float interp_floatvec( floatvec *fv , float x )
{
int ix , im1,ip1,ip2 , itop ;
float fx , val , abot,atop ;
if( fv == NULL || fv->ar == NULL ) return 0.0f ;
itop = fv->nar - 1 ;
if( itop <= 1 || fv->dx == 0.0 ) return(fv->ar[0]) ;
/* if input x is out of range, return the edge value */
fx = (x - fv->x0) / fv->dx ;
if( fx <= 0.0f ) return(fv->ar[0]) ;
else if( fx >= itop ) return(fv->ar[itop]) ;
/* input x is between point #ix and #ix+1 */
/* fractional offset between them is fx */
ix = (int)fx ; fx = fx - ix ;
/* get indexes below (im1) and above (ip1 and ip2) */
im1 = ix-1 ; if( im1 < 0 ) im1 = 0 ;
ip1 = ix+1 ;
if( ip1 > itop ){
ip1 = ip2 = itop ;
} else {
ip2 = ip1+1 ; if( ip2 > itop ) ip2 = itop ;
}
/* cubic interpolation between these 4 points */
val = P_M1(fx)*fv->ar[im1] + P_00(fx)*fv->ar[ix]
+ P_P1(fx)*fv->ar[ip1] + P_P2(fx)*fv->ar[ip2] ;
/* make sure result lies in the local range of values */
abot = fv->ar[ix] ; atop = fv->ar[ip1] ;
if( abot > atop ){ fx = abot; abot = atop; atop = fx; }
if( val < abot ) val = abot; else if( val > atop ) val = atop;
return(val) ;
}
void cub_shift( int n , float af , float * f )
{
int ii , ia , ix ;
float wt_m1 , wt_00 , wt_p1 , wt_p2 , aa ;
#ifdef SEPARATE_FINS
int ibot,itop ;
#endif
ENTRY("cub_shift") ;
af = -af ; ia = (int) af ; if( af < 0 ) ia-- ; /* ia = floor */
/* 15 Mar 2001: if shift is too large, return all zeros */
if( ia <= -n || ia >= n ){
for( ii=0 ; ii < n ; ii++ ) f[ii] = 0.0 ;
EXRETURN ;
}
aa = af - ia ;
wt_m1 = P_M1(aa) ; wt_00 = P_00(aa) ;
wt_p1 = P_P1(aa) ; wt_p2 = P_P2(aa) ;
if( n > nlcbuf ){
if( lcbuf != NULL ) free(lcbuf) ;
lcbuf = (float *) malloc( sizeof(float) * n ) ;
nlcbuf = n ;
}
#ifdef SEPARATE_FINS
ibot = 1-ia ; if( ibot < 0 ) ibot = 0 ;
itop = n-3-ia ; if( itop > n-1 ) itop = n-1 ;
for( ii=ibot ; ii <= itop ; ii++ ){
ix = ii + ia ;
lcbuf[ii] = wt_m1 * f[ix-1] + wt_00 * f[ix]
+ wt_p1 * f[ix+1] + wt_p2 * f[ix+2] ;
}
if( ibot > n ) ibot = n ; /* 15 Mar 2001 */
for( ii=0 ; ii < ibot ; ii++ ){
ix = ii + ia ;
lcbuf[ii] = wt_m1 * FINS(ix-1) + wt_00 * FINS(ix)
+ wt_p1 * FINS(ix+1) + wt_p2 * FINS(ix+2) ;
}
if( itop < 0 ) itop = -1 ; /* 15 Mar 2001 */
for( ii=itop+1 ; ii < n ; ii++ ){
ix = ii + ia ;
lcbuf[ii] = wt_m1 * FINS(ix-1) + wt_00 * FINS(ix)
+ wt_p1 * FINS(ix+1) + wt_p2 * FINS(ix+2) ;
}
#else /* not SEPARATE_FINS */
for( ii=0 ; ii < n ; ii++ ){
ix = ii + ia ;
if( ix > 0 && ix < n-2 )
lcbuf[ii] = wt_m1 * f[ix-1] + wt_00 * f[ix]
+ wt_p1 * f[ix+1] + wt_p2 * f[ix+2] ;
else
lcbuf[ii] = wt_m1 * FINS(ix-1) + wt_00 * FINS(ix)
+ wt_p1 * FINS(ix+1) + wt_p2 * FINS(ix+2) ;
}
#endif /* SEPARATE_FINS */
