user3488765 - 1 year ago 99

C# Question

Say I have an array that is stored in 0° rotation:

`0 0 1 0 0`

0 0 1 0 0

1 1 1 0 0

0 0 0 0 0

0 0 0 0 0

And I want it returned in a good approximation if I pass, for example 30° as parameter, it would be something like:

`0 0 0 1 0`

1 1 0 1 0

0 0 1 0 0

0 0 0 0 0

0 0 0 0 0

45° would be

`1 0 0 0 1`

0 1 0 1 0

0 0 1 0 0

0 0 0 0 0

0 0 0 0 0

I am aware of the solutions posted for 90° rotations. But I don't think that will help me here?

I don't have any examplecode because I currently wouldn't even know where to start looking. If there are any keywords I can google that point me in the directions of some formula I can adapt for this, that would also be great.

Spectre's code solution in C#:

`class Rotation`

{

public Rotation() {

A = new int[xs,ys]{

{0,0,0,9,0,0,0},

{0,0,0,9,0,0,0},

{0,0,0,9,0,0,0},

{9,9,9,9,0,0,0},

{0,0,0,0,0,0,0},

{0,0,0,0,0,0,0},

{0,0,0,0,0,0,0},

};

B = new int[xs, ys];

deg = (float)(Math.PI / 180.0);

}

public const int xs = 7; // matrix size

public const int ys = 7;

const int x0 = 3; // rotation center cell

const int y0 = 3;

readonly float deg;

public int[,] A;

public int[,] B;

//---------------------------------------------------------------------------

public void rotcv(float ang) {

rotcw(Rotation.x0, Rotation.y0, ang);

}

private void rotcw(int x0, int y0, float ang) // rotate A -> B by angle ang around (x0,y0) CW if ang>0

{

int x, y, ix0, iy0, ix1, iy1, q;

double xx, yy, fx, fy, c, s;

// circle kernel

c = Math.Cos(-ang); s = Math.Sin(-ang);

// rotate

for (y = 0; y < ys; y++)

for (x = 0; x < xs; x++)

{

// offset so (0,0) is center of rotation

xx = x - x0;

yy = y - y0;

// rotate (fx,fy) by ang

fx = ((xx * c) - (yy * s));

fy = ((xx * s) + (yy * c));

// offset back and convert to ints and weights

fx += x0; ix0 = (int)Math.Floor(fx); fx -= ix0; ix1 = ix0 + 1; if (ix1 >= xs) ix1 = ix0;

fy += y0; iy0 = (int)Math.Floor (fy); fy -= iy0; iy1 = iy0 + 1; if (iy1 >= ys) iy1 = iy0;

// bilinear interpolation A[fx][fy] -> B[x][y]

if ((ix0 >= 0) && (ix0 < xs) && (iy0 >= 0) && (iy0 < ys))

{

xx = (A[ix0,iy0]) + ((A[ix1,iy0] - A[ix0,iy0]) * fx);

yy = (A[ix0,iy0]) + ((A[ix1,iy0] - A[ix0,iy0]) * fx);

xx = xx + ((yy - xx) * fy); q =(int) xx;

}

else q = 0;

B[x,y] = q;

}

}

}

test:

`static void Main(string[] args)`

{

Rotation rot = new Rotation();

for (int x = 0; x < Rotation.xs; x++) {

for (int y = 0; y < Rotation.xs; y++) {

Console.Write(rot.A[x,y] + " ");

}

Console.WriteLine();

}

Console.WriteLine();

float rotAngle = 0;

while (true)

{

rotAngle += (float)(Math.PI/180f)*90;

rot.rotcv(rotAngle);

for (int x = 0; x < Rotation.xs; x++)

{

for (int y = 0; y < Rotation.xs; y++)

{

Console.Write(rot.B[x, y] + " ");

}

Console.WriteLine();

}

Console.WriteLine();

Console.ReadLine();

}

}

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Answer Source

Ok here it is as promised. First **C++** code:

```
//---------------------------------------------------------------------------
#include <math.h>
//---------------------------------------------------------------------------
const int xs=7; // matrix size
const int ys=7;
const int x0=3; // rotation center cell
const int y0=3;
const float deg=M_PI/180.0;
int A[xs][ys]=
{
{0,0,0,9,0,0,0},
{0,0,0,9,0,0,0},
{0,0,0,9,0,0,0},
{9,9,9,9,0,0,0},
{0,0,0,0,0,0,0},
{0,0,0,0,0,0,0},
{0,0,0,0,0,0,0},
};
int B[xs][ys];
//---------------------------------------------------------------------------
void rotcw(int x0,int y0,float ang) // rotate A -> B by angle ang around (x0,y0) CW if ang>0
{
int x,y,ix0,iy0,ix1,iy1,q;
float xx,yy,fx,fy,c,s;
// circle kernel
c=cos(-ang); s=sin(-ang);
// rotate
for (y=0;y<ys;y++)
for (x=0;x<xs;x++)
{
// offset so (0,0) is center of rotation
xx=x-x0;
yy=y-y0;
// rotate (fx,fy) by ang
fx=float((xx*c)-(yy*s));
fy=float((xx*s)+(yy*c));
// offset back and convert to ints and weights
fx+=x0; ix0=floor(fx); fx-=ix0; ix1=ix0+1; if (ix1>=xs) ix1=ix0;
fy+=y0; iy0=floor(fy); fy-=iy0; iy1=iy0+1; if (iy1>=ys) iy1=iy0;
// bilinear interpolation A[ix0+fx][iy0+fy] -> B[x][y]
if ((ix0>=0)&&(ix0<xs)&&(iy0>=0)&&(iy0<ys))
{
xx=float(A[ix0][iy0])+(float(A[ix1][iy0]-A[ix0][iy0])*fx);
yy=float(A[ix0][iy0])+(float(A[ix1][iy0]-A[ix0][iy0])*fx);
xx=xx+((yy-xx)*fy); q=xx;
} else q=0;
B[x][y]=q;
}
}
//---------------------------------------------------------------------------
```

Here 7x7 preview 15 deg steps:

It may be need a bit tweaking of the center by half of cell or something (the center is bleeding too much to my liking)

Matrix `A`

is source and `B`

is target ...

You can also add tresholding ... like:

```
if (q>=5) q=9; else q=0;
```

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