#include <stdio.h></stdio.h>

#include <stdlib.h></stdlib.h>

#include <string.h></string.h>

#include <assert.h></assert.h>

#include "traster.h"

/*

#include "img.h"

#include "file.h"

#include "toonz.h"

#include "raster.h"

#include "tmsg.h"

#include "copP.h"*/

#if defined(MACOSX) || defined(LINUX)

#define TRUE 1

#define FALSE 0

#endif

/*------------------------------------------------------------------------*/

namespace

{

UCHAR First_preseed_table[256] =

	{8, 0, 1, 0, 2, 2, 1, 0, 3, 3, 3, 3, 2, 2, 3, 3,

	 4, 4, 1, 0, 2, 2, 1, 0, 4, 4, 3, 3, 2, 2, 3, 3,

	 5, 5, 1, 5, 2, 2, 1, 5, 5, 5, 5, 5, 2, 2, 5, 5,

	 4, 4, 1, 5, 2, 2, 1, 5, 4, 4, 5, 5, 2, 2, 5, 5,

	 6, 6, 1, 6, 2, 2, 1, 6, 6, 6, 6, 6, 2, 2, 6, 6,

	 4, 4, 1, 0, 2, 2, 1, 0, 4, 4, 8, 8, 2, 2, 8, 8,

	 6, 6, 1, 6, 2, 2, 1, 6, 6, 6, 6, 6, 2, 2, 6, 6,

	 4, 4, 1, 0, 2, 2, 1, 0, 4, 4, 8, 8, 2, 2, 8, 8,

	 7, 7, 1, 7, 2, 2, 1, 7, 7, 7, 7, 7, 2, 2, 7, 7,

	 4, 4, 1, 0, 2, 2, 1, 0, 4, 4, 3, 3, 2, 2, 3, 3,

	 7, 7, 1, 7, 2, 2, 1, 7, 7, 7, 7, 7, 2, 2, 7, 7,

	 4, 4, 1, 5, 2, 2, 1, 5, 4, 4, 5, 5, 2, 2, 5, 5,

	 7, 7, 1, 7, 2, 2, 1, 7, 7, 7, 7, 7, 2, 2, 7, 7,

	 4, 4, 1, 0, 2, 2, 1, 0, 4, 4, 8, 8, 2, 2, 8, 8,

	 7, 7, 1, 7, 2, 2, 1, 7, 7, 7, 7, 7, 2, 2, 7, 7,

	 4, 4, 1, 0, 2, 2, 1, 0, 4, 4, 8, 8, 2, 2, 8, 8};