memcpy( f , lcbuf , sizeof(float)*n ) ;
EXRETURN ;
}
void algebraic_number_test()
{
typedef Coefficient_ Coefficient;
typedef Rational_ Rational;
typedef CGAL::internal::Algebraic_real_d_1<Coefficient,Rational, CGAL::Handle_policy_no_union, RepClass > Algebraic_real_d_1;
typedef typename CGAL::Polynomial_type_generator<Coefficient,1>::Type Poly;
CGAL::test_real_embeddable<Algebraic_real_d_1>();
// general test of comparable functionality
// TODO generates a precondition error in Algebraic_real_rep
//NiX::test_real_comparable<Algebraic_real_d_1>();
// test of constructors
Poly P_00(Coefficient(0)); // zero polynomial
Poly P_01(Coefficient(1)); // constant polynomial
Poly P_1(Coefficient(-1),Coefficient(1)); //(x-1)
Poly P_2(Coefficient(-2),Coefficient(1)); //(x-2)
Poly P_3(Coefficient(-3),Coefficient(1)); //(x-3)
Poly P_4(Coefficient(-4),Coefficient(1)); //(x-4)
Poly P_12=P_1*P_2; //(x-1)(x-2)
Poly P_123=P_1*P_2*P_3; //(x-1)(x-2)(x-3)
Poly P_s2(Coefficient(-2),Coefficient(0),Coefficient(1)); //(x^2-2)
Poly P_s3(Coefficient(-3),Coefficient(0),Coefficient(1)); //(x^2-3)
Poly P_s5(-Coefficient(5),Coefficient(0),Coefficient(1));
Poly P_s10(-Coefficient(10),Coefficient(0),Coefficient(1));
Poly P_s30(-Coefficient(30),Coefficient(0),Coefficient(1));
Poly P_s2510= P_s2*P_s5*P_s10;
Poly P_s530= P_s5 * P_s30;
Algebraic_real_d_1 tmp;
Algebraic_real_d_1 tmp1,tmp2;
Rational m;
// general constructors;
// default
// tmp = IS_Rational_ = 0
tmp = Algebraic_real_d_1();
assert(tmp.is_rational());
assert(tmp.rational()==0);
// from int
tmp = Algebraic_real_d_1(1);
assert(tmp.is_rational());
assert(tmp.rational()==1);
tmp = Algebraic_real_d_1(5);
assert(tmp.is_rational());
assert(tmp.rational()==5);
// from Field
tmp = Algebraic_real_d_1(Rational(0));
assert(tmp.is_rational());
assert(tmp.rational()==0);
tmp = Algebraic_real_d_1(Rational(1));
assert(tmp.is_rational());
assert(tmp.rational()==1);
tmp = Algebraic_real_d_1(Rational(5)/ Rational(2));
assert(tmp.is_rational());
assert(tmp.rational()== Rational(5)/ Rational(2));
// general constructor
// tmp = 1
#if 0
tmp = Algebraic_real_d_1(P_1,-2,+2);
// TODO different behavior with leda and core
assert(!tmp.is_rational());
assert(tmp==Rational(1));
assert(tmp.is_rational());
assert(tmp.rational()==1);
#endif
// special constructors
// from int
tmp = Algebraic_real_d_1(2);
assert(tmp.is_rational());
assert(tmp.rational()==Rational(2));
//from Rational
tmp = Algebraic_real_d_1(Rational(2));
assert(tmp.is_rational());
assert(tmp.rational()==Rational(2));
// member functions
// tmp IS_GENERAL == 2;
tmp = Algebraic_real_d_1(P_123,Rational(3)/2,Rational(5)/2);
assert(!tmp.is_rational());
