Is there a way to adjust xy coordinates to fit within a bounding box in Prawn PDF if they are larger then the height of the box?
I'm using the gem 'signature-pad-rails' to capture signatures which then stores the following:
[{"lx":98,"ly":23,"mx":98,"my":22},{"lx":98,"ly":21,"mx":98,"my":23},{"lx":98,"ly":18,"mx":98,"my":21}, ... {"lx":405,"ly":68,"mx":403,"my":67},{"lx":406,"ly":69,"mx":405,"my":68}]
I have the follow to show the signature in my pdf:
bounding_box([0, cursor], width: 540, height: 100) do
stroke_bounds
#witness_signature.each do |e|
stroke { line [e["lx"], 100 - e["ly"]],
[e["mx"], 100 - e["my"] ] }
end
end
But the signature runs off the page in some cases, isn't centre and just generally runs amuck.
Your question is pretty vague, so I'm guessing what you mean.
To rescale a sequence of coordinates (x[i], y[i]), i = 1..n to fit in a given bounding box of size (width, height) with origin (0,0) as in Postscript, first decide whether to preserve the aspect ratio of the original image. Fitting to a box won't generally do that. Since you probably don't want to distort the signature, say the answer is "yes."
When scaling an image into a box preserving aspect ratio, either the x- or y-axis determines the scale factor unless the box happens to have exactly the image's aspect. So next is to decide what to do with the "extra space" on the alternate axis. E.g. if the image is tall and thin compared to the bounding box, the extra space will be on the x-axis; if short and fat, it's the y-axis.
Let's say center the image within the extra space; that seems appropriate for a signature.
Then here is pseudocode to re-scale the points to fit the box:
x_min = y_min = +infty, x_max = y_max = -infty
for i in 1 to n
if x[i] < x_min, x_min = x[i]
if x[i] > x_max, x_max = x[i]
if y[i] < y_min, y_min = y[i]
if y[i] > y_max, y_max = y[i]
end for
dx = x_max - x_min
dy = y_max - y_min
x_scale = width / dx
y_scale = height / dy
if x_scale < y_scale then
// extra space is on the y-dimension
scale = x_scale
x_org = 0
y_org = 0.5 * (height - dy * scale) // equal top and bottom extra space
else
// extra space is on the x_dimension
scale = y_scale
x_org = 0.5 * (width - dx * scale) // equal left and right extra space
y_org = 0
end
for i in 1 to n
x[i] = x_org + scale * (x[i] - x_min)
y[i] = y_org + scale * (y[i] - y_min)
end
As my tile says that I want to get random number for origin (X-Axis & y-Axis) so in my whole screen in iPad landscape I have 1 rectangle, I want to get random number for origin which out of this rectangle, so obiously I want to get random number for X-Axis between max and min and same as for Y-Axis.
I tried with following answers but not helpful for me.
Generate Random Numbers Between Two Numbers in Objective-C
Generate a random float between 0 and 1
Generate random number in range in iOS?
For more clear see below image
In above image I just want to find random number (for origin) of GREEN screen. How can I achieve it ?
Edited
I had tried.
int randNum = rand() % ([max intValue] - [min intValue]) + [min intValue];
Same for both X-Axis & y-Axis.
If the blue exclusion rectangle is not "too large" compared to the green screen rectangle
then the easiest solution is to
create a random point inside the green rectangle,
check if the point lies inside the blue rectangle, and
repeat the process if necessary.
That would look like:
CGRect greenRect = ...;
CGRect blueRect = ...;
CGPoint p;
do {
p = CGPointMake(greenRect.origin.x + arc4random_uniform(greenRect.size.width),
greenRect.origin.y + arc4random_uniform(greenRect.size.height));
} while (CGRectContainsPoint(blueRect, p));
If I remember correctly, the expected number of iterations is G/(G - B), where G is
the area of the green rectangle and B is the area of the blue rectangle.
