have been searching for a mod operator in ios, just like the % in c, but no luck in finding it. Tried the answer in this link but it gives the same error.
I have a float variable 'rotationAngle' whose angle keeps incrementing or decrementing based on the users finger movement.
Some thing like this:
if (startPoint.x < pt.x) {
if (pt.y<936/2)
rotationAngle += pt.x - startPoint.x;
else
rotationAngle += startPoint.x - pt.x;
}
rotationAngle = (rotationAngle % 360);
}
I just need to make sure that the rotationAngle doesnot cross the +/- 360 limit.
Any help any body.
Thanks
You can use fmod (for double) and fmodf (for float) of math.h:
#import <math.h>
rotationAngle = fmodf(rotationAngle, 360.0f);
Use the fmod function, which does a floation-point modulo, for definition see here: http://www.cplusplus.com/reference/clibrary/cmath/fmod/. Examples of how it works (with the return values):
fmodf(100, 360); // 100
fmodf(300, 360); // 300
fmodf(500, 360); // 140
fmodf(1600, 360); // 160
fmodf(-100, 360); // -100
fmodf(-300, 360); // -300
fmodf(-500, 360); // -140
fmodf takes "float" as arguments, fmod takes "double" and fmodl takes "double long", but they all do the same thing.
I cast it to an int first
rotationAngle = (((int)rotationAngle) % 360);
if you want more accuracy use
float t = rotationAngle-((int)rotationAngle);
rotationAngle = (((int)rotationAngle) % 360);
rotationAngle+=t;
Related
Recently I had the idea to make a pendulum out of points using Processing, and with a little learning I solved it easily:
int contador = 0;
int curvatura = 2;
float pendulo;
void setup(){
size(300,300);
}
void draw(){
background(100);
contador = (contador + 1) % 360; //"CONTADOR" GOES FROM 0 TO 359
pendulo = sin(radians(contador))*curvatura; //"PENDULO" EQUALS THE SIN OF CONTADOR, SO IT GOES FROM 1 TO -1 REPEATEDLY, THEN IS MULTIPLIED TO EMPHASIZE OR REDUCE THE CURVATURE OF THE LINE.
tallo(width/2,height/3);
println(pendulo);
}
void tallo (int x, int y){ //THE FUNTION TO DRAW THE DOTTED LINE
pushMatrix();
translate(x,y);
float _y = 0.0;
for(int i = 0; i < 25; i++){ //CREATES THE POINTS SEQUENCE.
ellipse(0,0,5,5);
_y+=5;
rotate(radians(pendulo)); //ROTATE THEM ON EACH ITERATION, THIS MAKES THE SPIRAL.
}
popMatrix();
}
So, in a brief, what I did was a function that changed every point position with the rotate fuction, and then I just had to draw the ellipses in the origin coordinates as that is the real thing that changes position and creates the pendulum ilussion.
[capture example, I just need 2 more points if you are so gentile :)]
[capture example]
[capture example]
Everything was OK that far. The problem appeared when I tried to replace the ellipses for a path made of vertices. The problem is obvious: the path is never (visually) made because all vertices would be 0,0 as they move along with the zero coordinates.
So, in order to make the path possible, I need the absolute values for each vertex; and there's the question: How do I get them?
What I know I have to do is to remove the transform functions, create the variables for the X and Y position and update them inside the for, but then what? That's why I cleared this is a maths issue, which operation I have to add in the X and Y variables in order to make the path and its curvature possible?
void tallo (int x, int y){
pushMatrix();
translate(x,y);
//NOW WE START WITH THE CHANGES. LET'S DECLARE THE VARIABLES FOR THE COORDINATES
float _x = 0.0;
float _y = 0.0;
beginShape();
for(int i = 0; i < 25; i++){ //CREATES THE DOTS.
vertex(_x,_y); //CHANGING TO VERTICES AND CALLING THE NEW VARIABLES, OK.
