Question

I am trying to replace a part of an image with a rotated version of another one. The image source should appear in such a way that origin_source ends up at orign_dest in image *this. Also source should be rotated around origin_source before replacing pixels.

The code below works when R is a mirror matrix, but if I actually makes it to a rotation matrix, the resulting image becomes sheared. What is wrong?

void Image::imageApply(const Image& source,const Point& origin_dest,const Point& origin_source,const Point& direction)
{
Matrix22<double> R=transformRotationCreate(direction);
Point source_new_size=sqrt(2)*((Point){source.widthGet(),source.heightGet()});
Point blit_start=origin_dest;
for(unsigned int k=0;k<source_new_size.y;k++)
    {
    for(unsigned int l=0;l<source_new_size.x;l++)
        {
        Point point_source=(Point){l,k};
        Point point_dest=point_source-origin_source;
        point_dest*=R;
        point_dest+=blit_start;

        if(point_source.rectangleInIs((Point){0,0},(Point){source.widthGet(),source.heightGet()})
            &&point_dest.rectangleInIs((Point){0,0},(Point){widthGet(),heightGet()}))
            {
            (*this)(point_dest)=source(point_source);
            }
        }
    }
}

Here are some other functions used:

T=double

template<class T>
struct Matrix22
{
T xx;
T xy;
T yx;
T yy;
};

direction is a normalized vector

inline Matrix22<double> transformRotationCreate(const Vector2d<double>& direction)
{
return (Matrix22<double>){direction.x, -direction.y, direction.y, direction.x};
}

Also

Vector2d<T>& operator*=(const Matrix22<T>& M)
    {
    x=x*M.xx + y*M.xy;
    y=x*M.yx + y*M.yy;
    return *this;
    }

Answer 1

I solved it

First of all, the matrix-vector multiplication operator was wrong:

Vector2d<T>& operator*=(const Matrix22<T>& M)
    {
    T x_old=x;  //Need to save old x value (Stupid error but anyone does so sometimes)
    x=x*M.xx + y*M.xy;
    y=x_old*M.yx + y*M.yy;
    return *this;
    }

The final “rotate-and-paste” routine looks like this:

void Image::imageApply(const Image& source,const Point& origin_dest,const Point& origin_source,const Point& direction)
{
Matrix22<double> R=transformRotationCreate(direction);
Point blit_start=origin_dest-(Point){source.sizeMaxGet(),source.sizeMaxGet()};
Point blit_end=origin_dest+(Point){source.sizeMaxGet(),source.sizeMaxGet()};

for(unsigned int k=blit_start.y;k<blit_end.y;k++)
    {
    for(unsigned int l=blit_start.x;l<blit_end.x;l++)
        {
        Point point_dest=(Point){l,k};
        Point point_source=R*(point_dest - origin_dest) + origin_source;
        if(point_source.rectangleInIs((Point){0,0},(Point){source.widthGet(),source.heightGet()} ))
            {
            float alpha_source=source(point_source).alpha;
            (*this)(point_dest)=(1.0f-alpha_source)*(*this)(point_dest)
                                + alpha_source*source(point_source);
            }
        }
    }
}

Finally, the rotation direction was wrong, but that is just a swap of the xy factors in the transformation.