What if you first determined x within the green rectangle like this:
int randomX = arc4random()%greenRectangle.frame.size.width;
int randomY; // we'll do y later
Then check if this is inside the blue rectangle:
if(randomX < blueRectangle.frame.origin.x && randomX > (blueRectangle.frame.origin.x + blueRectangle.frame.size.width))
{
//in this case we are outside the rectangle with the x component
//so can randomly generate any y like this:
randomY = arc4random()%greenRectangle.frame.size.height;
}
//And if randomX is in the blue rectangle then we can use the space either before or after it:
else
{
//randomly decide if you are going to use the range to the left of blue rectangle or to the right
BOOL shouldPickTopRange = arc4random()%1;
if(shouldPickTopRange)
{
//in this case y can be any point before the start of blue rectangle
randomY = arc4random()%blueRectangle.frame.origin.y;
}
else
{
//in this case y can be any point after the blue rectangle
int minY = blueRectangle.frame.origin.y + blueRectangle.frame.size.height;
int maxY = greenRectangle.frame.size.height;
randomY = arc4random()%(maxY - minY + 1) + minY;
}
}
Then your random point would be:
CGPoint randomPoint = CGPointMake(randomX, randomY);
The only thing missing above is to check if your blue rectangle sits at y = 0 or at the very bottom of green rectangle.
[Apologies I did this with OS X, translation is straightforward]
A non-iterative solution:
- (NSPoint) randomPointIn:(NSRect)greenRect excluding:(NSRect)blueRect
{
// random point on green x-axis
int x = arc4random_uniform(NSWidth(greenRect)) + NSMinX(greenRect);
if (x < NSMinX(blueRect) || x > NSMaxX(blueRect))
{
// to the left or right of the blue, full height available
int y = arc4random_uniform(NSHeight(greenRect)) + NSMinY(greenRect);
return NSMakePoint(x, y);
}
else
{
// within the x-range of the blue, avoid it
int y = arc4random_uniform(NSHeight(greenRect) - NSHeight(blueRect)) + NSMinY(greenRect);
if (y >= NSMinY(blueRect))
{
// not below the blue, step over it
y += NSHeight(blueRect);
}
return NSMakePoint(x, y);
}
}
This picks a random x-coord in the range of green. If that point is outside the range of blue it picks a random y-coord in the range of green; otherwise it reduces the y range by the height of blue, produces a random point, and then increases it if required to avoid blue.
There are other solutions based on picking a uniform random point in the available area (green - blue) and then adjusting, but the complexity isn't worth it I think (I haven't done the stats).
Addendum
OK folk seem concerned over uniformity, so here is the algorithm mentioned in my last paragraph. We're picking an "point" with integer coords so the number of points to pick from is the green area minus the blue area. Pick a point randomly in this range. Now place it into one of the rectangles below, left, right or above the blue:
// convenience
int RectArea(NSRect r) { return (int)NSWidth(r) * (int)NSHeight(r); }
- (NSPoint) randomPointIn:(NSRect)greenRect excluding:(NSRect)blueRect
{
// not we are using "points" with integer coords so the
// bottom left point is 0,0 and the top right (width-1, height-1)
// you can adjust this to suit
// the number of points to pick from is the diff of the areas
int availableArea = RectArea(greenRect) - RectArea(blueRect);
int pointNumber = arc4random_uniform(availableArea);
// now "just" locate pointNumber into the available space
// we consider four rectangles, one each full width above and below the blue
// and one each to the left and right of the blue
int belowArea = NSWidth(greenRect) * (NSMinY(blueRect) - NSMinY(greenRect));
if (pointNumber < belowArea)
{
return NSMakePoint(pointNumber % (int)NSWidth(greenRect) + NSMinX(greenRect),
pointNumber / (int)NSWidth(greenRect) + NSMinY(greenRect));
}
// not below - consider to left
pointNumber -= belowArea;
int leftWidth = NSMinX(blueRect) - NSMinX(greenRect);
int leftArea = NSHeight(blueRect) * leftWidth;
if (pointNumber < leftArea)
{
return NSMakePoint(pointNumber % leftWidth + NSMinX(greenRect),
pointNumber / leftWidth + NSMinY(blueRect));
}
// not left - consider to right
pointNumber -= leftArea;
int rightWidth = NSMaxX(greenRect) - NSMaxX(blueRect);
int rightArea = NSHeight(blueRect) * rightWidth;
if (pointNumber < rightArea)
{
return NSMakePoint(pointNumber % rightWidth + NSMaxX(blueRect),
pointNumber / rightWidth + NSMinY(blueRect));
}
// it must be above
pointNumber -= rightArea;
return NSMakePoint(pointNumber % (int)NSWidth(greenRect) + NSMinX(greenRect),
pointNumber / (int)NSWidth(greenRect) + NSMaxY(blueRect));
}
This is uniform, but whether it is worth it you'll have to decide.