//rotate(radians(pendulo)); <--- HERE IS MY PROBLEM. HOW DO I CONVERT THIS INTO X AND Y COORDINATES?
//_x = _x + ????;
_y = _y + 5 /* + ???? */;
}
endShape();
popMatrix();
}
We need to have in mind that pendulo's x and y values changes in each iteration of the for, it doesn't has to add the same quantity each time. The addition must be progressive. Otherwise, we would see a straight line rotating instead of a curve accentuating its curvature (if you increase curvatura's value to a number greater than 20, you will notice the spiral)
So, rotating the coordinates was a great solution to it, now it's kind of a muddle to think the mathematical solution to the x and y coordinates for the spiral, my secondary's knowledges aren't enough. I know I have to create another variable inside the for in order to do this progression, but what operation should it have?
I would be really glad to know, maths
You could use simple trigonometry. You know the angle and the hypotenuse, so you use cos to get the relative x position, and sin to the y. The position would be relative to the central point.
But before i explain in detail and draw some explanations, let me propose another solution: PVectors
void setup() {
size(400,400);
frameRate(60);
center = new PVector(width/2, height/3); //defined here because width and height only are set after size()
}
void draw() {
background(255);
fill(0);
stroke(0);
angle = arc_magn*sin( (float) frameCount/60 );
draw_pendulum( center );
}
PVector center;
float angle = 0;
float arc_magn = HALF_PI;
float wire_length = 150;
float rotation_angle = PI/20 /60 ; //we divide it by 60 so the first part is the rotation in one second
void draw_pendulum(PVector origin){
PVector temp_vect = PVector.fromAngle( angle + HALF_PI);
temp_vect.setMag(wire_length);
PVector final_pos = new PVector(origin.x+temp_vect.x, origin.y+temp_vect.y );
ellipse( final_pos.x, final_pos.y, 40, 40);
line(origin.x, origin.y, final_pos.x, final_pos.y);
}
You use PVector class static method fromAngle( float angle ) that returns a unity vector of the given angle, then use .setMag() to define it's length.
Those PVector methods will take care of the trigonometry for you.
If you still want to know the math behind it, i can make another example.
I have Hough-Transform implemented using Opencvsharp (opencv), and get the lines detected on my image in console application/windows-from-application:
lines = edgeImg.HoughLines2(storage, HoughLinesMethod.Probabilistic, 1, Math.PI / 180, 60, 100, 100);
for (int i = 0; i < lines.Total; i++)
{
CvLineSegmentPoint segP= lines.GetSeqElem<CvLineSegmentPoint>(i).Value;
double angle = Math.Atan2((segP.P2.Y) - (segP.P1.Y), (segP.P2.X) - (segP.P1.X)) * 180 / Math.PI;
if (Math.Abs(angle) <= 60)
continue;
if (segP.P1.Y > segP.P2.Y + 20 || segP.P1.Y < segP.P2.Y - 20)
src.Line(segP.P1, segP.P2, CvColor.blue, 2, LineType.AntiAlias, 0);
}
I have tried different methods for visualizing the rho-theta space. since "HoughLinesMethod" does all the transformation internally, I have tried to get these values from x,y in the reverse way:
double angle = Math.Atan2(dy, dx) * 180 / Math.PI;
double theta = 90 - angle;
var thetaRad = theta*Math.PI/180;
double rho = (x1 * Math.Cos(thetaRad) + y1 * Math.Sin(thetaRad));
my first question is if I need to get two values for rho/theta, both for x1,y1 and also x2,y2 ; or calculating only one "rho/theta" would be the right intersect?
Thanks!
second, how can I visualize them in the right format? (what I currently see on my outout image is some random white dots at the top left corner of my output)
third, is it rational to get rho,theta values back in this way or you would suggest to perform the hough transform by myself and reduce the complexity? (I used opencvsharp function for better and efficient performance!)
I want to generate a square wave sound on iPhone, I found a sine wave code on Web (sorry forgotten the link), but i want to generate Square wave format.
