Fundamentals of Coordinate Systems

Qt employs two distinct coordinate systems for graphics rendering:

Device Coordinate System

• Origin positioned at top-left corner (0,0)
• Measured in physical pixels
• X-axis extends rightward, Y-axis extends downward

Logical Coordinate System

• Abstract mathematical representation
• Unit measurement determined by application requirements
• Coordinate directions customizable based on specific use cases

Key Implementation Details

• QPainter operates exclusively in logical coordinates
• Logical coordinates undergo transformation to device coordinates
• Default configuraton aligns logical and device coordinate systems

Viewport and Window Concepts

These represent dual perspectives of the same rectanuglar region:

• Viewport: Physical rectangle in device coordinates
• Window: Corresponding rectangle in logical coordinates
• Bi-directional mapping exists between coordinate points
• Coordinate transformations enable mutual conversion

Coordinate Transformation Implementation

void CustomWidget::renderArea(QPaintEvent*)
{
    QPainter renderer(this);
    
    renderer.setViewport(40, 40, width()-80, height()-80);
    renderer.setWindow(-8, 3, 16, -6);
    renderer.fillRect(-8, 3, 16, -6, Qt::darkBlue);
}

Waveform Visualization Implementation

Header Definition

#ifndef RENDER_WIDGET_H
#define RENDER_WIDGET_H

#include <QWidget>

class RenderWidget : public QWidget
{
    Q_OBJECT
protected:
    void paintEvent(QPaintEvent*) override;
public:
    explicit RenderWidget(QWidget* parent = nullptr);
};

#endif

Implementation Logic

#include "render_widget.h"
#include <QPainter>
#include <QtMath>

RenderWidget::RenderWidget(QWidget* parent) : QWidget(parent) {}

void RenderWidget::paintEvent(QPaintEvent*)
{
    QPainter renderer(this);
    QPen drawingPen(Qt::cyan);
    
    drawingPen.setWidthF(0.02);
    renderer.setPen(drawingPen);
    
    renderer.setViewport(60, 60, width()-120, height()-120);
    renderer.setWindow(-12, 3, 24, -6);
    renderer.fillRect(-12, 3, 24, -6, QColor(20, 20, 20));
    
    for(float vertical = -3, horizontal = -12; horizontal <= 12; vertical += 0.4, horizontal += 1.2)
    {
        renderer.drawLine(QPointF(-12, vertical), QPointF(12, vertical));
        renderer.drawLine(QPointF(horizontal, 3), QPointF(horizontal, -3));
    }
    
    for(float xPos = -12; xPos < 12; xPos += 0.002)
    {
        float yPos = qSin(xPos);
        renderer.drawPoint(QPointF(xPos, yPos));
    }
}

Application Entry Point

#include "render_widget.h"
#include <QApplication>

int main(int argc, char* argv[])
{
    QApplication app(argc, argv);
    RenderWidget widget;
    widget.show();
    return app.exec();
}