Okay. This was bothering me, so I did the work. It's a lot of source code, but computationally lightweight and probabilistically correct (haven't tested).
With all due respect to #MartinR, I think this is superior insofar as it doesn't loop (consider the case where the contained rect covers a very large portion of the outer rect). And with all due respect to #CRD, it's a pain, but not impossible to get the desired probabilities. Here goes:
// Find a random position in rect, excluding a contained rect called exclude
//
// It looks terrible, but it's just a lot of bookkeeping.
// Divide rect into 8 regions, like a tic-tac-toe board, excluding the center square
// Reading left to right, top to bottom, call these: A,B,C,D, (no E, it's the center) F,G,H,I
// The random point must be in one of these regions, choose by throwing a random dart, using
// cumulative probabilities to choose. The likelihood that the dart will be in regions A-I is
// the ratio of each's area to the total (less the center)
// With a target rect, correctly selected, we can easily pick a random point within it.
+ (CGPoint)pointInRect:(CGRect)rect excluding:(CGRect)exclude {
// find important points in the grid
CGFloat xLeft = CGRectGetMinX(rect);
CGFloat xCenter = CGRectGetMinX(exclude);
CGFloat xRight = CGRectGetMaxX(exclude);
CGFloat widthLeft = exclude.origin.x-CGRectGetMinX(rect);
CGFloat widthCenter = exclude.size.width;
CGFloat widthRight = CGRectGetMaxY(rect)-CGRectGetMaxX(exclude);
CGFloat yTop = CGRectGetMinY(rect);
CGFloat yCenter = exclude.origin.y;
CGFloat yBottom = CGRectGetMaxY(exclude);
CGFloat heightTop = exclude.origin.y-CGRectGetMinY(rect);
CGFloat heightCenter = exclude.size.height;
CGFloat heightBottom = CGRectGetMaxY(rect)-CGRectGetMaxY(exclude);
// compute the eight regions
CGFloat areaA = widthLeft * heightTop;
CGFloat areaB = widthCenter * heightTop;
CGFloat areaC = widthRight * heightTop;
CGFloat areaD = widthLeft * heightCenter;
CGFloat areaF = widthRight * heightCenter;
CGFloat areaG = widthLeft * heightBottom;
CGFloat areaH = widthCenter * heightBottom;
CGFloat areaI = widthRight * heightBottom;
CGFloat areaSum = areaA+areaB+areaC+areaD+areaF+areaG+areaH+areaI;
// compute the normalized probabilities
CGFloat pA = areaA/areaSum;
CGFloat pB = areaB/areaSum;
CGFloat pC = areaC/areaSum;
CGFloat pD = areaD/areaSum;
CGFloat pF = areaF/areaSum;
CGFloat pG = areaG/areaSum;
CGFloat pH = areaH/areaSum;
// compute cumulative probabilities
CGFloat cumB = pA+pB;
CGFloat cumC = cumB+pC;
CGFloat cumD = cumC+pD;
CGFloat cumF = cumD+pF;
CGFloat cumG = cumF+pG;
CGFloat cumH = cumG+pH;
// now pick which region we're in, using cumulatvie probabilities
// whew, maybe we should just use MartinR's loop. No No, we've come too far!