Could you help me please?
const double amplitude = 0.25;
ViewController *viewController =
(__bridge ViewController *)inRefCon;
double theta = viewController->theta;
double theta_increment = 2.0 * M_PI * viewController->frequency / viewController->sampleRate;
const int channel = 0;
Float32 *buffer = (Float32 *)ioData->mBuffers[channel].mData;
for (UInt32 frame = 0; frame < inNumberFrames; frame++)
{
buffer[frame] = sin(theta) * amplitude;
theta += theta_increment;
if (theta > 2.0 * M_PI)
{
theta -= 2.0 * M_PI;
}
}
viewController->theta = theta;
Sum of the odd harmonics
A perfect square wave is the sum of all the odd harmonics divided by the harmonic number up to infinity. In the real world you have to stop of course - specifically at the nyquist frequency in digital. Below is a picture of the fundamental plus the first 3 odd harmonics. You can see how the square begins to take shape.
In your code sample, this would mean wrapping the sine generation in another loop. Something like this:
double harmNum = 1.0;
while (true)
{
double freq = viewController->frequency * harmNum;
if (freq > viewController->sampleRate / 2.0)
break;
double theta_increment = 2.0 * M_PI * freq / viewController->sampleRate;
double ampl = amplitude / harmNum;
// and then the rest of your code.
for (UInt32 frame = ....
The main problem you'll have is that you need to track theta for each of the harmonics.
A cheater solution
A cheat would be to draw a square like you would on paper. Divide the sample rate by the frequency by 2 and then produce that number of -1 and that number of +1.
For example, for a 1kHz sine at 48kHz. 48000/1000/2 = 24 so you need to output [-1,-1,-1,....,1,1,1,.....] where there are 24 of each.
A major disadvantage is that you'll have poor frequency resolution. Like if your sample rate were 44100 you can't produce exactly 1kHz. because that would require 22.05 samples at -1 and 22.05 samples at 1 so you have to round down.
Depending on your requirements this might an easier way to go since you can implement it with a counter and the last count between invocations (as you're tracking theta now)
In my application, a user taps 3 times and an angle will be created by the 3 points that were tapped. It draws the angle perfectly. I am trying to calculate the angle at the second tap, but I think I am doing it wrong (probably a math error). I haven't covered this in my calculus class yet, so I am going off of a formula on wikipedia.
http://en.wikipedia.org/wiki/Law_of_cosines
Here is what I am trying:
Note: First, Second, and Third are CGPoints created at the user's tap.
CGFloat xDistA = (second.x - third.x);
CGFloat yDistA = (second.y - third.y);
CGFloat a = sqrt((xDistA * xDistA) + (yDistA * yDistA));
CGFloat xDistB = (first.x - third.x);
CGFloat yDistB = (first.y - third.y);
CGFloat b = sqrt((xDistB * xDistB) + (yDistB * yDistB));
CGFloat xDistC = (second.x - first.x);
CGFloat yDistC = (second.y - first.y);
CGFloat c = sqrt((xDistC * xDistC) + (yDistC * yDistC));
CGFloat angle = acos(((a*a)+(b*b)-(c*c))/((2*(a)*(b))));
NSLog(#"FULL ANGLE IS: %f, ANGLE IS: %.2f",angle, angle);
Sometimes, it gives the angle as 1 which doesn't make sense to me. Can anyone explain why this is, or how to fix it please?
Not sure if this is the main problem but it is a problem
Your answer gives the angle at the wrong point:
To get the angle in green (which is probably angle you want based on your variable names "first", "second" and "third), use:
CGFloat angle = acos(((a*a)+(c*c)-(b*b))/((2*(a)*(c))));
Here's a way that circumvents the law of cosines and instead calculates the angles of the two vectors. The difference between the angles is the searched value:
CGVector vec1 = { first.x - second.x, first.y - second.y };
CGVector vec2 = { third.x - second.x, third.y - second.y };
CGFloat theta1 = atan2f(vec1.dy, vec1.dx);
CGFloat theta2 = atan2f(vec2.dy, vec2.dx);
CGFloat angle = theta1 - theta2;
NSLog(#"angle: %.1f°, ", angle / M_PI * 180);
Note the atan2 function that takes the x and y components as separate arguments and thus avoids the 0/90/180/270° ambiguity.
