How to draw a gradient color wheel correctly using paint event without jagged edges

Question

I use the rotate method to draw the circle, but this creates gradual irregularities (visible on the outside of the circle).

Furthermore, I can only get this result if I iterate ten times the hue value in the for loop. If I use the wheel for other purposes (e.g., dynamically changing it), the recalculation would require a lot of computing power, which will lead to performance problems.

I can use QPainter::SmoothPixelTransformation to get a slightly better result, but the problem is still that the circle is drawn messily. That's not what I want.

The question is therefore whether I should use QPainter::rotate() here, or should I look for other methods? If so, I need an example.

.h

#include <QWidget>

class ColorWheel : public QWidget
{
    Q_OBJECT

public:
    ColorWheel(QWidget *parent = nullptr);
    ~ColorWheel();

    static QPixmap wheel(int width, int height);
signals:

    // QWidget interface
protected:
    virtual void paintEvent(QPaintEvent *) override;

private:
    QPixmap m_wheel;
    QRect m_wheelRect;
};

.cpp

#include "colorwheel.h"
#include <QPainter>

ColorWheel::ColorWheel(QWidget *parent)
    : QWidget(parent)
{
    setFixedSize(400,400);
    m_wheelRect = rect().marginsRemoved(QMargins(18,18,18,18));
    m_wheel = wheel(width(),height());
}

ColorWheel::~ColorWheel()
{
}

void ColorWheel::paintEvent(QPaintEvent *)
{
    QPainter painter(this);
   // painter.setRenderHints(QPainter::Antialiasing|QPainter::SmoothPixmapTransform);
    painter.setPen(QPen(Qt::black, 3));
   // painter.drawEllipse(m_wheelRect);
    painter.drawPixmap(m_wheelRect, m_wheel);
}

QPixmap ColorWheel::wheel(int width, int height)
{
    // |- {1} init wheels pixmap with wheelrect size and fill transperent
    QPixmap wheel = QPixmap(width, height);
    wheel.fill(Qt::transparent);

    // |- {2} paint on the pixmap
    QPainter painter(&wheel);
    painter.setRenderHint(QPainter::Antialiasing);
    painter.translate(width/2,height/2);

    // |- {3} draw filled rects
    qreal pxWidth = (((qreal)width) / 257) / 2.0;
    qreal steps = 0;
    for (int hue = 0; hue <= 3590; ++hue) {
        painter.rotate(360.0/3590.0);
        for (int saturation = 0; saturation <= 255; ++saturation, steps+=pxWidth) {
            QColor clr = QColor::fromHsv(hue/10,saturation, 255);
            painter.fillRect(QRectF(steps, 0, pxWidth, 1.0),clr);
        }
        steps = 0;
    }
    return wheel;
}