CGFloat dart = uniformRandomUpTo(1.0);
CGRect targetRect;
// top row
if (dart < pA) {
targetRect = CGRectMake(xLeft, yTop, widthLeft, heightTop);
} else if (dart >= pA && dart < cumB) {
targetRect = CGRectMake(xCenter, yTop, widthCenter, heightTop);
} else if (dart >= cumB && dart < cumC) {
targetRect = CGRectMake(xRight, yTop, widthRight, heightTop);
}
// middle row
else if (dart >= cumC && dart < cumD) {
targetRect = CGRectMake(xRight, yCenter, widthRight, heightCenter);
} else if (dart >= cumD && dart < cumF) {
targetRect = CGRectMake(xLeft, yCenter, widthLeft, heightCenter);
}
// bottom row
else if (dart >= cumF && dart < cumG) {
targetRect = CGRectMake(xLeft, yBottom, widthLeft, heightBottom);
} else if (dart >= cumG && dart < cumH) {
targetRect = CGRectMake(xCenter, yBottom, widthCenter, heightBottom);
} else {
targetRect = CGRectMake(xRight, yBottom, widthRight, heightBottom);
}
// yay. pick a point in the target rect
CGFloat x = uniformRandomUpTo(targetRect.size.width) + CGRectGetMinX(targetRect);
CGFloat y = uniformRandomUpTo(targetRect.size.height)+ CGRectGetMinY(targetRect);
return CGPointMake(x, y);
}
float uniformRandomUpTo(float max) {
return max * arc4random_uniform(RAND_MAX) / RAND_MAX;
}
Try this code, Worked for me.
-(CGPoint)randomPointInRect:(CGRect)r
{
CGPoint p = r.origin;
p.x += arc4random_uniform((u_int32_t) CGRectGetWidth(r));
p.y += arc4random_uniform((u_int32_t) CGRectGetHeight(r));
return p;
}
I don't like piling onto answers. However, the provided solutions do not work, so I feel obliged to chime in.
Martin's is fine, and simple... which may be all you need. It does have one major problem though... finding the answer when the inner rectangle dominates the containing rectangle could take quite a long time. If it fits your domain, then always choose the simplest solution that works.
jancakes solution is not uniform, and contains a fair amount of bias.
The second solution provided by dang just plain does not work... because arc4_random takes and returns uint32_t and not a floating point value. Thus, all generated numbers should fall into the first box.
You can address that by using drand48(), but it's not a great number generator, and has bias of its own. Furthermore, if you look at the distribution generated by that method, it has heavy bias that favors the box just to the left of the "inner box."
You can easily test the generation... toss a couple of UIViews in a controller, add a button handler that plots 100000 "random" points and you can see the bias clearly.
So, I hacked up something that is not elegant, but does provide a uniform distribution of random numbers in the larger rectangle that are not in the contained rectangle.
You can surely optimize the code and make it a bit easier to read...
Caveat: Will not work if you have more than 4,294,967,296 total points. There are multiple solutions to this, but this should get you moving in the right direction.
- (CGPoint)randomPointInRect:(CGRect)rect
excludingRect:(CGRect)excludeRect
{
excludeRect = CGRectIntersection(rect, excludeRect);
if (CGRectEqualToRect(excludeRect, CGRectNull)) {
return CGPointZero;
}
CGPoint result;
uint32_t rectWidth = rect.size.width;
uint32_t rectHeight = rect.size.height;
uint32_t rectTotal = rectHeight * rectWidth;
uint32_t excludeWidth = excludeRect.size.width;
uint32_t excludeHeight = excludeRect.size.height;
uint32_t excludeTotal = excludeHeight * excludeWidth;
if (rectTotal == 0) {
return CGPointZero;
}
if (excludeTotal == 0) {
uint32_t r = arc4random_uniform(rectHeight * rectWidth);
result.x = r % rectWidth;
result.y = r /rectWidth;
return result;
}
uint32_t numValidPoints = rectTotal - excludeTotal;
uint32_t r = arc4random_uniform(numValidPoints);
uint32_t numPointsAboveOrBelowExcludedRect =
(rectHeight * excludeWidth) - excludeTotal;
if (r < numPointsAboveOrBelowExcludedRect) {
result.x = (r % excludeWidth) + excludeRect.origin.x;
result.y = r / excludeWidth;
if (result.y >= excludeRect.origin.y) {
result.y += excludeHeight;
}
} else {
r -= numPointsAboveOrBelowExcludedRect;
uint32_t numPointsLeftOfExcludeRect =
rectHeight * excludeRect.origin.x;
if (r < numPointsLeftOfExcludeRect) {
uint32_t rowWidth = excludeRect.origin.x;
result.x = r % rowWidth;
result.y = r / rowWidth;
} else {
r -= numPointsLeftOfExcludeRect;
CGFloat startX =
excludeRect.origin.x + excludeRect.size.width;
uint32_t rowWidth = rectWidth - startX;
result.x = (r % rowWidth) + startX;
result.y = r / rowWidth;
}
}
return result;
}
I have a project that uses a tilemap. I have a separate tilemap for low-res (29x29 Tilesize) and high-res (58x58). I have these methods to calculate tileCoord to position and back again.
