which algorithm should i use to change/modify the curves - iphone

I have made an application which draws a number of curves, using UIBezierPath. Now I'm trying to implement a modification functionality in it. To modify the particular curve one thing I can do is to draw all the curves again; I have not yet implemented this. But I think this algorithm would not be very efficient when the number of curves increases because I have to store all the points in the array and I have to run for loop to draw each curve every time I go for modification.
I am looking for more efficient algorithm. It will be helpful if someone can provide example code.

You can represent individual curves as UIBezierPaths and draw them separately by creating one CAShapeLayer per curve and assigning the shape layer's path property to the corresponding CGPath property of the bezier path. To update an individual curve, you then just have to manipulate one bezier path and the corresponding shape layers path property.

Redraw the curve until you have a performance problem as measured with Instruments. If that occurs again use Instruments to pinpoint the best way to optimize.
It is easy to get sucked into spending time on optimizations that are never needed. Initially it is much better to put that time and thinking into creating a "clean" code.

Related

Different ways to detect size of image on mesh versus size of mesh

I'm creating a puzzle game that generates random sized pieces with 2D meshes. The images contain transparent portions and sometimes a piece is completely transparent. I need to detect what percentage of a piece is transparent. One way I found to do this is to go pixel by pixel. I posted my solution to this HERE. However, this process adds a few seconds during loading which I'd like to avoid and I'm looking for other ideas
I've considered using the selection outline of a MeshCollider to somehow to get a surface area I can compare to the surface area of the mesh but everything I find is on the rendering of outline with specialized shaders. Does anyone have any ideas on to solve this?
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1) I guess you could add a PolygonCollider2D to your sprite and use its Path for the outline and calculation of the surface area. Not sure however if this will be faster.
PolygonCollider2D.GetPath:
A path is a cyclic sequence of line segments between points that define the outline of the Collider
Checking PolygonCollider2D.GetTotalPointCount or path length may be good enough to determine if the sprite is 'empty'.
Sprite.vertices, Sprite.triangles may also be helpful.
2) You could also improve performance of your first approach:
instead of calling GetPixel as you do now use GetPixels or GetPixels32 and loop through the array in one for loop.
Using GetPixels can be faster than calling GetPixel repeatedly, especially for large textures. In addition, GetPixels can access individual mipmap levels. For most textures, even faster is to use GetPixels32 which returns low precision color data without costly integer-to-float conversions.
check only every 2nd or nth pixel as it should be good enough for approximation
limit number of type casts

Finding area with CGContextEOFillPath

I am interested in using the CGContextEOFillPath feature provided by apple. I am guessing with the way the EOFill works, it probably has a way to take the filled in areas and calculate an area.
So my question is does anyone know of a way to use CGContextEOFillPath and find the area of the filled in sections.
If this isn't something that is easily done, maybe some pointers to a better way of doing this would be helpful. Though I need to use the EO style graphing.
Thanks.
What do you mean "Calculate the area"?
As in calculate the surface area of a complex shape?
It depends on your shapes.
Are they all polygons?
What about circles?
There are well known formulas for calculating the area of a polygon. (Wikipedia has it) Part of that calculation involves using an ABS() function because shapes drawn "counterclockwise" have the opposite sign as those drawn "clockwise". If you're looking to simulate the EO behavior, you can simply ignore the sign change, because, for you, it's desirable.
If you have more complicated shapes that involve curves, then you need to break the problem down into multiple parts - one part to solve for polygons - one to solve for circles - one to solve for other shapes, etc.

How to determine intersection of CGPaths

My Question is something similar to this.
I have 2 CGPathRef and 1 will be moved by finger touch. I want to find that whether the 2 CGPathRef are intersected? That question was asked almost 2 years ago and I want to know whether something has been found in the mean time.
This is fairly old, but I found it looking for a similar solution, in my problem I wanted to find when a circle overlapped with a path (a special case of your question).
I solved this by using CGPathCreateCopyByStrokingPath to create a stroked version of the original path using the radius of the circle as the stroke width. If the center point of the circle overlaps the stroked path then the original path overlaps the circle.
BOOL CGPathIntersectsCircle(CGPathRef path, CGPoint center, CGFloat radius)
{
CGPathRef fuzzyPath;
fuzzyPath = CGPathCreateCopyByStrokingPath(path, NULL, radius,
kCGLineCapRound,
kCGLineJoinRound, 0.0);
if (CGPathContainsPoint(fuzzyPath, NULL, center, NO))
{
CGPathRelease(fuzzyPath);
return YES;
}
CGPathRelease(fuzzyPath);
return NO;
}
Edit: A minor bug where the fuzzyPath was not released.
I have written a small pixel based path collision detection API for CGPathRefs. It requires that you add a few source directories to your project, and it only works with ARC, but it should at least show you how one might do something like this. It basically draws the two paths on two separate contexts, and then does pixel-by-pixel checks to see if any pixels are on both paths. Obviously this would be slow to run every time the user drags their finger, but it certainly could be done once every half second or so, maybe not even on the main thread.
This is the easiest way I've found of doing something like this, and it may easily be that there's no better way, besides using lots of math.
The source on Github
A quick Youtube demo.
Generally speaking, finding the intersection of two arbitrary CGPaths is going to be very complex.
There are ways to do approximations. Checking the intersections of the bounding boxes is a good first step. You can also subdivide the curve and repeat the process to get better approximations. Another option is to flatten the paths and see if any of the line segments of the flattened paths intersect.
For the general case, however, things get very nasty very fast. Consider, for example, the fact that two cubic bezier segments (never mind an entire path... just one segment) can intersect with another segment at up to 6 points. The more segments in your path, the more potential intersections. There is also the problem of degenerate bezier curves where a segment has a cusp that just touches one point of another segment. Does that count as an intersection? (sometimes yes, sometimes no)
It's not clear from your question, but you might also want to consider the intersections of the strokes that are applied to the curves, and correctly account for line joins and miters. That that gets even harder. Macromedia FreeHand (a drawing program similar to Adobe Illustrator) had a very large, complex, intensely mathematical library for discovering arbitrary bezier curve intersections. The problem is not easily solved.
To find the intersection of two CAShapeLayers, we can use below method, CAShapeLayer won't return frame. But we can get the refPath frame using CGPathGetBoundingBox. But this one will give the frame in rectangle.I thing you may understand.
if (CGRectIntersectsRect(CGPathGetBoundingBox(layer.path), CGPathGetBoundingBox(layer.path)))

