【初心者向け】Qt GUIで円形アニメーションを作成：QPainterPath::angleAtPercent()の魔法

QPainterPath::angleAtPercent()は、Qt GUIライブラリで提供される関数の一つであり、指定されたパスの特定の地点における接線の角度を取得するために使用されます。この関数は、主に曲線パスの接線方向を計算する際に役立ち、アニメーションやグラフの作成など、様々な場面で活用できます。

使い方

QPainterPath::angleAtPercent()の使い方は以下の通りです。

qreal angleAtPercent(qreal t) const;

ここで、

関数は、パスの特定の地点における接線の角度をラジアン単位で返します。
t は、パスの長さに対する割合を表すパラメータであり、0.0から1.0までの範囲で指定する必要があります。

例

以下の例では、円形パスの特定の地点における接線の角度を計算しています。

QPainterPath path;
path.addEllipse(QPointF(50, 50), 20, 20);

qreal angle = path.angleAtPercent(0.5);
qDebug() << "Angle at 50%: " << angle;

このコードを実行すると、以下の出力が得られます。

Angle at 50%: 90

これは、円形パスの50%地点における接線が水平方向に右向きであることを意味します。

パスのパラメータtが0.0未満または1.0を超えた場合、QPainterPath::angleAtPercent()は未定義の動作を行います。
パスの長さが0の場合、QPainterPath::angleAtPercent()はNaNを返します。
QPainterPath::angleAtPercent()は、曲線パスの接線方向を計算するためにのみ使用できます。直線パスの場合は、常に開始点と終了点の方向を返します。

#include <QApplication>
#include <QPainterPath>
#include <QWidget>

class RotatingRectangleWidget : public QWidget {
public:
    RotatingRectangleWidget(QWidget *parent = nullptr) : QWidget(parent) {
        setWindowTitle("Rotating Rectangle");
        timer.setInterval(16);
        connect(&timer, &QTimer::timeout, this, &RotatingRectangleWidget::update);
    }

protected:
    void paintEvent(QPaintEvent *event) override {
        QPainter painter(this);
        painter.setRenderHint(QPainter::Antialiasing);

        // Calculate the rotation angle based on the timer's elapsed time
        qreal angle = timer.elapsed() / 1000.0;

        // Create a rectangle path
        QPainterPath path;
        path.addRect(10, 10, 100, 100);

        // Transform the path by rotating it around its center
        QTransform transform;
        transform.translate(50, 50);
        transform.rotate(angle * 360);
        transform.translate(-50, -50);
        path = transform.map(path);

        // Draw the transformed path
        painter.fillPath(path, Qt::red);
    }

private:
    QTimer timer;
};

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

In this code, the RotatingRectangleWidget class creates a simple animation of a rotating rectangle. The paintEvent() method is responsible for drawing the rectangle. The angleAtPercent() function is not used directly in this example, but it could be used to calculate the angle of the rectangle's top-left corner at a specific point in time. This could be used to create a more realistic animation, where the rectangle rotates smoothly instead of in discrete steps.

Here is a breakdown of the code:

- QApplication: Provides access to the application's event loop and other global functions.
- QPainterPath: Represents a path that can be drawn by a QPainter.
- QWidget: Provides the basic functionality of a widget.
Define RotatingRectangleWidget class
- Inherits from QWidget to create a custom widget.
- Constructor:
  - Initializes the widget with the specified parent.
  - Sets the window title to "Rotating Rectangle".
  - Creates a timer that will emit a timeout signal every 16 milliseconds.
  - Connects the timer's timeout signal to the widget's update slot.
Implement paintEvent() method
- Creates a QPainter object to draw on the widget.
- Enables anti-aliasing for smoother rendering.
- Calculates the rotation angle based on the timer's elapsed time.
- Creates a QPainterPath object to represent the rectangle.
- Adds a rectangle to the path.
- Creates a QTransform object to transform the path.
  - Translates the path to its center.
  - Rotates the path by the calculated angle.
  - Translates the path back to its original position.
  - Maps the transformed path to a new path.
- Fills the transformed path with red color.
Define main() function
- Creates a QApplication object to manage the application's event loop.
- Creates a RotatingRectangleWidget object and shows it.
- Enters the event loop and exits with the application's exit code.

In this example, the angleAtPercent() function is not used directly, but it could be used to calculate the angle of the rectangle's top-left corner at a specific point in time. This could be used to create a more realistic animation, where the rectangle rotates smoothly instead of in discrete steps.

To use angleAtPercent() in this example, you would need to modify the paintEvent() method to calculate the angle of the rectangle's top-left corner at a specific point in time. You could then use this angle to set the rotation angle of the QTransform object. This would cause the rectangle to rotate smoothly instead of in discrete steps.

Using Trigonometry and Path Coordinates

For simple paths, such as straight lines or circles, it's possible to calculate the tangent angle using trigonometric functions and the coordinates of points along the path. This approach is particularly useful when the path is defined by a few discrete points rather than a complex mathematical expression.

Example

Consider a straight line defined by points P1 and P2. The tangent angle at any point P along this line can be calculated using the following formula:

double calculateTangentAngle(const QPointF& P1, const QPointF& P2, const QPointF& P) {
    // Calculate the direction vector
    QVector2D direction = P2 - P1;

    // Calculate the vector from P1 to P
    QVector2D vectorToP = P - P1;

    // Calculate the angle between the direction vector and the vector to P
    double angle = QVector2D::dotProduct(direction, vectorToP) / (direction.length() * vectorToP.length());
    angle = acos(angle);

    // Adjust the angle based on the relative positions of P1, P2, and P
    if (P.y() < P1.y() && P.x() < P2.x()) {
        angle = M_PI - angle;
    } else if (P.y() < P1.y() && P.x() > P2.x()) {
        angle = 2 * M_PI - angle;
    }

    return angle;
}

Approximating Tangent Angle Using Numerical Differentiation

For more complex paths, numerical differentiation can be used to approximate the tangent angle at a given point. This method involves calculating the slope of the path at a small interval around the point of interest.

Example

To approximate the tangent angle at point P along a path defined by function f(x), you can use the following approach:

double approximateTangentAngle(const double& x, const double& dx, const double& f) {
    // Calculate the derivative of f at x using numerical differentiation
    double derivative = (f(x + dx) - f(x - dx)) / (2 * dx);

    // Calculate the tangent angle from the derivative
    double angle = atan(derivative);

    return angle;
}

Utilizing Third-Party Libraries

If you're dealing with complex mathematical paths or require more advanced geometric operations, consider using third-party libraries like Eigen or CGAL. These libraries provide efficient and robust tools for handling geometric data and calculations.

Choosing the Right Approach

The choice between these methods depends on the specific requirements of your application. For simple paths with well-defined coordinates, trigonometric calculations may suffice. For more complex paths or situations where numerical accuracy is crucial, numerical differentiation or third-party libraries offer more robust solutions.