static UCHAR Next_point_table[2048] =

	{8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0,

	 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,

	 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 2,

	 2, 2, 1, 2, 2, 2, 2, 2, 2, 0, 1, 2, 2, 2, 2, 2,

	 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0,

	 3, 3, 1, 1, 1, 1, 1, 1, 3, 0, 1, 1, 1, 1, 1, 1,

	 3, 3, 3, 2, 2, 2, 2, 2, 3, 0, 0, 2, 2, 2, 2, 2,

	 3, 3, 1, 2, 2, 2, 2, 2, 3, 0, 1, 2, 2, 2, 2, 2,

	 4, 4, 4, 4, 4, 4, 4, 4, 4, 0, 0, 4, 0, 4, 4, 4,

	 4, 4, 1, 4, 1, 4, 4, 4, 4, 0, 1, 4, 1, 4, 4, 4,

	 4, 4, 4, 4, 2, 4, 4, 4, 4, 0, 0, 4, 2, 4, 4, 4,

	 4, 4, 1, 4, 2, 4, 4, 4, 4, 0, 1, 4, 2, 4, 4, 4,

	 3, 3, 3, 4, 3, 4, 4, 4, 3, 0, 0, 4, 0, 4, 4, 4,

	 3, 3, 1, 4, 1, 4, 4, 4, 3, 0, 1, 4, 1, 4, 4, 4,

	 3, 3, 3, 4, 2, 4, 4, 4, 3, 0, 0, 4, 2, 4, 4, 4,

	 3, 3, 1, 4, 2, 4, 4, 4, 3, 0, 1, 4, 2, 4, 4, 4,

	 5, 5, 5, 5, 5, 5, 5, 5, 5, 0, 0, 5, 0, 0, 0, 0,

	 5, 5, 1, 5, 1, 1, 1, 1, 5, 0, 1, 5, 1, 1, 1, 1,

	 5, 5, 5, 5, 2, 2, 2, 2, 5, 0, 0, 5, 2, 2, 2, 2,

	 5, 5, 1, 5, 2, 2, 2, 2, 5, 0, 1, 5, 2, 2, 2, 2,

	 3, 3, 3, 5, 3, 3, 3, 3, 3, 0, 0, 5, 0, 0, 0, 0,

	 3, 3, 1, 5, 1, 1, 1, 1, 3, 0, 1, 5, 1, 1, 1, 1,

	 3, 3, 3, 5, 2, 2, 2, 2, 3, 0, 0, 5, 2, 2, 2, 2,

	 3, 3, 1, 5, 2, 2, 2, 2, 3, 0, 1, 5, 2, 2, 2, 2,

	 5, 5, 5, 5, 5, 4, 4, 4, 5, 0, 0, 5, 0, 4, 4, 4,

	 5, 5, 1, 5, 1, 4, 4, 4, 5, 0, 1, 5, 1, 4, 4, 4,

	 5, 5, 5, 5, 2, 4, 4, 4, 5, 0, 0, 5, 2, 4, 4, 4,

	 5, 5, 1, 5, 2, 4, 4, 4, 5, 0, 1, 5, 2, 4, 4, 4,

	 3, 3, 3, 5, 3, 4, 4, 4, 3, 0, 0, 5, 0, 4, 4, 4,

	 3, 3, 1, 5, 1, 4, 4, 4, 3, 0, 1, 5, 1, 4, 4, 4,

	 3, 3, 3, 5, 2, 4, 4, 4, 3, 0, 0, 5, 2, 4, 4, 4,

	 3, 3, 1, 5, 2, 4, 4, 4, 3, 0, 1, 5, 2, 4, 4, 4,

	 6, 6, 6, 6, 6, 6, 6, 6, 6, 0, 0, 6, 0, 6, 0, 0,

	 6, 6, 1, 6, 1, 6, 1, 1, 6, 0, 1, 6, 1, 6, 1, 1,

	 6, 6, 6, 6, 2, 6, 2, 2, 6, 0, 0, 6, 2, 6, 2, 2,

	 6, 6, 1, 6, 2, 6, 2, 2, 6, 0, 1, 6, 2, 6, 2, 2,

	 3, 3, 3, 6, 3, 6, 3, 3, 3, 0, 0, 6, 0, 6, 0, 0,

	 3, 3, 1, 6, 1, 6, 1, 1, 3, 0, 1, 6, 1, 6, 1, 1,

	 3, 3, 3, 6, 2, 6, 2, 2, 3, 0, 0, 6, 2, 6, 2, 2,

	 3, 3, 1, 6, 2, 6, 2, 2, 3, 0, 1, 6, 2, 6, 2, 2,

	 6, 6, 6, 6, 6, 6, 4, 4, 6, 0, 0, 6, 0, 6, 4, 4,

	 6, 6, 1, 6, 1, 6, 4, 4, 6, 0, 1, 6, 1, 6, 4, 4,

	 6, 6, 6, 6, 2, 6, 4, 4, 6, 0, 0, 6, 2, 6, 4, 4,

