图像的旋转之c++实现（qt + 不调包）

1.基本原理

   本章所讲的图像旋转算法就是让图像按照其中心点旋转指定角度。图像在旋转之后，其内容不会变形，只是角度改变了，但图像的大小会变化（图像一般会变大，能包含住原先的内容）。图像的旋转变化，比较复杂，涉及到多次矩阵变换。

1.旋转公式

    在下图中将坐标为(x0, y0)的像素点顺时针旋转角度后，其坐标变成(x, y)，其中r表示像素坐标距离原点的距离，表示旋转前像素点与原点连线的度数。

    可推导出公式：

2.坐标变换

    图像坐标系与数学坐标系是不相同，所以在旋转过程中需要进行两次坐标变换。

    1）旋转操作前

    将图像坐标系转到数学坐标系，公式中，W和H为原始图像的宽高。

    2）旋转操作后

    将旋转后图像的数学坐标系转到图像坐标系（相当于转回来），公式中，Wnew和Hnew分别表示输出图像的宽高。

3.旋转公式

    有了前面的铺垫，我们知道图像的旋转要经过如下三步才能完成：

    1.输入图像的坐标系转数学坐标系

    2.通过旋转关系计算出旋转后的坐标

    3.旋转坐标系（数学坐标系）转图像坐标系

    总的公式可见下面（输出坐标映射到原坐标）：

 

2.代码实现（代码是我以前自学图像处理时写的，代码很粗糙没做任何优化，但很好理解）

/*图像的旋转函数（最临近插值法） angle为旋转度数，以弧度表示*/
QImage* MainWindow::RotateNormal(QImage* image,double angle)
{
    int srcX1, srcX2, srcX3, srcX4;
    int srcY1, srcY2, srcY3, srcY4;

    srcX1 = 0;
    srcY1 = 0;
    srcX2 = image->width() - 1;
    srcY2 = 0;
    srcX3 = 0;
    srcY3 = image->height() - 1;
    srcX4 = image->width() - 1;
    srcY4 = image->height() - 1;

    double fSin = sin(angle);
    double fCos = cos(angle);

    double tranX1, tranX2, tranX3, tranX4;
    double tranY1, tranY2, tranY3, tranY4;

    tranX1 = fCos * srcX1 + fSin * srcY1;
    tranY1 = -fSin * srcX1 + fCos * srcY1;
    tranX2 = fCos * srcX2 + fSin * srcY2;
    tranY2 = -fSin * srcX2 + fCos * srcY2;
    tranX3 = fCos * srcX3 + fSin * srcY3;
    tranY3 = -fSin * srcX3 + fCos * srcY3;
    tranX4 = fCos * srcX4 + fSin * srcY4;
    tranY4 = -fSin * srcX4 + fCos * srcY4;

    unsigned int outWidth = (unsigned int)(max(fabs(tranX4 - tranX1), fabs(tranX3 - tranX2)) + 1.5);
    unsigned int outHeight = (unsigned int)(max(fabs(tranY4 - tranY1), fabs(tranY3 - tranY2)) + 1.5);

    QImage* newImage = new QImage(outWidth,outHeight,QImage::Format_ARGB32);

    double num1 = -0.5 * outWidth * fCos - 0.5 * outHeight * fSin + 0.5 * image->width();
    double num2 =  0.5 * outWidth * fSin - 0.5 * outHeight * fCos + 0.5 * image->height();

    unsigned char* copyPixel = NULL;
    unsigned char* objPixel = NULL;
    int x = 0;
    int y = 0;

    for(long j = 0; j < (long)outHeight; j++)
    {
        for(long i = 0; i <(long)outWidth; i++)
        {
            x = (int)(i * fCos + j * fSin + num1 + 0.5);
            y = (int)(-i * fSin + j * fCos + num2 + 0.5);

            if(x == image->width())
            {
                x--;
            }
            if(y == image->height())
            {
                y--;
            }
            copyPixel = image->bits() + y * image->width() * 4  + x * 4;
            objPixel = newImage->bits() + j * outWidth * 4 + i * 4;

            if(x >= 0 && x < image->width() && y >=0 && y < image->height())
            {
                memcpy(objPixel, copyPixel, 4);
            }
        }
    }
    return newImage;
}

