Question

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?

Answer 1

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!