	 6, 6, 1, 6, 2, 6, 4, 4, 6, 0, 1, 6, 2, 6, 4, 4,

	 3, 3, 3, 6, 3, 6, 4, 4, 3, 0, 0, 6, 0, 6, 4, 4,

	 3, 3, 1, 6, 1, 6, 4, 4, 3, 0, 1, 6, 1, 6, 4, 4,

	 3, 3, 3, 6, 2, 6, 4, 4, 3, 0, 0, 6, 2, 6, 4, 4,

	 3, 3, 1, 6, 2, 6, 4, 4, 3, 0, 1, 6, 2, 6, 4, 4,

	 5, 5, 5, 5, 5, 6, 5, 5, 5, 0, 0, 5, 0, 6, 0, 0,

	 5, 5, 1, 5, 1, 6, 1, 1, 5, 0, 1, 5, 1, 6, 1, 1,

	 5, 5, 5, 5, 2, 6, 2, 2, 5, 0, 0, 5, 2, 6, 2, 2,

	 5, 5, 1, 5, 2, 6, 2, 2, 5, 0, 1, 5, 2, 6, 2, 2,

	 3, 3, 3, 5, 3, 6, 3, 3, 3, 0, 0, 5, 0, 6, 0, 0,

	 3, 3, 1, 5, 1, 6, 1, 1, 3, 0, 1, 5, 1, 6, 1, 1,

	 3, 3, 3, 5, 2, 6, 2, 2, 3, 0, 0, 5, 2, 6, 2, 2,

	 3, 3, 1, 5, 2, 6, 2, 2, 3, 0, 1, 5, 2, 6, 2, 2,

	 5, 5, 5, 5, 5, 6, 4, 4, 5, 0, 0, 5, 0, 6, 4, 4,

	 5, 5, 1, 5, 1, 6, 4, 4, 5, 0, 1, 5, 1, 6, 4, 4,

	 5, 5, 5, 5, 2, 6, 4, 4, 5, 0, 0, 5, 2, 6, 4, 4,

	 5, 5, 1, 5, 2, 6, 4, 4, 5, 0, 1, 5, 2, 6, 4, 4,

	 3, 3, 3, 5, 3, 6, 4, 4, 3, 0, 0, 5, 0, 6, 4, 4,

	 3, 3, 1, 5, 1, 6, 4, 4, 3, 0, 1, 5, 1, 6, 4, 4,

	 3, 3, 3, 5, 2, 6, 4, 4, 3, 0, 0, 5, 2, 6, 4, 4,

	 3, 3, 1, 5, 2, 6, 4, 4, 3, 0, 1, 5, 2, 6, 4, 4,

	 7, 7, 7, 7, 7, 7, 7, 7, 7, 0, 0, 7, 0, 7, 7, 0,

	 7, 7, 1, 7, 1, 7, 7, 1, 7, 0, 1, 7, 1, 7, 7, 1,

	 7, 7, 7, 7, 2, 7, 7, 2, 7, 0, 0, 7, 2, 7, 7, 2,

	 7, 7, 1, 7, 2, 7, 7, 2, 7, 0, 1, 7, 2, 7, 7, 2,

	 3, 3, 3, 7, 3, 7, 7, 3, 3, 0, 0, 7, 0, 7, 7, 0,

	 3, 3, 1, 7, 1, 7, 7, 1, 3, 0, 1, 7, 1, 7, 7, 1,

	 3, 3, 3, 7, 2, 7, 7, 2, 3, 0, 0, 7, 2, 7, 7, 2,

	 3, 3, 1, 7, 2, 7, 7, 2, 3, 0, 1, 7, 2, 7, 7, 2,

	 7, 7, 7, 7, 7, 7, 7, 4, 7, 0, 0, 7, 0, 7, 7, 4,

	 7, 7, 1, 7, 1, 7, 7, 4, 7, 0, 1, 7, 1, 7, 7, 4,

	 7, 7, 7, 7, 2, 7, 7, 4, 7, 0, 0, 7, 2, 7, 7, 4,

	 7, 7, 1, 7, 2, 7, 7, 4, 7, 0, 1, 7, 2, 7, 7, 4,

	 3, 3, 3, 7, 3, 7, 7, 4, 3, 0, 0, 7, 0, 7, 7, 4,

	 3, 3, 1, 7, 1, 7, 7, 4, 3, 0, 1, 7, 1, 7, 7, 4,

	 3, 3, 3, 7, 2, 7, 7, 4, 3, 0, 0, 7, 2, 7, 7, 4,

	 3, 3, 1, 7, 2, 7, 7, 4, 3, 0, 1, 7, 2, 7, 7, 4,

	 5, 5, 5, 5, 5, 7, 7, 5, 5, 0, 0, 5, 0, 7, 7, 0,

	 5, 5, 1, 5, 1, 7, 7, 1, 5, 0, 1, 5, 1, 7, 7, 1,

	 5, 5, 5, 5, 2, 7, 7, 2, 5, 0, 0, 5, 2, 7, 7, 2,

	 5, 5, 1, 5, 2, 7, 7, 2, 5, 0, 1, 5, 2, 7, 7, 2,

	 3, 3, 3, 5, 3, 7, 7, 3, 3, 0, 0, 5, 0, 7, 7, 0,

	 3, 3, 1, 5, 1, 7, 7, 1, 3, 0, 1, 5, 1, 7, 7, 1,

	 3, 3, 3, 5, 2, 7, 7, 2, 3, 0, 0, 5, 2, 7, 7, 2,

