Bug in RotatedRect::boundingRect() method (Feature #3396)

I tried to get the smallest bounding box for a rotated rectangle. However, the result of RotatedRect::boundingRect() method is not correct all time and in some cases it return rectangles much bigger than the original one.

I checked the source code for of this method. There is a mathematical solution to this problem. I implemented and tested it. Given the major and minor axis as well as the amount of the rotation of the RotatedRect, the smallest bounding box can be calculated as follow:

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float t1 = atan(-(majorAxe*sin(degree))/(minorAxe*cos(degree)));
float t2 = t1 + 3.1415;

float maxX = x + majorAxe*cos(t1)*cos(degree)-minorAxe*sin(t1)*sin(degree);
float minX = x + majorAxe*cos(t2)*cos(degree)-minorAxe*sin(t2)*sin(degree);

t1 = atan((minorAxe*cos(degree))/(majorAxe*sin(degree)));
t2 = t1 + 3.1415;

float maxY = y + minorAxe*sin(t1)*cos(degree)+majorAxe*cos(t1)*sin(degree);
float minY = y + minorAxe*sin(t2)*cos(degree)+majorAxe*cos(t2)*sin(degree);
if (minY > maxY) {
float temp = minY;
minY = maxY;
maxY = temp;
}
if (minX > maxX) {
float temp = minX;
minX = maxX;
maxX = temp;
}

Rect r(minX,minY,maxX-minX,maxY-minY);

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To speed up the computations, the code can be optimized to avoid redundant sin and cos calls. Also, the code can be more optimized by utilizing simple Trigonometric equations. So the more optimized code can be as follows:

float c_degree = cos(degree);
float s_degree = sin(degree);
float t1 = atan(-(majorAxe*s_degree)/(minorAxe*c_degree));
float c_t1 = cos(t1);
float s_t1 = sin(t1);
float w1 = majorAxe*c_t1*c_degree;
float w2 = minorAxe*s_t1*s_degree;
float maxX = x + w1-w2;
float minX = x - w1+w2;

t1 = atan((minorAxe*c_degree)/(majorAxe*s_degree));
c_t1 = cos(t1);
s_t1 = sin(t1);

w1 = minorAxe*s_t1*c_degree;
w2 = majorAxe*c_t1*s_degree;
float maxY = y + w1+w2;
float minY = y - w1-w2;

if (minY > maxY) {
float temp = minY;
minY = maxY;
maxY = temp;
}

if (minX > maxX) {
float temp = minX;
minX = maxX;
maxX = temp;
}

Rect r(minX,minY,maxX-minX,maxY-minY);