- (CGPoint)tileCoordForPosition:(CGPoint)position {
int x = position.x / _tileMap.tileSize.width;
int y = ((_tileMap.mapSize.height * _tileMap.tileSize.height) - position.y) / _tileMap.tileSize.height;
return ccp(x, y);
}
- (CGPoint)positionForTileCoord:(CGPoint)tileCoord {
int x = (tileCoord.x * _tileMap.tileSize.width) + _tileMap.tileSize.width/2;
int y = (_tileMap.mapSize.height * _tileMap.tileSize.height) - (tileCoord.y * _tileMap.tileSize.height) - _tileMap.tileSize.height/2;
return ccp(x, y);
}
I got this from RayWenderLich and I do honeslty not understand how it works, and why it has to be so complicated. But this doesn't work when I use retina tilemaps, only on 480x320. Can someone clever come up with a way to make this work for HD? Does not have to work on low-res either, I do not plan on supporting sub-iOS 7.
I want the output to be in the low-res coordinate scale tho, as you might know, cocos2d does the resizing to HD for you. (By multiplying by two)
i think this will work
- (CGPoint)tileCoordForPosition:(CGPoint)position {
int x = position.x/29;
int y = ((11*29)-position.y) / 29;
return ccp(x, y);
}
- (CGPoint)positionForTileCoord:(CGPoint)tileCoord {
double x = tileCoord.x * 29 + 14.5;
double y = (11*29) - (tileCoord.y * 29) - 14.5;
return ccp(x, y);
}
Here you're trying to compute your map X coordinate:
int x = position.x / _tileMap.tileSize.width;
The problem here is that (as of v0.99.5-rc0, cocos2d generally uses points for positions, but CCTMXTiledMap always uses pixels for tileSize. On a low-res device, 1 point = 1 pixel, but on a Retina device, 1 point = 2 pixels. Thus on a Retina device, you need to multiply by 2.
You can use the CC_CONTENT_SCALE_FACTOR() macro to fix this:
int x = CC_CONTENT_SCALE_FACTOR() * position.x / _tileMap.tileSize.width;
Here you're trying to compute yoru map Y coordinate:
int y = ((_tileMap.mapSize.height * _tileMap.tileSize.height) - position.y) / _tileMap.tileSize.height;
The extra math here is trying to account for the difference between Cocos2D's normal coordinate system and your map's flipped coordinate system. In standard Cartesian coordinates, the origin is at the lower left and Y coordinates increase as you move up. In a flipped coordinate system, the origin is at the upper left and Y coordinates increase as you move down. Thus you must subtract your position's Y coordinate from the height of the map (in scene units, which are points) to flip it to map coordinates.
The problem again is that _tileMap.tileSize is in pixels, not points. You can again fix that by using CC_CONTENT_SCALE_FACTOR():
CGFloat tileHeight = _tileMap.tileSize.height / CC_CONTENT_SCALE_FACTOR();
int y = ((_tileMap.mapSize.height * tileHeight) - position.y) / tileHeight;
I would like to show a maximum movement overlay in my hex map. For example:
Center point is at 50,50
Maximum allowed movement is 5 hexes.