	 3, 3, 1, 5, 2, 7, 7, 2, 3, 0, 1, 5, 2, 7, 7, 2,

	 5, 5, 5, 5, 5, 7, 7, 4, 5, 0, 0, 5, 0, 7, 7, 4,

	 5, 5, 1, 5, 1, 7, 7, 4, 5, 0, 1, 5, 1, 7, 7, 4,

	 5, 5, 5, 5, 2, 7, 7, 4, 5, 0, 0, 5, 2, 7, 7, 4,

	 5, 5, 1, 5, 2, 7, 7, 4, 5, 0, 1, 5, 2, 7, 7, 4,

	 3, 3, 3, 5, 3, 7, 7, 4, 3, 0, 0, 5, 0, 7, 7, 4,

	 3, 3, 1, 5, 1, 7, 7, 4, 3, 0, 1, 5, 1, 7, 7, 4,

	 3, 3, 3, 5, 2, 7, 7, 4, 3, 0, 0, 5, 2, 7, 7, 4,

	 3, 3, 1, 5, 2, 7, 7, 4, 3, 0, 1, 5, 2, 7, 7, 4,

	 6, 6, 6, 6, 6, 6, 7, 6, 6, 0, 0, 6, 0, 6, 7, 0,

	 6, 6, 1, 6, 1, 6, 7, 1, 6, 0, 1, 6, 1, 6, 7, 1,

	 6, 6, 6, 6, 2, 6, 7, 2, 6, 0, 0, 6, 2, 6, 7, 2,

	 6, 6, 1, 6, 2, 6, 7, 2, 6, 0, 1, 6, 2, 6, 7, 2,

	 3, 3, 3, 6, 3, 6, 7, 3, 3, 0, 0, 6, 0, 6, 7, 0,

	 3, 3, 1, 6, 1, 6, 7, 1, 3, 0, 1, 6, 1, 6, 7, 1,

	 3, 3, 3, 6, 2, 6, 7, 2, 3, 0, 0, 6, 2, 6, 7, 2,

	 3, 3, 1, 6, 2, 6, 7, 2, 3, 0, 1, 6, 2, 6, 7, 2,

	 6, 6, 6, 6, 6, 6, 7, 4, 6, 0, 0, 6, 0, 6, 7, 4,

	 6, 6, 1, 6, 1, 6, 7, 4, 6, 0, 1, 6, 1, 6, 7, 4,

	 6, 6, 6, 6, 2, 6, 7, 4, 6, 0, 0, 6, 2, 6, 7, 4,

	 6, 6, 1, 6, 2, 6, 7, 4, 6, 0, 1, 6, 2, 6, 7, 4,

	 3, 3, 3, 6, 3, 6, 7, 4, 3, 0, 0, 6, 0, 6, 7, 4,

	 3, 3, 1, 6, 1, 6, 7, 4, 3, 0, 1, 6, 1, 6, 7, 4,

	 3, 3, 3, 6, 2, 6, 7, 4, 3, 0, 0, 6, 2, 6, 7, 4,

	 3, 3, 1, 6, 2, 6, 7, 4, 3, 0, 1, 6, 2, 6, 7, 4,

	 5, 5, 5, 5, 5, 6, 7, 5, 5, 0, 0, 5, 0, 6, 7, 0,

	 5, 5, 1, 5, 1, 6, 7, 1, 5, 0, 1, 5, 1, 6, 7, 1,

	 5, 5, 5, 5, 2, 6, 7, 2, 5, 0, 0, 5, 2, 6, 7, 2,

	 5, 5, 1, 5, 2, 6, 7, 2, 5, 0, 1, 5, 2, 6, 7, 2,

	 3, 3, 3, 5, 3, 6, 7, 3, 3, 0, 0, 5, 0, 6, 7, 0,

	 3, 3, 1, 5, 1, 6, 7, 1, 3, 0, 1, 5, 1, 6, 7, 1,

	 3, 3, 3, 5, 2, 6, 7, 2, 3, 0, 0, 5, 2, 6, 7, 2,

	 3, 3, 1, 5, 2, 6, 7, 2, 3, 0, 1, 5, 2, 6, 7, 2,

	 5, 5, 5, 5, 5, 6, 7, 4, 5, 0, 0, 5, 0, 6, 7, 4,

	 5, 5, 1, 5, 1, 6, 7, 4, 5, 0, 1, 5, 1, 6, 7, 4,

	 5, 5, 5, 5, 2, 6, 7, 4, 5, 0, 0, 5, 2, 6, 7, 4,

	 5, 5, 1, 5, 2, 6, 7, 4, 5, 0, 1, 5, 2, 6, 7, 4,

	 3, 3, 3, 5, 3, 6, 7, 4, 3, 0, 0, 5, 0, 6, 7, 4,

	 3, 3, 1, 5, 1, 6, 7, 4, 3, 0, 1, 5, 1, 6, 7, 4,

	 3, 3, 3, 5, 2, 6, 7, 4, 3, 0, 0, 5, 2, 6, 7, 4,

	 3, 3, 1, 5, 2, 6, 7, 4, 3, 0, 1, 5, 2, 6, 7, 4};

/*------------------------------------------------------------------------*/

int Lx;

int Displace_vector[8];

#define E_PIX(pix) \

	(*(pix + 1))

#define W_PIX(pix) \

	(*(pix - 1))

