I am working on a graphic application in which the user draws lines.
The lines are not smooth. I see the problem especially when drawing the lines slowly.
What would be the correct way to smoothen the lines?
I read the following great article: http://www.merowing.info/2012/04/drawing-smooth-lines-with-cocos2d-ios-inspired-by-paper/
It fixed some of the problem, but not all of it. Still, when drawing lines slowly, they look jagged:
The problem is actually that you have too many sample points.
This is why the problem is exacerbated when the user inputs points slowly, rather than quickly. One possible solution is to use some sort of best-fitting line equation (e.g. Least Squares) to reduce the number of points and simplify it to an approximation.
There are more sophisticated approaches to smoothing user input, but in this simple case all you really need to do is reduce the sample size.
Related
I enjoy computer graphics.
I was wondering what the fastest engine was with the following functionality:
Draws triangles with 4 color channels rgba and allows for the drawing of point and directional lights.
Texturing would be a cool additional feature, but again I am looking for the fastest engine, not the most functional. Camera animation and object animation will be imperative.
Finally there are really 2 answers for this question, 1 for general development and one for web, but if you can only speak to one or the other your contributions will be appreciated!
There are quite a lot of engines that do the job. One of the most known is for example Unity, where you also have tons of other features in good performance.
But I think you are not really looking for an engine but an API. Examples are OpenGL or DirectX (already mentioned). OpenGL even has a specific web content (WebGL).
There is one more problem: the triangles should be semitransparent. What is missing in the other answer is the question if the triangles are already ordered. OpenGL for example is good in rendering objects where it does not matter which triangle is nearest to the viewer. It "searches" this one on the fly and shows only the triangle that is visible. But with semitransparent triangles it is possible to see different triangles overlapping each other and therefore it is not only necessary to know which triangle is in the front, but which triangle comes directly after that and so on. OpenGL offers blending for this feature, but is necessary to order the semitransparent triangles manually before rendering. This is called the Painters Algorithm. While Sorting of objects is a complex problem, exspecially with a large number of objects, this could take quite long time.
For this there is another solution called "depth peeling". The idea is to render all triangles multiple times with OpenGL. The first time you get all the triangles which are in the front. Now you render all triangles again, but without the triangles in the front. This results in the second nearest triangles to the viewer. After that all triangles are rendered again, but without the first two "peels", which results in the third nearest triangles and so on. This is expensive because everything has to get rendered multiple times, but in cases where there is a very large number of triangles this is faster than sorting (and more precise due to overlapping triangles). In most cases four peels are enough for good results. For further read I suggest the following paper of Everitt: http://gamedevs.org/uploads/interactive-order-independent-transparency.pdf
Your best bet is probably OpenGL. In the case of the web, you could use WebGL and in the case of native desktop or mobile development you could directly use OpenGL.
I need to be able to turn a black and white image into series of lines (start, end points) and circles (start point, radius). I have a "pen width" that's constant.
(I'm working with a screen that can only work with this kind of graphics).
Problem is, I don't want to over complicate things - I could represent any image with loads of small lines, but it would take a lot of time to draw, so I basically want to "approximate" the image using those lines and circles.
I've tried several approaches (guessing lines, working area by area, etc) but none had any reasonable results without using a lot of lines and circles.
Any idea on how to approach this problem?
Thanks in advance!
You don't specify what language you are working in here but I'd suggest OpenCV if possible. If not, then most decent CV libraries ought to support the features that I'm about to describe here.
You don't say if the input is already composed of simple shapes ( lines and polygons) or not. Assuming that it's not, i.e. it's a photo or frame from a video for example, you'll need to do some edge extraction to find the lines that you are going to model. Use a Canny or other edge detector to convert the image into a series of lines.
I suggest that you then extract Circles as they are the richest feature that you can model directly. You should consider using a Hough Circle transform to locate circles in your edge image. Once you've located them you need to remove them from the edge image (to avoid duplicating them in the line processing section below).
Now, for each pixel in the edge image that's 'on' you want to find the longest line segment that it's a part of. There are a number of algorithms for doing this, simplest would be Probabilistic Hough Transform (also available in openCV) to extract line segments which will give you control over the minimum length, allowed gaps etc. You may also want to examine alternatives like LSWMS which has OpenCV source code freely available.
Once you have extracted the lines and circles you can plot them into a new image or save the coordinates for your output device.
Imagine you have a chessboard textured triangle shown in front of you.
Then imagine you move the camera so that you can see the triangle from one side, when it nearly looks as a line.
You will provably see the line as grey, because this is the average color of the texels shown in a straight line from the camera to the end of the triangle. The GPU does this all the time.
Now, how is this implemented? Should I sample every texel in a straight line and average the result to get the same output? Or is there another more efficient way to do this? Maybe using mipmaps?
It does not matter if you look at the object from the side, front, or back; the implementation remains exactly the same.
The exact implementation depends on the required results. A typical graphics API such as Direct3D has many different texture sample techniques, which all have different properties. Have a look at the documentation for some common sampling techniques and an explanation.
If you start looking at objects from an oblique angle, the texture on the triangle might look distorted with most sampling techniques, and Anisotropic Filtering is often used in these scenario's.
