Rotating a rectangle - c++

Question

I'm trying to rotate a rectangle using a slider.
The slider has -100 to +100 values. I'd like to use this to rotate the rectangle.
I have tried a few things, including calculating the corners of the rectangle and then messing around with a matrix, thus unsuccessful.
(I prefer using the matrix)
An easier solution would be to define fixed points from the beginning, instead of only working with the sides of the rectangle.
In the code below I can resize the rectangle using a slider.
Dialog::Dialog(QWidget *parent) :
QDialog(parent),
ui(new Ui::Dialog)
{
ui->setupUi(this);
a = 230; //positioning
b = 150; //positioning
c = 200; //size of drawing
d = 150; //size of drawing
connect(ui->horizontalSlider,SIGNAL(valueChanged(int)),this,SLOT(update()));
}
Dialog::~Dialog()
{
delete ui;
}
void Dialog::paintEvent(QPaintEvent *e)
{
QPainter painter(this);
painter.fillRect(a - ui->horizontalSlider->value(),
b - ui->horizontalSlider->value(),
c + ui->horizontalSlider->value() * 2,
d + ui->horizontalSlider->value() * 2, Qt::green);
}
Any form of help is much appreciated.

Answer 1

You can move your painter and rotate canvas to achieve it:
void Dialog::paintEvent(QPaintEvent *e)
{
QPainter painter(this);
painter.save();
painter.translate(a, b);//Move pen.
painter.rotate(30);//rotate canvas.
painter.fillRect(-ui->horizontalSlider->value(),
-ui->horizontalSlider->value(),
c + ui->horizontalSlider->value() * 2,
d + ui->horizontalSlider->value() * 2, Qt::green);
painter.restore();
}

Answer 2

Firstly here is the rotation matrix that will rotate any point in X-Y space around the Z axis (which is facing you) by the angle given by t radians:
R = [ cos(t), -sin(t);
sin(t), cos(t)]
To get the rotate point you must be rotating around a specific point on the X-Y plane. I assume you want to rotate the rect around its centre.
Let c be the pixel coordinates of the centre:
c = [cx;
cy]
The rotated points are then:
P = R*(p-c) + c
where P is the rotated point and p is the rectangle point to rotate, both are [2x1] vectors, as is c. Note that I am using Matrix algebra, so the multiplication is matrix multiplication, not scalar multiplication.
The next issue is then drawing the rectangle. I am not familiar with Qt rect drawing but from the documentation, doing what you want with fillRect will not work, as it assumes that the rectangle is unrotated.
You can use drawPolygon to do what you want, when you have the rotated coordinates.

Answer 3

I solved it by using "painter.drawLine( ax, ay, bx, by );" to draw the rectangle. Afterwards I used the following formula for each line:
double ax = MidPointWidth + (-(Size + minWidth)) * cos(Angle) - (Size + minHeight) * sin(Angle);
double ay = MidPointHeight + (-(Size + minWidth)) * sin(Angle) + (Size + minHeight) * cos(Angle);
Hope this will help someone.