assert(tmp.polynomial()==P_123);
assert(tmp.low()==Rational(3)/2);
assert(tmp.high()==Rational(5)/2);
assert(tmp.sign_at_low()==P_123.sign_at(Rational(3)/2));
// refine
tmp = Algebraic_real_d_1(P_123,Rational(3)/2,Rational(5)/2);
tmp.refine();
assert(tmp.is_rational());
assert(tmp.rational()==Rational(2));
// tmp IS_GENERAL = sqrt 2
tmp = Algebraic_real_d_1(P_s2*P_3,Rational(1),Rational(2));
tmp.refine();
assert(tmp.low() >= Rational(1));
assert(tmp.high() <= Rational(3)/2);
// strong_refine
// tmp IS_GENERAL == 2;
tmp = Algebraic_real_d_1(P_123,Rational(3)/2,Rational(5)/2);
m = Rational(2);
tmp.strong_refine(m);
assert(tmp.is_rational());
assert(tmp.rational()==Rational(2));
// tmp IS_GENERAL = sqrt 2
tmp = Algebraic_real_d_1(P_s2*P_3,Rational(1),Rational(2));
m = Rational(3)/2;
tmp.strong_refine(m);
assert(tmp.low()!=m);
assert(tmp.high()!=m);
// refine_to(a,b)
// tmp IS_GENERAL = sqrt 2
tmp = Algebraic_real_d_1(P_s2*P_4,Rational(0),Rational(3));
assert(!tmp.is_rational());
tmp.refine_to(Rational(1), Rational(2));
assert(tmp.low() >= Rational(1));
assert(tmp.high() <= Rational(2));
// tmp IS_REAL = sqrt 2
tmp = Algebraic_real_d_1(P_s2,Rational(0),Rational(3));
assert(!tmp.is_rational());
tmp.refine_to(Rational(1), Rational(2));
assert(tmp.low() >= Rational(1));
assert(tmp.high() <= Rational(2));
// compare(rat)
// tmp IS_GENERAL = sqrt 2
tmp = Algebraic_real_d_1(P_s2*P_3,Rational(1),Rational(2));
m = Rational(1);
assert(tmp.compare(m)==1);
m = Rational(2);
assert(tmp.compare(m)==-1);
// tmp IS_GENERAL = 3
tmp = Algebraic_real_d_1(P_s2*P_3,Rational(2),Rational(4));
m = Rational(3);
assert(tmp.compare(m)==0);
assert(tmp.is_rational());
assert(tmp.rational()==Rational(3));
assert(CGAL::degree(tmp.polynomial()) == 1);
assert(tmp.polynomial().evaluate(Coefficient(3)) == Coefficient(0));
// compare_distinct()
tmp1 = Algebraic_real_d_1(P_s530, Rational(2), Rational(3)); // sqrt(5) = 2.236...
tmp2 = Algebraic_real_d_1(P_s530, Rational(5), Rational(6)); // sqrt(30) = 5.477...
assert(tmp1.compare_distinct(tmp2) == CGAL::SMALLER);
assert(tmp2.compare_distinct(tmp1) == CGAL::LARGER);
//member functions
// is_root_of
tmp1 = Algebraic_real_d_1(P_s2510,Rational(1)/2,Rational(3)/2);
assert(tmp1.is_root_of(P_s530*P_s2));
tmp1 = Algebraic_real_d_1(P_s2510,Rational(1)/2,Rational(3)/2);
assert(!tmp1.is_root_of(P_s530));
//rational_between
{
Rational r;
tmp1 = Algebraic_real_d_1(P_s2,Rational(1),Rational(2)); //sqrt2
tmp2 = Algebraic_real_d_1(P_s3,Rational(1),Rational(3)); //sqrt3
r = tmp1.rational_between(tmp2);
assert(tmp1.compare(r)==CGAL::SMALLER);
assert(tmp2.compare(r)==CGAL::LARGER);