Given an input of 2D points, I would like to segment them in lines. So if you draw a zig-zag style line, each of the segments should be recognized as a line. Usually, I would use OpenCV's
cvHoughLines or a similar approach (PCA with an outlier remover), but in this case the program is not allowed to make "false-positive" errors. If the user draws a line and it's not recognized - it's ok, but if the user draws a curcle and it comes out as a square - it's not ok. So I have an upper bound on the error - but if it's a long line and some of the points have a greater distance from the approximated line, it's ok again. Summed up:
-line detection
-no false positives
-bounded, dynamically adjusting error
Oh, and the points are drawn in sequence, just like hand drawing.
At least it does not have to be fast. It's for a sketching tool. Anyone has an idea?
This has the same difficulty as voice and gesture recognition. In other words, you can never be 100% sure that you've found all the corners/junctions, and among those you've found you can never be 100% sure they are correct. The reason you can't be absolutely sure is because of ambiguity. The user might have made a single stroke, intending to create two lines that meet at a right angle. But if they did it quickly, the 'corner' might have been quite round, so it wouldn't be detected.
So you will never be able to avoid false positives. The best you can do is mitigate them by exploring several possible segmentations, and using contextual information to decide which is the most likely.
There are lots of papers on sketch segmentation every year. This seems like a very basic thing to solve, but it is still an open topic. The one I use is out of Texas A&M, called MergeCF. It is nicely summarized in this paper: http://srlweb.cs.tamu.edu/srlng_media/content/objects/object-1246390659-1e1d2af6b25a2ba175670f9cb2e989fe/mergeCF-sbim09-fin.pdf.
Basically, you find the areas that have high curvature (higher than some fraction of the mean curvature) and slow speed (so you need timestamps). Combining curvature and speed improves the initial fit quite a lot. That will give you clusters of points, which you reduce to a single point in some way (e.g. the one closest to the middle of the cluster, or the one with the highest curvature, etc.). This is an 'over fit' of the stroke, however. The next stage of the algorithm is to iteratively pick the smallest segment, and see what would happen if it is merged with one of its neighboring segments. If merging doesn't increase the overall error too much, you remove the point separating the two segments. Rinse, repeat, until you're done.
It has been a while since I've looked at the new segmenters, but I don't think there have been any breakthroughs.
In my implementation I use curvature median rather than mean in my initial threshold, which seems to give me better results. My heavily modified implementation is here, which is definitely not a self-contained thing, but it might give you some insight. http://code.google.com/p/pen-ui/source/browse/trunk/thesis-code/src/org/six11/sf/CornerFinder.java
Crayon Physics Deluxe is a commercial game that came out recently. Watch the video on the main link to get an idea of what I'm talking about.
It allows you to draw shapes and have them react with proper physics. The goal is to move a ball to a star across the screen using contraptions and shapes you build.
While the game is basically a wrapper for the popular Box2D Physics Engine, it does have one feature that I'm curious about how it is implemented.
Its drawing looks very much like a Crayon. You can see the texture of the crayon and as it draws it varies in thickness and darkness just like an actual crayon drawing would look like.
(source: kloonigames.com)
(source: kloonigames.com)
The background texture is freely available here.
What kind of algorithm would be used to render those lines in a way that looks like a Crayon? Is it a simple texture applied with a random thickness and darkness or is there something more going on?
I remember reading (a long time ago) a short description of an algorithm to do so:
for the general form of the line, you split the segment in two at a random point, and move this point slightly away from it's position (the variation depending on the distance of the point to the extremity). Repeat recursively/randomly. In this way, you lines are not "perfect" (straight line)
for a given segment you can "overshoot" a little bit, by extending one extremity or the other (or both). In this way, you don't have perfect joints. If i remember well, the best was to extends the original extremities, but you can do this for the sub-segment if you want to visibly split them.
draw the lines with pattern/stamp
there was also the (already mentioned) possibility to drawn with different starting and ending opacity (to mimic the tendency to release the pen at the end of drawing)
You can use a different size for the stamp on the beginning and the end of the line (also to mimic the tendency to release the pen at the end of drawing). For the same effect, you can also draw the line twice, with a small variation for one of the extremity (be careful with the alpha in this case, as the line will be drawn twice)
Last, for a given line, you can do the previous modifications several times (ie draw the line twice, with different variations) : human tend to repeat a line if they make some mistakes.
Regards
If you blow the image up you can see a repeating stamp-pattern .. there's probably a small assortment that it uses as it moves from a to b - might even rotate them ..
The wavering of the line can't be all that difficult to do. Divide into a bunch of random segments, pick positions slightly away from the direct route and draw splines.
Here's a paper that uses a lot of math to simulate the deposition of wax on paper using a model of friction. But I think your best bet is to just use a repeating pattern, as another reader mentioned, and vary the opacity according to pressure.
For the imperfect line drawing parts, I have a blog entry describing how to do it using bezier curves.
You can base darkness on speed. That's just measuring the distance traveled by the cursor between this frame and the last frame (remember Pythagorean theorem) and then when you go to draw that line segment on screen, adjust the alpha (opacity) according to the distance you measured.
There is a paper available called Mimicking Hand Drawn Pencil Lines which covers a bit of what you are after. Although it doesn't present a very detailed view of the algorithm, the authors do cover the basics of the steps that they used.
This paper includes high level descriptions of how they generated the lines, as well as how they generated the textures for the lines, and they get results which are similar to what you want.
This article on rendering chart series to look like XKCD comics has an algorithm for perturbing lines which may be relevant. It doesn't cover calculating the texture of a crayon drawn line, but it does offer an approach to making a straight line look imperfect in a human-like way.
Example output:
I believe the easiest way would simply be to use a texture with random darkness (some gradients, maybe) throughout, and set size randomly.