#define N_PIX(pix) \

	(*(pix + Lx))

#define S_PIX(pix) \

	(*(pix - Lx))

#define SW_PIX(pix) \

	(*(pix - Lx - 1))

#define NW_PIX(pix) \

	(*(pix + Lx - 1))

#define NE_PIX(pix) \

	(*(pix + Lx + 1))

#define SE_PIX(pix) \

	(*(pix - Lx + 1))

#define NEIGHBOURS_CODE(pix)     \

	(((SW_PIX(pix) != 0) << 0) | \

	 ((S_PIX(pix) != 0) << 1) |  \

	 ((SE_PIX(pix) != 0) << 2) | \

	 ((W_PIX(pix) != 0) << 3) |  \

	 ((E_PIX(pix) != 0) << 4) |  \

	 ((NW_PIX(pix) != 0) << 5) | \

	 ((N_PIX(pix) != 0) << 6) |  \

	 ((NE_PIX(pix) != 0) << 7))

/*------------------------------------------------------------------------*/

#define FIRST_PRESEED(code) \

	First_preseed_table[code]

/*------------------------------------------------------------------------*/

#define NEXT_POINT(code, preseed) \

	Next_point_table[(code << 3) | preseed]

/*------------------------------------------------------------------------*/

#define UPDATE_POS(displ_code, x_pos, y_pos) \

	switch (displ_code) { \

	case 0: x_pos--; y_pos--; break; \

	case 1:          y_pos--; break; \

	case 2: x_pos++; y_pos--; break; \

	case 3: x_pos--;          break; \

	case 4: x_pos++;          break; \

	case 5: x_pos--; y_pos++; break; \

	case 6:          y_pos++; break; \

	case 7: x_pos++; y_pos++; break; \

	default: assert(FALSE); \

	}

/*------------------------------------------------------------------------*/

/*=============================================================================*/

/*---------------------------------------------------------------------------*/

static int fillByteRaster(const TRaster32P &rin, TRasterGR8P &rout)

{

	bool ret = false;

	assert(rin->getLx() == rout->getLx() - 2 && rin->getLy() == rout->getLy() - 2);

	memset(rout->getRawData(), 0, rout->getLx() * rout->getLy());

	for (int i = 0; i < rin->getLy(); i++) {

		TPixel32 *bufIn = (TPixel32 *)rin->getRawData() + i * rin->getWrap();

		UCHAR *bufOut = (UCHAR *)rout->getRawData() + (i + 1) * rout->getWrap() + 1;

		for (int j = 0; j < rin->getLx(); j++, bufIn++, bufOut++)

			if (bufIn->m != 0) {

				ret = true;

				*bufOut = 1;

			}

	}

	return ret;

}

/*---------------------------------------------------------------------------*/

static void initialize_displace_vector(void)