r = tmp2.rational_between(tmp1);
assert(tmp1.compare(r)==CGAL::SMALLER);
assert(tmp2.compare(r)==CGAL::LARGER);
}
// to_double()
tmp = Algebraic_real_d_1(P_1*P_3*P_4, Rational(0), Rational(2));
assert(fabs(tmp.to_double() - 1.0) < 1e-10);
tmp = Algebraic_real_d_1(P_1*P_3, Rational(0), Rational(2));
assert(fabs(tmp.to_double() - 1.0) < 1e-10);
tmp = Algebraic_real_d_1(P_1, Rational(0), Rational(2));
assert(fabs(tmp.to_double() - 1.0) < 1e-10);
//IO tested in _test_algebraic_kernel_1.h
// test for Handle with union
{
typedef
CGAL::internal::Algebraic_real_d_1
<Coefficient,Rational,::CGAL::Handle_policy_union> Int;
Int i(5);
Int j(5);
Int k(6);
assert( ! i.identical( j));
assert( ! i.identical( k));
assert( ! j.identical( k));
assert( i == j);
assert( ! (i == k));
assert( i.identical( j));
assert( ! i.identical( k));
assert( ! j.identical( k));
// code coverage
assert( i == j);
}
// test for Handle without union
{
typedef
CGAL::internal::Algebraic_real_d_1
<Coefficient,Rational,::CGAL::Handle_policy_no_union> Int;
Int i(5);
Int j(5);
Int k(6);
assert( ! i.identical( j));
assert( ! i.identical( k));
assert( ! j.identical( k));
assert( i == j);
assert( ! (i == k));
assert( ! i.identical( j));
assert( ! i.identical( k));
assert( ! j.identical( k));
}
// to_interval
// {
// Algebraic_real_d_1 TMP;
// assert(CGAL::in(25.0,CGAL::to_interval(Algebraic_real_d_1(25))));
// assert(CGAL::in(sqrt(2),CGAL::to_interval(Algebraic_real_d_1(P_s2,1,2))));
// assert(CGAL::in(sqrt(2),CGAL::to_interval(Algebraic_real_d_1(P_s2510,1,2))));
// assert(CGAL::in(-sqrt(2),CGAL::to_interval(Algebraic_real_d_1(P_s2510,-2,-1))));
// assert(CGAL::in(sqrt(5),CGAL::to_interval(Algebraic_real_d_1(P_s2510,2,3))));
// assert(CGAL::in(-sqrt(5),CGAL::to_interval(Algebraic_real_d_1(P_s2510,-3,-2))));
// assert(CGAL::in(sqrt(10),CGAL::to_interval(Algebraic_real_d_1(P_s2510,3,4))));
// assert(CGAL::in(-sqrt(10),CGAL::to_interval(Algebraic_real_d_1(P_s2510,-4,-3))));
// }
//simplify
{
// just a synatx check
Algebraic_real_d_1(P_s2510,1,2).simplify();
}
}
MRI_IMAGE *mri_rota( MRI_IMAGE *im, float aa, float bb, float phi )
{
float rot_dx , rot_dy , rot_cph , rot_sph , top,bot,val ;
MRI_IMAGE *imfl , *newImg ;
MRI_IMARR *impair ;
float *far , *nar ;
float xx,yy , fx,fy ;
int ii,jj, nx,ny , ix,jy , ifx,jfy ;
float f_jm1,f_j00,f_jp1,f_jp2 , wt_m1,wt_00,wt_p1,wt_p2 ;
#ifdef USE_CGRID
if( p_first ){
p_first = 0 ;
xx = 1.0 / CGRID ;
for( ii=0 ; ii <= CGRID ; ii++ ){
yy = ii * xx ;
p_m1[ii] = P_M1(yy) ;
p_00[ii] = P_00(yy) ;
p_p1[ii] = P_P1(yy) ;
p_p2[ii] = P_P2(yy) ;
}
}
#endif
if( im == NULL || ! MRI_IS_2D(im) ){
