I'm looking for a good method to shift grid points around in a numerical problem that I am solving (gradient descent). I was hoping someone knew of a good resource that discussed simple methods to shift the positions of grid points to make a resulting integration more accurate. I don't think I need a fancy method, just something for one dimension. I'm having more trouble finding a simple explanation than I thought I would.
Something like shifting the points towards larger values of the function I'm integrating would be fine, but I don't want to guess on how to write the cost function for shifting the grid points and want to do something established instead of making a new method.
Related
I have these items already successfully placed vertically with position: absolute and a calculated top value–
my library of choice for all things time related (dayjs) also comes with functionality to check if one item overlaps with another one, nice.
Each item has a startedAt and endedAt property holding ISO datetime strings, i.e. 2022-03-31T17:34Z – using dayjs I can convert them to anything the overlap detection needs.
In the screenshot you can see some examples of overlaps we would like to see in the final result. After some research the TUI calendar solves the issue pretty much just like we want it.
For a lot of reasons we can't use tui-calendar as a whole and extracting the logic to place the items (basically get width and left for each overlapping item) is way beyond my skills (although I think I've found the functions that are responsible for this)
So far I've failed miserably to solve this myself; both using recursion and loops :X
Questions:
– Is there an easier way?
– Is there a dedicated library to solve this?
– Any ideas how to kickstart a solution myself?
Kinda desperate here :D
Thanks!
It's even written in the doc that Camera.unproject() assumes that the screen has it'origin in the top left corner, on the other hand Camera.project() assumes that the screen has its origin in the bottom left corner. This is so annoying. Is this intentional? Am I not getting something?
tmp3.x = selected.pos.x;
tmp3.y = selected.pos.y;
camera.unproject(tmp3);
camera.project(tmp3);
This flips the vector, where it should return the same vector.
EDIT:
First I was trying to use Viewport.project() and Viewport.unproject() to convert points from one viewport to another (to position a context menu over a game element).They also inherit this naming confusion, and it's not even mentioned in the javadocs there.
PS. I really like libGdx. I've just written this to maybe spare some headache for someone in the future as I didn't find this anywhere on the web pointed out directly.
The Javadoc for the project method explains why. I think the assumption is that the most common reason to project a point is to line something up with the UI which will also be Y-up. But when I projecting, it is most likely to convert a touch coordinate to world coordinates.
Or in another way of looking at it, everything you do in OpenGL is Y-up so everything's designed to be Y-up or to get you there.
Not saying this is necessarily the best way; just trying to guess at the thought process. It probably wouldn't hurt to submit a PR for another type of project method of you need one, or you could subclass whichever type of camera you're using and add the additional method.
Can somebody walk me through how this madness works:
http://www.youtube.com/watch?v=KL8QLLmUvbg
Specifically I'm interested in equally distributing a given number of squares along a path. I'm also wondering if this would work with multiple line segments-- this is one curved segment and I need a solution to distribute objects across one big line with multiple curves in it.
Basically I'm trying to make a tail that realistically follows a character.
Thanks
First a Bezier spline is a curve parametrized by t. However t is not arc-length along the curve. So the procedure is this.
Calculate the length of the bezier curve.
Find the t values that divide the curve into N equal length segments.
However these two steps are tricky.
The first has a closed form solution only for quadratic Beziers. (You can find the solution here )
Otherwise you use a subdivide and approximate approach, or a numerical integration approach (and in some sense these are equivalent - I'd go the numerical integration approach as this has better provable behavior at the cost of slightly trickier implementation, but you may or may not care about that.)
The second is basically a guess a t value, and improve approach (using the same style of calculation at each step as step 1). I'd implement this using a secant style search, as I suspect the derivatives required to use a Newton's method search would be too expensive to calculate.
Once you've got the positions of the objects, you need to use the curve tangent and cotangent to create a local reference frame for the object. This allows the objects to sit nicely in the path of the curve, rather than all having the same orientation. Note that this only works nicely in 2D - in 3D you can still get some weird behavior with object orientation.
You can start by looking into how a bezier curve is calculated. Wikipedia has some nice animations with the explanation and this link has some as3 code.
but if you're trying to create a tail, there are simpler ways of doing that, like using following behaviour or a physics library
I ended up creating a following behavior system like Daniel recommended for simplicities sake. But to elaborate on Michael's awesome answer I stumbled onto this tutorial which details the the spline technique.
http://gamedev.tutsplus.com/tutorials/implementation/create-a-glowing-flowing-lava-river-using-bezier-curves-and-shaders/
I am working on a simple drawing application, and i need an algorithm to make flood fills.
The user workflow will look like this (similar to Flash CS, just more simpler):
the user draws straight lines on the workspace. These are treated as vectors, and can be selected and moved after they are drawn.
user selects the fill tool, and clicks on the drawing area. If the area is surrounded by lines in every direction a fill is applied to the area.
if the lines are moved after the fill is applied, the area of fill is changed accordingly.
Anyone has a nice idea, how to implement such algorithm? The main task is basically to determine the line segments surrounding a point. (and storing this information somehow, incase the lines are moved)
EDIT: an explanation image: (there can be other lines of course in the canvas, that do not matter for the fill algorithm)
EDIT2: a more difficult situation:
EDIT3: I have found a way to fill polygons with holes http://alienryderflex.com/polygon_fill/ , now the main question is, how do i find my polygons?
You're looking for a point location algorithm. It's not overly complex, but it's not simple enough to explain here. There's a good chapter on it in this book: http://www.cs.uu.nl/geobook/
When I get home I'll get my copy of the book and see if I can try anyway. There's just a lot of details you need to know about. It all boils down to building a DCEL of the input and maintain a datastructure as lines are added or removed. Any query with a mouse coord will simply return an inner halfedge of the component, and those in particular contain pointers to all of the inner components, which is exactly what you're asking for.
One thing though, is that you need to know the intersections in the input (because you cannot build the trapezoidal map if you have intersecting lines) , and if you can get away with it (i.e. input is few enough segments) I strongly suggest that you just use the naive O(n²) algorithm (simple, codeable and testable in less than 1 hour). The O(n log n) algorithm takes a few days to code and use a clever and very non-trivial data structure for the status. It is however also mentioned in the book, so if you feel up to the task you have 2 reasons to buy it. It is a really good book on geometric problems in general, so for that reason alone any programmer with interest in algorithms and datastructures should have a copy.
Try this:
http://keith-hair.net/blog/2008/08/04/find-intersection-point-of-two-lines-in-as3/
The function returns the intersection (if any) between two lines in ActionScript. You'll need to loop through all your lines against each other to get all of them.
Of course the order of the points will be significant if you're planning on filling them - that could be harder!
With ActionScript you can use beginFill and endFill, e.g.
pen_mc.beginFill(0x000000,100);
pen_mc.lineTo(400,100);
pen_mc.lineTo(400,200);
pen_mc.lineTo(300,200);
pen_mc.lineTo(300,100);
pen_mc.endFill();
http://www.actionscript.org/resources/articles/212/1/Dynamic-Drawing-Using-ActionScript/Page1.html
Flash CS4 also introduces support for paths:
http://www.flashandmath.com/basic/drawpathCS4/index.html
If you want to get crazy and code your own flood fill then Wikipedia has a decent primer, but I think that would be reinventing the atom for these purposes.
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.