This is the code I use for overlay:
for (int height = lowHeight; height <= highHeight; height++)
{
for (int width = lowWidth; width <= highWidth; width++)
{
[self hexOnMap:height :width :#"green"];
}
}
width being xCoordinate 50
height being yCoordinate 50
lowHeight = height - 5
highHeight = height + 5
lowWidth = width - 5
hightWidth = width + 5
Obviously my loop is not working as the corners are more than 5 hexes in movement. As I feel my IQ having dropping by the minute, someone please show me the obvious :) And the movement value of 5 is NOT static.
EDIT: #DPenner
Thanks for your reply. I tried something similar but this cursed thing still refuses to work. Your code displays this result:
EDIT 2: #DPenner - You ALMOST had it. I am uploading the overlay with your code so you can see. I ended up finding a great article last night which gave me the clues I needed to solve this problem. BUT I REALLY appreciate your help and trying to solve this!!!
I've deleted my old answer since it was completely wrong: I forgot to consider that adjacent hexes can sometimes differ in both x and y coordinates. Catching that is tricky but the following code should work:
If the center X coordinate is even:
for (int width = lowWidth; width <= highWidth; width++)
{
double heightNeeded = 5 - abs((centerX - width)/2.0);
for (int height = centerY - (int)ceil(heightNeeded); height <= centerY + (int)floor(heightNeeded); height++)
{
[self hexOnMap:height :width :#"green"];
}
}
If the center X coordinate is odd, swap the floor and ceiling functions. Change the 5 for a different sized overlay.
I checked it by hand, and it seemed to work fine. The outer loop is the width/X loop since its the X coordinates that zigzag across horizontally, which the ceil and floor functions "fix" in the inner height/Y loop.
After almost 24 hours of no sleep, I found a great article dealing with exactly this issue. The article is here:
http://keekerdc.com/2011/03/hexagon-grids-coordinate-systems-and-distance-calculations/
and here is the code to make it all work:
for (int y = minY; y <= maxY; y++)
{
for (int x = minX; x <= maxX; x++)
{
int xDistance = (x - startXcoordinate);
int yStart = 0;
if(x > startXcoordinate)
yStart = -1;
int yDistance = ((xDistance * -1) + yStart) / 2;
yDistance = yDistance + (y - startYcoordinate);
int z = (xDistance + yDistance)* -1 ;
int maxDistance = 0;
if(abs(xDistance) > maxDistance)
maxDistance = abs(xDistance);
if(abs(yDistance) > maxDistance)
maxDistance = abs(yDistance);
if(abs(z) > maxDistance)
maxDistance = abs(z);
if(abs(maxDistance) <= patrolRange)
[self hexOnMap:y :x :#"green"];
}
}
I need to be able to rotate an image around a given point so that what ever part of the image appears in the center of my container is the center of rotation.
To calculate the center points, I am currently just taking the inverse of the translation applied to the image:
Rotate.CenterX = Translate.X * -1;
Rotate.CenterY = Translate.Y * -1;
However, the current calculation i'm using is not sufficient as it does not work if the image has been translated after being rotated.
I'm sure it's a reasonably straight forward trig function, I just can't think what it is!
Cheers
If you are working with GDI+ then use the following:
double ImWidth = (double)Im.Width;
double ImHeight = (double)Im.Height;
double XTrans = -(ImWidth * X);
double YTrans = -(ImHeight * Y);
g.TranslateTransform((float)XTrans, (float)YTrans);
g.TranslateTransform((float)(ImWidth / 2.0 - XTrans), (float)(ImHeight / 2.0 - YTrans));
g.RotateTransform((float)Angle);
g.TranslateTransform(-((float)(ImWidth / 2.0 - XTrans)), -((float)(ImHeight / 2.0 - YTrans)));
If you are working with WPF graphic objects, use the following transform group:
TransformGroup TC = new TransformGroup();
RotateTransform RT = new RotateTransform(Angle);
RT.CenterX = Im.Width / 2.0;
RT.CenterY = Im.Height / 2.0;
TranslateTransform TT = new TranslateTransform(-X * Im.PixelWidth, -Y * Im.PixelHeight);
TC.Children.Add(TT);
TC.Children.Add(RT);
X & Y are the percent values you want to translate the image in (if the image is 1000 pixels and X is 0.1 then the image will be translated 100 pixels). This is how I needed the function to work but you can easily change it otherwise.