/*图像的旋转函数（双线性插值法） angle为旋转度数，以弧度表示*/
QImage* MainWindow::RotateInterpolation(QImage* image,double angle)
{
    int srcX1, srcX2, srcX3, srcX4;
    int srcY1, srcY2, srcY3, srcY4;

    srcX1 = 0;
    srcY1 = 0;
    srcX2 = image->width() - 1;
    srcY2 = 0;
    srcX3 = 0;
    srcY3 = image->height() - 1;
    srcX4 = image->width() - 1;
    srcY4 = image->height() - 1;

    double fSin = sin(angle);
    double fCos = cos(angle);

    double tranX1, tranX2, tranX3, tranX4;
    double tranY1, tranY2, tranY3, tranY4;

    tranX1 = fCos * srcX1 + fSin * srcY1;
    tranY1 = -fSin * srcX1 + fCos * srcY1;
    tranX2 = fCos * srcX2 + fSin * srcY2;
    tranY2 = -fSin * srcX2 + fCos * srcY2;
    tranX3 = fCos * srcX3 + fSin * srcY3;
    tranY3 = -fSin * srcX3 + fCos * srcY3;
    tranX4 = fCos * srcX4 + fSin * srcY4;
    tranY4 = -fSin * srcX4 + fCos * srcY4;

    long outWidth = (unsigned int)(max(fabs(tranX4 - tranX1), fabs(tranX3 - tranX2)) + 1.5);
    long outHeight = (unsigned int)(max(fabs(tranY4 - tranY1), fabs(tranY3 - tranY2)) + 1.5);

    QImage* newImage = new QImage(outWidth,outHeight,QImage::Format_ARGB32);

    double num1 = -0.5 * outWidth * fCos - 0.5 * outHeight * fSin + 0.5 * image->width();
    double num2 =  0.5 * outWidth * fSin - 0.5 * outHeight * fCos + 0.5 * image->height();

    double x = 0.0;
    double  y = 0.0;

    int r,g,b;
    for (long  j = 0; j < outHeight; j++)
    {

        for(long i =0; i < outWidth; i++)
        {
            x = (i * fCos + j * fSin + num1 + 0.5);
            y = (-i * fSin + j * fCos + num2 + 0.5);


            if (x > image->width() || x < 0 || y > image->height() || y < 0)
                continue;
            int x1, x2, y1, y2;
            x1= ( int)x;
            x2 = x1 + 1;
            y1 = ( int)y;
            y2 = y1 + 1;

            QColor oldcolor1;
            QColor oldcolor2;
            QColor oldcolor3;
            QColor oldcolor4;
            double u, v;
            u = x - x1;
            v = y - y1;
            if ((x >= image->width() - 1 ) && (y >= image->height() - 1 ))
            {
            oldcolor1 = QColor(image->pixel(x1,y1));
            r = oldcolor1.red();
            g = oldcolor1.green();
            b = oldcolor1.blue();
            }
            else if (x >= image->width() - 1)
            {
                oldcolor1 = QColor(image->pixel(x1,y1));
                oldcolor3 = QColor(image->pixel(x1,y2));
                r = oldcolor1.red() * (1 - v) + oldcolor3.red() * v;
                g = oldcolor1.green() * (1 - v) + oldcolor3.green() * v;
                b = oldcolor1.blue() * (1 - v) + oldcolor3.blue() * v;
            }
            else if (x > image->height() - 1)
            {
                oldcolor1 = QColor(image->pixel(x1,y1));
                oldcolor2 = QColor(image->pixel(x2,y1));
                r = oldcolor1.red() * (1 - u) + oldcolor2.red() * u;
                g = oldcolor1.green() * (1 - u) + oldcolor2.green() * u;
                b = oldcolor1.blue() * (1 - u) + oldcolor2.blue() * u;
            }
            else
            {
                oldcolor1 = QColor(image->pixel(x1,y1));
                oldcolor2 = QColor(image->pixel(x2,y1));
                oldcolor3 = QColor(image->pixel(x1,y2));
                oldcolor4 = QColor(image->pixel(x2,y2));
                int r1,g1,b1;
                r = oldcolor1.red() * (1 - u) + oldcolor2.red() * u;
                g = oldcolor1.green() * (1 - u) + oldcolor2.green() * u;
                b = oldcolor1.blue() * (1 - u) + oldcolor2.blue() * u;

                r1 = oldcolor3.red() * (1 - u) + oldcolor4.red() * u;
                g1 = oldcolor3.green() * (1 - u) + oldcolor4.green() * u;
                b1 = oldcolor3.blue() * (1 - u) + oldcolor4.blue() * u;

                r = r * (1 - v) + r1 * v;
                g = g * (1 - v) + g1 * v;
                b = b * (1 - v) + b1 * v;
            }

          newImage->setPixel(i, j, qRgb(r, g, b));
        }
    }
    return newImage;
}

3.参考资料：

    数字图像处理——技术详解与Visual C++实践（左飞等著），写代码与写博客的时间相差两年，至于还参考其他的资料不，我已经忘记了，如若需要，我可以补上去