#include "newton.h"
#include <QMouseEvent>

Newton::Newton(QWidget *parent):
    QWidget(parent),
    numPoints(0),
    xmin(-8.), 
    xmax(8.), 
    ymin(-6.),
    ymax(6.),
    xCoeff(1.), 
    yCoeff(1.)
{
}

void Newton::defineMap() {
    int w = width();
    int h = height();

    xCoeff = (double) w / (xmax - xmin);
    yCoeff = (double) h / (ymax - ymin);
}

QPointF Newton::map(QPointF p) const {
    return QPointF(
        (p.x() - xmin)*xCoeff,
        (ymax - p.y())*yCoeff
    );
}

QPointF Newton::invMap(QPointF p) const {
    return QPointF(
        xmin + p.x()/xCoeff,
        ymax - p.y()/yCoeff
    );
}

void Newton::paintEvent(QPaintEvent*) {
    QPainter qp(this);
    qp.setRenderHint(QPainter::Antialiasing);
    drawAxes(&qp);
    if (numPoints > 0) {
        drawPoints(&qp);
        drawPolynomial(&qp);
    }
}

void Newton::drawAxes(QPainter* qp) {
    int w = width();
    int h = height();
    QColor lightGray(220, 220, 220);
    QColor gray(128, 128, 128);
    QColor black(0, 0, 0);

    qp->setBrush(QBrush(lightGray));
    qp->drawRect(0, 0, w, h);

    qp->setPen(gray);

    QPointF p0, p1;
    int ix = (int) xmin;
    while (ix <= (int) xmax) {
        if (ix == 0) {
            ++ix;
            continue;
        }
        p0 = map(QPointF(ix, ymin));
        p1 = map(QPointF(ix, ymax));
        qp->drawLine(p0, p1);
        ++ix;
    }

    int iy = (int) ymin;
    while (iy <= (int) ymax) {
        if (iy == 0) {
            ++iy;
            continue;
        }
        p0 = map(QPointF(xmin, iy));
        p1 = map(QPointF(xmax, iy));
        qp->drawLine(p0, p1);
        ++iy;
    }

    qp->setPen(black);
    p0 = map(QPointF(xmin, 0.));
    p1 = map(QPointF(xmax, 0.));
    qp->drawLine(p0, p1);

    p0 = map(QPointF(0., ymin));
    p1 = map(QPointF(0., ymax));
    qp->drawLine(p0, p1);
}

void Newton::drawPoints(QPainter* qp) {
    qp->setPen(QPen(Qt::red, 2));
    QPointF dx(0.2, 0.), dy(0., 0.2);
    QPointF p0, p1;
    for (int i = 0; i < numPoints; ++i) {
        QPointF t(nodeX[i], nodeY[i]);
        p0 = map(t - dx);
        p1 = map(t + dx);
        qp->drawLine(p0, p1);

        p0 = map(t - dy);
        p1 = map(t + dy);
        qp->drawLine(p0, p1);
    }
}

void Newton::drawPolynomial(QPainter* qp) {
    double x = xmin;
    double dx = 0.05;
    double y = newtonPolValue(numPoints-1, nodeX, a, x);
    QPointF p = map(QPointF(x, y));

    QPainterPath path;
    path.moveTo(p);
    while (x < xmax) {
        x += dx;
        y = newtonPolValue(numPoints-1, nodeX, a, x);
        p = map(QPointF(x, y));
        path.lineTo(p);
    }

    qp->strokePath(path, QPen(Qt::blue, 2));
}

void Newton::mousePressEvent(QMouseEvent* event) {
    if (event->button() == Qt::RightButton) {
        numPoints = 0;
        update();
        return;
    }

    if (numPoints >= MAX_POINTS)
        numPoints = 0;
    QPointF t = invMap(
        QPointF(event->x(), event->y())
    );
    nodeX[numPoints] = t.x();
    nodeY[numPoints] = t.y();
    ++numPoints;

    computeNewtonPol(numPoints-1, nodeX, nodeY, a);
    update();
}

void Newton::clear() {
    numPoints = 0;
    update();
}

// Value of Newton interpolation polynomial in point t
double newtonPolValue(
    int n,              // Number of nodes - 1
    const double* x,    // Nodes of interpolation: x0, x1, ..., xn
    const double* a,    // Coefficients of Newton polynomial
    double t
) {
    double s = a[0];
    double p = 1.;
    for (int i = 1; i <= n; ++i) {
        p *= (t - x[i-1]);
        s += a[i] * p;
    }
    return s;
}

// Compute the coefficients of Newton interpolation polynomial
void computeNewtonPol(
    int n,              // Number of nodes - 1
    const double* x,    // Nodes of interpolation: x0, x1, ..., xn
    const double* y,    // Values in these nodes
    double* a           // Coefficients of Newton polynomial
) {
    a[0] = y[0];
    for (int i = 1; i <= n; ++i) {
        double p = 1.;
        for (int j = 0; j < i; ++j)
            p *= (x[i] - x[j]);

        a[i] = (y[i] - newtonPolValue(i-1, x, a, x[i])) / p;
    }
}