difficulty calculating angle of a point on a circle - c++

Question

I'm having a bit of trouble with the geometry for a function I'm writing. I have a class that contains various sprites. This container class needs to be able to move, rotate, and scale while keeping all the child sprite's relative position, rotation, and scale intact.
I'm running into issues when rotating the container. The angle calculated by atan2 seems to be random. I wrote a simple console application that does and outputs the math behind a function I'm using (it's hard to properly show the code, as it relies on various outside sources). I did this to make sure it wasn't another part of the code causing my error. But my results are the same with the console application. Here is the code (it's stand-alone. you can easily run it)
#include<math.h>
#include<iostream>
using namespace std;
int main()
{
float containerX = 0;
float containerY = 0;
float childX = 10;
float childY = 0;
for(int i = 0; i <= 360; i += 36)
{
float radius = sqrt(pow(containerX - childX, 2) + pow(containerY - childY, 2));
float angle = atan2 (containerY - childY, containerX - childX);
float newAngle = angle + (i / 180.0 * 3.14);
childX = containerX + radius * cos(newAngle);
childY = containerY + radius * sin(newAngle);
std::cout << "New angle: " << newAngle * 180.0 / 3.14 << " New Position: " << childX << ", " << childY << std::endl;
}
while(1!=2) {} // This line is so I can read the console output
return 0;
}
My output is as follows:
New angle: 180.091 New Position: -10, -8.74228e-007
New angle: 36 New Position: 8.09204, 5.87528
New angle: -72.0913 New Position: 3.08108, -9.51351
New angle: 216 New Position: -8.10139, -5.86238
New angle: 179.909 New Position: -9.99995, 0.0318542
New angle: 179.817 New Position: -9.99988, 0.0477804
New angle: 215.726 New Position: -8.12931, -5.8236
New angle: 287.635 New Position: 3.00522, -9.53775
New angle: 395.543 New Position: 8.15704, 5.78469
New angle: 179.27 New Position: -9.99897, 0.143339
New angle: 359.178 New Position: 9.99846, -0.175189
I know that the problem has something to do with me calculating the angle with atan2, since if I just convert i to radians (i is iterating through degrees 0 and 360 in increments of 36) and pass that to cos and sin, I get points in order around the circle. If I use my "newAngle" variable though, I get random points around the circumference of the circle (bottom left, rop right, near bottom left, left of circle, right of circle, etc)
Thanks for reading this. I really appreciate it. I'm totally stuck. Any help would be wonderful.

Answer 1

float angle = atan2 (containerY - childY, containerX - childX);
float newAngle = angle + (i / 180.0 * 3.14);
In the first line, you're getting the new angle. In the second line, you're not just adding 36 degrees, instead you're adding i degrees, so in every iteration the code is adding an increasing angle to the new angle which itself is already increasing, hence the sporadic behavior.
Two different solutions:
1) Replace the first line with
float angle = 3.14159; // allow the loop to add to it
or
2) Change the i to a 36 in the line
float newAngle = angle + (36 / 180.0 * 3.14);
Don't do both! Choose one.

Answer 2

float angle = atan2 (containerY - childY, containerX - childX);
Make it
float angle = atan2 (childY - containerY, childX - containerX);
As originally written, you are flipping the child coordinates around the center of rotation on every iteration (in other words, adding an extra 180 degrees offset). You could see this easily if you don't adjust the angle at all: float newAngle = angle;. Your coordinates would oscillate between -10 and 10.

Answer 3

I hinted at it in my comment, but this is how you could have broken down your issue to see the problem: http://ideone.com/nTGXuv
#include <cmath>
#include <iostream>
#include <utility>
std::pair<float, float> rotate(std::pair<float, float> origin, std::pair<float, float> start, unsigned int degrees)
{
std::pair<float, float> diff = std::make_pair(start.first - origin.first, start.second - origin.second);
float currentAngle = ::atan2(diff.second, std::abs(diff.first));
float newAngle = currentAngle + (degrees / 180.0 * 3.1415926539);
float radius = std::sqrt(diff.first * diff.first + diff.second * diff.second);
float cosAngle = ::cos(newAngle);
float sinAngle = ::sin(newAngle);
float x = origin.first + radius * cosAngle;
float y = origin.second + radius * sinAngle;
return std::make_pair(x, y);
}
int main()
{
std::pair<float, float> origin = std::make_pair(0.0, 0.0);
std::pair<float, float> start = std::make_pair(1.0, 0.0);
const unsigned int degrees = 45;
for (unsigned int i = 0; i < 360; i += degrees)
{
std::pair<float, float> newPos = rotate(origin, start, i);
std::cout << "Rotated to " << i << " degrees: (" << newPos.first << ", " << newPos.second << ")" << std::endl;
}
return 0;
}