fprintf(stderr,"*** mri_rota only works on 2D images!\n") ; EXIT(1) ;
}
/** if complex image, break into pairs, do each separately, put back together **/
if( im->kind == MRI_complex ){
MRI_IMARR *impair ;
MRI_IMAGE * rim , * iim , * tim ;
impair = mri_complex_to_pair( im ) ;
if( impair == NULL ){
fprintf(stderr,"*** mri_complex_to_pair fails in mri_rota!\n") ; EXIT(1) ;
}
rim = IMAGE_IN_IMARR(impair,0) ;
iim = IMAGE_IN_IMARR(impair,1) ; FREE_IMARR(impair) ;
tim = mri_rota( rim , aa,bb,phi ) ; mri_free( rim ) ; rim = tim ;
tim = mri_rota( iim , aa,bb,phi ) ; mri_free( iim ) ; iim = tim ;
newImg = mri_pair_to_complex( rim , iim ) ;
mri_free( rim ) ; mri_free( iim ) ;
MRI_COPY_AUX(newImg,im) ;
return newImg ;
}
/** rotation params **/
rot_cph = cos(phi) ; rot_sph = sin(phi) ;
rot_dx = (0.5 * im->nx) * (1.0-rot_cph) - aa*rot_cph - bb*rot_sph
-(0.5 * im->ny) * rot_sph ;
rot_dy = (0.5 * im->nx) * rot_sph + aa*rot_sph - bb*rot_cph
+(0.5 * im->ny) * (1.0-rot_cph) ;
/** other initialization **/
nx = im->nx ; /* image dimensions */
ny = im->ny ;
if( im->kind == MRI_float ) imfl = im ;
else imfl = mri_to_float( im ) ;
far = MRI_FLOAT_PTR(imfl) ; /* access to float data */
newImg = mri_new( nx , nx , MRI_float ) ; /* output image */
nar = MRI_FLOAT_PTR(newImg) ; /* output image data */
bot = top = far[0] ;
for( ii=0 ; ii < nx*ny ; ii++ )
if( far[ii] < bot ) bot = far[ii] ;
else if( far[ii] > top ) top = far[ii] ;
/*** loop over output points and warp to them ***/
for( jj=0 ; jj < nx ; jj++ ){
xx = rot_sph * jj + rot_dx - rot_cph ;
yy = rot_cph * jj + rot_dy + rot_sph ;
for( ii=0 ; ii < nx ; ii++ ){
xx += rot_cph ; /* get x,y in original image */
yy -= rot_sph ;
ix = (xx >= 0.0) ? ((int) xx) : ((int) xx)-1 ; /* floor */
jy = (yy >= 0.0) ? ((int) yy) : ((int) yy)-1 ;
#ifdef USE_CGRID
ifx = (xx-ix)*CGRID + 0.499 ;
wt_m1 = p_m1[ifx] ; wt_00 = p_00[ifx] ;
wt_p1 = p_p1[ifx] ; wt_p2 = p_p2[ifx] ;
#else
fx = xx-ix ;
wt_m1 = P_M1(fx) ; wt_00 = P_00(fx) ;
wt_p1 = P_P1(fx) ; wt_p2 = P_P2(fx) ;
#endif
if( ix > 0 && ix < nx-2 && jy > 0 && jy < ny-2 ){
float * fym1, *fy00 , *fyp1 , *fyp2 ;
fym1 = far + (ix-1 + (jy-1)*nx) ;
fy00 = fym1 + nx ;
fyp1 = fy00 + nx ;
fyp2 = fyp1 + nx ;
f_jm1 = wt_m1 * fym1[0] + wt_00 * fym1[1]
+ wt_p1 * fym1[2] + wt_p2 * fym1[3] ;
f_j00 = wt_m1 * fy00[0] + wt_00 * fy00[1]
+ wt_p1 * fy00[2] + wt_p2 * fy00[3] ;
f_jp1 = wt_m1 * fyp1[0] + wt_00 * fyp1[1]
+ wt_p1 * fyp1[2] + wt_p2 * fyp1[3] ;
f_jp2 = wt_m1 * fyp2[0] + wt_00 * fyp2[1]
+ wt_p1 * fyp2[2] + wt_p2 * fyp2[3] ;
} else {
f_jm1 = wt_m1 * FINS(ix-1,jy-1)
+ wt_00 * FINS(ix ,jy-1)
+ wt_p1 * FINS(ix+1,jy-1)
+ wt_p2 * FINS(ix+2,jy-1) ;
