对数计算尺 📏

对数可以有效地把乘法转换成加法运算,比如:
$$l{n}^{A\ast B}=l{n}^A+l{n}^B$$

对数计算尺就是利用对数性质把乘法换成加法的一种辅助工具.

图片来自《程序员的数学1》

小玩意很有意思

示例代码

用Qt的视图框架写个demo

#include <QtWidgets>

QList<qreal> tickVals;
int times = 200;
class SimpleItem : public QGraphicsItem
{
public:
    QRectF rect;
    int moveSteps = 0;
    QColor background;
    SimpleItem():QGraphicsItem(),rect(0,0,600,30){
        rect.setWidth(qLn(tickVals.size())*times+20);
        qDebug() << tickVals ;

    }

    QRectF boundingRect() const override
    {
        return rect;
    }

    void paint(QPainter *painter, const QStyleOptionGraphicsItem *option,
               QWidget *widget) override
    {
        if(background.isValid())
            painter->fillRect(rect,background);
        painter->drawRect(rect);
        for (int i = 0; i < tickVals.size(); ++i) {
            auto tv = tickVals.at(i);
            painter->drawLine(QLineF(tv,0,tv,rect.height()));
            painter->drawText(tv,20,QString::number(i+1));
        }
    }

    // QGraphicsItem interface
protected:
    virtual void keyPressEvent(QKeyEvent *event) override {
        switch (event->key()) {
        case Qt::Key_Right:
            moveSteps++;
            moveSteps = moveSteps < tickVals.size() ? moveSteps : (tickVals.size()-1);
            setPos(QPointF(tickVals.at(moveSteps),pos().y()));
            break;
        case Qt::Key_Left:
            moveSteps--;
            moveSteps = moveSteps < 0 ? 0 : moveSteps;
            setPos(QPointF(tickVals.at(moveSteps),pos().y()));
            break;
        // case Qt::Key_Down:
        //     setPos(pos()+QPointF(0,rect.height()));
        //     break;
        // case Qt::Key_Up:
        //     setPos(pos()+QPointF(0,-rect.height()));
        //     break;
        default:
            break;
        }
    }
};



int main(int argc, char** argv)
{
    for (int i = 1; i <= 15; ++i) {
        qreal t2 = qLn(i);
        tickVals << (t2)*times;
    }
    QApplication a(argc,argv);

    QGraphicsView view;
    QGraphicsScene scene;
    view.setScene(&scene);

    auto si1 = new SimpleItem;
    auto si2 = new SimpleItem;

    si1->background = Qt::red;
    si2->background = Qt::green;

    si2->setFlags(QGraphicsItem::ItemIsMovable | QGraphicsItem::ItemIsSelectable | QGraphicsItem::ItemIsFocusable);
    si1->moveBy(0,si1->rect.height());

    scene.addItem(si1);
    scene.addItem(si2);

    si2->setSelected(true);
    si2->setFocus();

    view.scale(0.5,0.5);
    // si2->grabKeyboard();


    view.show();
    a.exec();
    return 0;
}