example that is perhaps more telling.
Imagine a single disk (as above) moving towards a motionless, rigid, near one-dimensional pin tip that provides the previous high friction but low stickiness. If the disk passes at a distance that it just kisses the edge, you can imagine that a fraction of its linear energy will be converted to rotational energy.
However, one thing you know for certain is that there is a maximum rotational energy after this touch: the disk cannot end up spinning at such a speed that it's outer edge is moving at a speed higher than the original linear speed. So, if the disk was moving at one meter per second, it can't end up in a situation where its outer edge is moving at more than one meter per second.
So, now that we have a long essay, there are a few straightforward concepts that should aid intuition:
The sine of the angle of the impact will affect the resulting rotation.
The linear energy will determine the maximum possible rotational energy.
A single parameter can simulate the relevant coefficients of friction to the point of being interesting to look at in simulation.
You should have a look at Physics for Game Developers - it's hard to go wrong with an O'Reilly book.
Unless you have an excellent reason for reinventing the wheel,
I'd suggest taking a good look at the source code of some open source physics engines, like Open Dynamics Engine or Bullet. Efficient algorithms in this area are an artform, and the best implementations no doubt are found in the wild, in throroughly peer-reviewed projects like these.
Please have a look at this references!
If you want to go really into Mecanics, this is the way to go, and its the correct and mathematically proper way!
Glocker Ch., Set-Valued Force Laws: Dynamics of Non-Smooth Systems. Lecture Notes in Applied Mechanics 1, Springer Verlag, Berlin, Heidelberg 2001, 222 pages. PDF (Contents, 149 kB)
Pfeiffer F., Glocker Ch., Multibody Dynamics with Unilateral Contacts. JohnWiley & Sons, New York 1996, 317 pages. PDF (Contents, 398 kB)
Glocker Ch., Dynamik von Starrkörpersystemen mit Reibung und Stößen. VDI-Fortschrittberichte Mechanik/Bruchmechanik, Reihe 18, Nr. 182, VDI-Verlag, Düsseldorf, 1995, 220 pages. PDF (4094 kB)