f_j00 = wt_m1 * FINS(ix-1,jy)
+ wt_00 * FINS(ix ,jy)
+ wt_p1 * FINS(ix+1,jy)
+ wt_p2 * FINS(ix+2,jy) ;
f_jp1 = wt_m1 * FINS(ix-1,jy+1)
+ wt_00 * FINS(ix ,jy+1)
+ wt_p1 * FINS(ix+1,jy+1)
+ wt_p2 * FINS(ix+2,jy+1) ;
f_jp2 = wt_m1 * FINS(ix-1,jy+2)
+ wt_00 * FINS(ix ,jy+2)
+ wt_p1 * FINS(ix+1,jy+2)
+ wt_p2 * FINS(ix+2,jy+2) ;
}
#define THIRTYSIX 2.7777778e-2 /* 1./36.0, actually */
#ifdef USE_CGRID
jfy = (yy-jy)*CGRID + 0.499 ;
val = ( p_m1[jfy] * f_jm1 + p_00[jfy] * f_j00
+ p_p1[jfy] * f_jp1 + p_p2[jfy] * f_jp2 ) * THIRTYSIX ;
#else
fy = yy-jy ;
val = ( P_M1(fy) * f_jm1 + P_00(fy) * f_j00
+ P_P1(fy) * f_jp1 + P_P2(fy) * f_jp2 ) * THIRTYSIX ;
#endif
if( val < bot ) nar[ii+jj*nx] = bot ; /* too small! */
else if( val > top ) nar[ii+jj*nx] = top ; /* too big! */
else nar[ii+jj*nx] = val ; /* just right */
}
}
/*** cleanup and return ***/
if( im != imfl ) mri_free(imfl) ; /* throw away unneeded workspace */
MRI_COPY_AUX(newImg,im) ;
return newImg ;
}
template <class Type> void Bench_PackB_IM<Type>::verif()
{
INT def = (INT)(NRrandom3() * 1000);
verif( rectangle(Pt2di(1,0),Pt2di(2,1)));
for (INT k=0; k<10 ; k++)
{
verif( rectangle(Pt2di(k,0),Pt2di(k+1,10) ),def);
verif( rectangle(Pt2di(k,0),Pt2di(k+10,10) ),def);
verif( rectangle(Pt2di(k,0),Pt2di(k+100,10)),def);
verif( rectangle(Pt2di(k,0),Pt2di(k+200,10)),def);
}
verif( im1.all_pts());
verif( rectangle(Pt2di(-10,-20),sz+Pt2di(30,40)),def);
verif( disc(sz/2.0,euclid(sz)/1.8),def);
{
for (INT k=0 ; k<10 ; k++)
{
Pt2dr c = sz/2.0 + Pt2dr(NRrandom3(),NRrandom3())*20;
REAL ray = 1+NRrandom3()*100;
verif(disc(c,ray),def);
}
}
ELISE_COPY(disc(CentreRand(),RayonRand()),1,im1.out()| pck.out());
verif(im1.all_pts());
ELISE_COPY(disc(CentreRand(),RayonRand()),frandr()*8,im1.out()| pck.out());
verif(im1.all_pts());
INT NbPts = (INT)(3 + NRrandom3()*10);
ElList<Pt2di> Lpt;
{
for (INT k=0; k<NbPts ; k++)
Lpt = Lpt+Pt2di(CentreRand());
}
ELISE_COPY(polygone(Lpt),NRrandom3()<0.1,im1.out()| pck.out());
verif(im1.all_pts());
ModifCSte(rectangle(Pt2di(5,0),Pt2di(10,10)),2);
verif(im1.all_pts());
ModifLut(rectangle(Pt2di(0,5),Pt2di(12,12)),FX&3);
verif(im1.all_pts());
//ModifCSte(disc(Pt2di(50,50),20),3);
ModifCSte(disc(Pt2dr(50,50),20),3); // __NEW
verif(im1.all_pts());
for (INT NbC =0 ; NbC < 20 ; NbC++)
{
ElList<Pt2di> lPt;
for (INT iPt =0 ; iPt < 20; iPt ++)
{
lPt = lPt + Pt2di(CentreRand());
}
ModifCSte(polygone(lPt),INT(NRrandom3() * 3));
verif(im1.all_pts());
}
Pt2di P_00 (0,0);
Pt2di P_10 (sz.x,0);
Pt2di P_01 (0,sz.y);
ElList<Pt2di> lP1;
lP1 = lP1 + P_00; lP1 = lP1 + P_01; lP1 = lP1 + P_10;
ModifCSte(polygone(lP1),7);
verif(im1.all_pts());
TiffVerif();
}