The cosine formula implementation looks right; did you take into account that acos() returns the angle in radians, not in degrees? In order to convert into degrees, multiply the angle by 180 and divide by Pi (3.14159...).
The way I have done it is to calculate the two angles separately using atan2(y,x) then using this function.
static inline double
AngleDiff(const double Angle1, const double Angle2)
{
double diff = 0;
diff = fabs(Angle1 - Angle2);
if (diff > <Pi>) {
diff = (<2Pi>) - diff;
}
return diff;
}
The function deals in radians, but you can change <Pi> to 180 and <2Pi> to 360
Using this answer to compute angle of the vector:
CGFloat angleForVector(CGFloat dx, CGFloat dy) {
return atan2(dx, -dy) * 180.0/M_PI;
}
// Compute angle at point Corner, that is between AC and BC:
CGFloat angle = angleForVector(A.x - Corner.x, A.y - Corner.y)
- angleForVector(B.x - Corner.x, B.y - Corner.y);
NSLog(#"FULL ANGLE IS: %f, ANGLE IS: %.2f",angle, angle);
I am attempting to simply make objects orbit around a center point, e.g.
The green and blue objects represent objects which should keep their distance to the center point, while rotating, based on an angle which I pass into method.
I have attempted to create a function, in objective-c, but it doesn't work right without a static number. e.g. (It rotates around the center, but not from the true starting point or distance from the object.)
-(void) rotateGear: (UIImageView*) view heading:(int)heading
{
// int distanceX = 160 - view.frame.origin.x;
// int distanceY = 240 - view.frame.origin.y;
float x = 160 - view.image.size.width / 2 + (50 * cos(heading * (M_PI / 180)));
float y = 240 - view.image.size.height / 2 + (50 * sin(heading * (M_PI / 180)));
view.frame = CGRectMake(x, y, view.image.size.width, view.image.size.height);
}
My magic numbers 160, and 240 are the center of the canvas in which I'm drawing the images onto. 50 is a static number (and the problem), which allows the function to work partially correctly -- without maintaining the starting poisition of the object or correct distance. I don't know what to put here unfortunately.
heading is a parameter that passes in a degree, from 0 to 359. It is calculated by a timer and increments outside of this class.
Essentially what I would like to be able to drop any image onto my canvas, and based on the starting point of the image, it would rotate around the center of my circle. This means, if I were to drop an image at Point (10,10), the distance to the center of the circle would persist, using (10,10) as a starting point. The object would rotate 360 degrees around the center, and reach it's original starting point.
The expected result would be to pass for instance (10,10) into the method, based off of zero degrees, and get back out, (15,25) (not real) at 5 degrees.
I know this is very simple (and this problem description is entirely overkill), but I'm going cross eyed trying to figure out where I'm hosing things up. I don't care about what language examples you use, if any. I'll be able to decipher your meanings.
Failure Update
I've gotten farther, but I still cannot get the right calculation. My new code looks like the following:
heading is set to 1 degree.
-(void) rotateGear: (UIImageView*) view heading:(int)heading
{
float y1 = view.frame.origin.y + (view.frame.size.height/2); // 152
float x1 = view.frame.origin.x + (view.frame.size.width/2); // 140.5
float radius = sqrtf(powf(160 - x1 ,2.0f) + powf(240 - y1, 2.0f)); // 90.13
// I know that I need to calculate 90.13 pixels from my center, at 1 degree.
float x = 160 + radius * (cos(heading * (M_PI / 180.0f))); // 250.12
float y = 240 + radius * (sin(heading * (M_PI / 180.0f))); // 241.57
// The numbers are very skewed.
view.frame = CGRectMake(x, y, view.image.size.width, view.image.size.height);
}
I'm getting results that are no where close to where the point should be. The problem is with the assignment of x and y. Where am I going wrong?