Kink detection in drawn polylines

Users can sketch in my app using a very simple tool (move mouse while holding LMB). This results in a series of mousemove events and I record the cursor location at each event. The resulting polyline curve tends to be rather dense, with recorded points almost every other pixel. I'd like to smooth this pixelated polyline, but I don't want to smooth intended kinks. So how do I figure out where the kinks are?
The image shows the recorded trail (red pixels) and the 'implied' shape as a human would understand it. People tend to slow down near corners, so there is usually even more noise here than on the straight bits.
Polyline tracker http://www.freeimagehosting.net/uploads/c83c6b462a.png
What you're describing may be related to gesture recognition techniques, so you could search on them for ideas.
The obvious approach is to apply a curve fit, but that will have the effect of smoothing away all the interesting details and kinks. Another approach suggested is to look at speeds and accelerations, but that can get hairy (direction changes can be very fast or very slow and deliberate)
A fairly basic but effective approach is to simplify the samples directly into a polyline.
For example, work your way through the samples (e.g.) from sample 1 to sample 4, and check if all 4 samples lie within a reasonable error of the straight line between 1 & 4. If they do, then extend this to points 1..5 and repeat until such a time as the straight line from the start point to the end point no longer provides a resonable approximation to the curve defined by those samples. Create a line segment up to the previous sample point and start accumulating a new line segment.
You have to be careful about your thresholds when the samples are too close to each other, so you might want to adjust the sensitivity when regarding samples fewer than 4-5 pixels away from each other.
This will give you a set of straight lines that will follow the original path fairly accurately.
If you require additional smoothing, or want to create a scalable vector graphic, then you can then curve-fit from the polyline. First, identify the kinks (the places in your polyline where the angle between one line and the next is sharp - e.g. anything over 140 degrees is considered a smooth curve, anything less than that is considered a kink) and break the polyline at those discontinuities. Then curve-fit each of these sub-sections of the original gesture to smooth them. This will have the effect of smoothing the smooth stuff and sharpening the kinks. (You could go further and insert small smooth corner fillets instead of these sharp joints to reduce the sharpness of the joins)
Brute force, but it may just achieve what you want.
Rather than trying to do this from the resultant data, have you considered looking at the timing of the data as it comes in? If the mouse stops or slows noticably, you use the trend since the last 'kink' (the last time the mouse slowed) to establish the direction of travel. If the user goes off in a new direction, you call it a kink, otherwise, you ignore the current slowing trend and start waiting for the next one.
Well, one way would be to use a true curve-fitting algorithm. Generate a bezier curve (with exact endpoints, using Catmull-Rom or something similar), then optimize & recursively subdivide (using distance from actual line points as a cost metric). This may be too complicated for your use-case, though.
Record the order the pixels are drawn in. Then, compute the slope between pixels that are "near" but not "close". I'm guessing a graph of the slope between pixel(i) and pixel(i+7) might exhibit easily identifable "jumps" around kinks in the curve.

Line smoothing in Cocoa Touch

How would I smooth a line (UIBeizerPath) or a set of points? Right now it draws it jagged. I read about spline interpolation, could anyone point me to an implementation of this in cocoa or C or give me an alternate line smoothing algorithm.
I don't think you need to do Bezier paths with curves. You can keep drawing straight line segments but add more data points with interpolation. This is especially important because I'm assuming you want to smooth only on one axis so you don't end up with odd things like loops in your graph.
So you want to add more points to your source data, between the existing points, and use an interpolation algorithm that's more sophisticated than a linear interpolation. There are many to choose from. Quadratic? Sine-based? Many, and it depends on what kind of data you're using.
Quartz (which UIKit uses for drawing, and in many places makes you use directly for drawing) has anti-aliasing support built-in. Most contexts have it turned on already, so you should not have aliased (jagged) drawing unless you're turning anti-aliasing off. So, stop doing that. :-)
The contexts that don't have it turned on by default are mostly those where it isn't appropriate, such as PDF contexts and CGLayer contexts. The documentation implies that those contexts don't even support anti-aliasing, which makes some amount of sense.
CGContext provides a couple of functions for turning anti-aliasing on and off, but you should never need to call them except when you want aliasing, which you don't. You could try turning it on using those functions; if that works, then you should investigate why it was ever off in the first place.
Are you drawing the path from within a CALayer? That may be why it's off; there's an Info.plist key you have to turn on to get anti-aliasing turned on by default in such contexts.
I've found that if you draw a line or an image on the edge of your frame that it will appear jagged. Move the line in a few (or grow your frame) and it should appear nice and crisp. Again, not sure if that's your question or not but it has bit me a few times.
For instance if you are displaying an image inside a CALayer, make sure there is space between the image and the frame if you are doing anything but 90 degree angles.