{

	Displace_vector[0] = -Lx - 1;

	Displace_vector[1] = -Lx;

	Displace_vector[2] = -Lx + 1;

	Displace_vector[3] = -1;

	Displace_vector[4] = +1;

	Displace_vector[5] = Lx - 1;

	Displace_vector[6] = Lx;

	Displace_vector[7] = Lx + 1;

}

/*------------------------------------------------------------------------*/

static int find_next_seed(const TRasterGR8P &r, int first_seed,

						  UCHAR *&seed, int &x_pos, int &y_pos)

{

	static int Curr_x = 0, Curr_y = 0;

	UCHAR *pix;

	if (first_seed) {

		Curr_x = 0;

		Curr_y = 0;

	}

	seed = 0;

	for (; Curr_y < r->getLy(); Curr_y++) {

		pix = (UCHAR *)r->getRawData() + Curr_y * r->getWrap() + Curr_x;

		for (; Curr_x < r->getLx(); Curr_x++, pix++)

			if (*pix == 1 &&

				(!E_PIX(pix) ||

				 !W_PIX(pix) ||

				 !N_PIX(pix) ||

				 !S_PIX(pix))) {

				seed = pix;

				x_pos = Curr_x;

				y_pos = Curr_y;

				return true;

			}

		Curr_x = 0;

	}

	return false;

}

/*------------------------------------------------------------------------*/

#define COMPUTE_NUM_DEN(x_pos, y_pos, old_x_pos, old_y_pos) \

	{                                                       \

		aux = old_x_pos * y_pos - x_pos * old_y_pos;        \

		den += aux;                                         \

		x_num += (x_pos + old_x_pos) * aux;                 \

		y_num += (y_pos + old_y_pos) * aux;                 \

	}

/*------------------------------------------------------------------------*/

void doComputeCentroid(const TRasterGR8P &r, TPoint &cp)

{

	int preseed, displ, prewalker, code;

	UCHAR *seed, *walker;

	int x_num = 0, y_num = 0, den = 0;

	int x_pos, y_pos, old_x_pos, old_y_pos;

	int aux, old_displ = -1;

	int first_seed;

	Lx = r->getLx();

	Displace_vector[0] = -Lx - 1;

	Displace_vector[1] = -Lx;

	Displace_vector[2] = -Lx + 1;

	Displace_vector[3] = -1;

	Displace_vector[4] = +1;

	Displace_vector[5] = Lx - 1;

	Displace_vector[6] = Lx;

	Displace_vector[7] = Lx + 1;

	first_seed = TRUE;

	while (find_next_seed(r, first_seed, seed, x_pos, y_pos)) {

		first_seed = FALSE;

		*seed |= 0x2;

		code = NEIGHBOURS_CODE(seed);

		preseed = FIRST_PRESEED(code);

		if (preseed == 8)

			continue;

		displ = NEXT_POINT(code, preseed);

		walker = seed + Displace_vector[displ];

		old_x_pos = x_pos;

		old_y_pos = y_pos;

		UPDATE_POS(displ, x_pos, y_pos)

		COMPUTE_NUM_DEN(x_pos, y_pos, old_x_pos, old_y_pos)

		prewalker = displ ^ 0x7;

		while ((walker != seed) || (preseed != prewalker)) {

			*walker |= 0x2;

			displ = NEXT_POINT(NEIGHBOURS_CODE(walker), prewalker);

			walker += Displace_vector[displ];

			old_x_pos = x_pos;

			old_y_pos = y_pos;

			UPDATE_POS(displ, x_pos, y_pos)

			COMPUTE_NUM_DEN(x_pos, y_pos, old_x_pos, old_y_pos)

			prewalker = displ ^ 0x7;

		}

	}

	if (den)

		cp = TPoint(tround(x_num / (3.0 * den)), tround(y_num / (3.0 * den)));

}

} //namespace

TPoint computeCentroid(const TRaster32P &r)

{

	TPoint ret(1, 1);

	TRasterGR8P raux(r->getLx() + 2, r->getLy() + 2);

	if (fillByteRaster(r, raux))

		doComputeCentroid(raux, ret);

	ret.x--;

	ret.y--; /* per il bordo aggiunto */

	return ret;

}