You can find the distance of the point from the centre pretty easily:
radius = sqrt((160 - x)^2 + (240 - y)^2)
where (x, y) is the initial position of the centre of your object. Then just replace 50 by the radius.
http://en.wikipedia.org/wiki/Pythagorean_theorem
You can then figure out the initial angle using trigonometry (tan = opposite / adjacent, so draw a right-angled triangle using the centre mass and the centre of your orbiting object to visualize this):
angle = arctan((y - 240) / (x - 160))
if x > 160, or:
angle = arctan((y - 240) / (x - 160)) + 180
if x < 160
http://en.wikipedia.org/wiki/Inverse_trigonometric_functions
Edit: bear in mind I don't actually know any Objective-C but this is basically what I think you should do (you should be able to translate this to correct Obj-C pretty easily, this is just for demonstration):
// Your object gets created here somewhere
float x1 = view.frame.origin.x + (view.frame.size.width/2); // 140.5
float y1 = view.frame.origin.y + (view.frame.size.height/2); // 152
float radius = sqrtf(powf(160 - x1 ,2.0f) + powf(240 - y1, 2.0f)); // 90.13
// Calculate the initial angle here, as per the first part of my answer
float initialAngle = atan((y1 - 240) / (x1 - 160)) * 180.0f / M_PI;
if(x1 < 160)
initialAngle += 180;
// Calculate the adjustment we need to add to heading
int adjustment = (int)(initialAngle - heading);
So we only execute the code above once (when the object gets created). We need to remember radius and adjustment for later. Then we alter rotateGear to take an angle and a radius as inputs instead of heading (this is much more flexible anyway):
-(void) rotateGear: (UIImageView*) view radius:(float)radius angle:(int)angle
{
float x = 160 + radius * (cos(angle * (M_PI / 180.0f)));
float y = 240 + radius * (sin(angle * (M_PI / 180.0f)));
// The numbers are very skewed.
view.frame = CGRectMake(x, y, view.image.size.width, view.image.size.height);
}
And each time we want to update the position we make a call like this:
[objectName rotateGear radius:radius angle:(adjustment + heading)];
Btw, once you manage to get this working, I'd strongly recommend converting all your angles so you're using radians all the way through, it makes it much neater/easier to follow!
The formula for x and y coordinates of a point on a circle, based on radians, radius, and center point:
x = cos(angle) * radius + center_x
y = sin(angle) * radius + center_y
You can find the radius with HappyPixel's formula.
Once you figure out the radius and the center point, you can simply vary the angle to get all the points on the circle that you'd want.
If I understand correctly, you want to do InitObject(x,y). followed by UpdateObject(angle) where angle sweeps from 0 to 360. (But use radians instead of degrees for the math)
So you need to track the angle and radius for each object.:
InitObject(x,y)
relative_x = x-center.x
relative_y = y-center.y
object.radius = sqrt((relative_x)^2, (relative_y)^2)
object.initial_angle = atan(relative_y,relative_x);
And
UpdateObject(angle)
newangle = (object.initial_angle + angle) % (2*PI )
object.x = cos(newangle) * object.radius + center.x
object.y = sin(newangle) * object.radius + center.y
dx=dropx-centerx; //target-source
dy=-(dropy-centery); //minus = invert screen coords to cartesian coords
radius=sqrt(dy*dy+dx*dx); //faster if your compiler optimizer is bad
if dx=0 then dx=0.000001; //hackpatchfudgenudge*
angle=atan(dy/dx); //set this as start angle for the angle-incrementer
Then go with the code you have and you'll be fine. You seem to be calculating radius from current position each time though? This, like the angle, should only be done once, when the object is dropped, or else the radius might not be constant.
*instead of handling 3 special cases for dx=0, if you need < 1/100 degree precision for the start angle go with those instead, google Polar Arctan.