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|
/****************************************************************
*****************************************************************
Triang.c : Ce module contient les routines necessaires
au calcul de la triangulation d'un ensemble
de points.
N.B. : 1) La methode de triangulation est dite "incremental build-and-delete".
Elle est plus longue que d'autres, mais elle permet l'insertion
d'un point a la fois dans un reseau deja forme, et aussi l'enlevement
d'un point sans tout recalculer.
A l'inverse, on pourrait mettre en route une methode plus rapide,
mais qui oblige a recalculer l'ensemble du reseau a chaque
nouvelle insertion d'un point.
2) On peut choisir avec un "flag" global entre une optimisation
en vitesse (défaut) et une optimisation en volume des
structures utilisees (OPTIMIZED_MEMORY)). Vu les problemes generaux
rencontres dans la presentation de donnees dans l'interface,
j'ai choisi par defaut l'optimisation en vitesse.
Contient les routines suivantes :
Usage externe :
---------------
int Triangulate ( GeoPt *Pts, int N_Pts,
Triangle **Triangles, int *N_Triangles,
int **CtPts, int *NCtPts )
int RemovesOnePointToTriangulation ( int num, GeoPt *Pts,
Triangle **Triangles,
int *N_Triangles )
int AddsOnePointToTriangulation ( int num, GeoPt *Pts,
Triangle **Triangles,
int *N_Triangles )
Usage interne :
---------------
Triangle *Allocates_Triangle ( void )
int Computes_Center_And_Radius_Of_Triangle ( GeoPt *Pt1, GeoPt *Pt2,
GeoPt *Pt3, GeoPt *Center, double *R)
double Theta ( GeoPt Pt1, GeoPt Pt2 )
double AngleOfView ( GeoPt ViewPt, GeoPt Pt1, GeoPt Pt2 )
int Compare_Theta ( const void *F1, const void *F2 )
int Is_InCircle ( GeoPt *Center, double Radius, GeoPt *Pt )
ou
( GeoPt *Pt1, GeoPt *Pt2,
GeoPt *Pt3, GeoPt *Pt)
Triangulation globale :
- - - - - - - - - - - -
int Wrap ( GeoPt *Pts, int N_Pts,
int *N_CPts, IndexedPt **IPts )
int Init_Triangulation ( IndexedGeoPt *IPts, int N_Cpts,
int *N_Triangles, Triangle **First, Triangle **Last )
Triangulation globale et addition d'un point :
- - - - - - - - - - - - - - - - - - - - - - -
int Finds_Enclosing_Polygon_For_Addition ( int num, GeoPt *Pts,
IndexedGeoPt **IPts, int *NPtsPoly,
int *N_Triangles, Triangle **First, Triangle **Last )
int Adds_New_Triangles ( int num, GeoPt *Pt,
IndexedGeoPt *IPts, int NPtsPoly,
int *N_Triangles, Triangle **First, Triangle **Last )
int Adds_One_Point_To_Triangulation ( int num, GeoPt *Pts, IndexedGeoPt *IPts,
int *N_Triangles, Triangle **First, Triangle **Last )
Enlevement d'un point :
- - - - - - - - - - - -
int Finds_Enclosing_Polygon_For_Deletion ( int num, GeoPt *Pts,
IndexedGeoPt **IPts, int *NPtsPoly,
int *N_Triangles, Triangle **First, Triangle **Last )
int Rebuilds_New_Triangles ( IndexedGeoPt *IPts, int NPtsPoly,
int *N_Triangles, Triangle **Last )
NOTE : on utilise en interne une autre structure, pour les tris
"sur place"
typedef struct _IndexedGeoPt {
GeoPt *Pt ;
int num ;
} IndexedGeoPt ;
Copyright : Environnement Canada & COGITECH Jean Souviron 2000
Auteur : Jean Souviron (COGITECH Jean Souviron)
Janvier 2000
Please insert these copyrights in each code where you use
part of this software. Failure to do so is a direct violation of the
international copyright laws.
*****************************************************************
*****************************************************************
*/
/*
--------- Include files generaux -----
*/
#include <stdlib.h>
#include <math.h>
/*
--------- Include files specifiques ---
*/
#include <limits.h>
/* sur certaines versions, ce sera <values.h> ou <float.h> */
/*
--- Inclusion des structures nécessaires
*/
#include "TriStructs.h"
/*
--- structure locale (pour les tris "sur place")
*/
typedef struct _IndexedGeoPt {
GeoPt *Pt ;
int num ;
} IndexedGeoPt ;
/*
--- Pour avoir un epsilon correct dans les calculs
*/
#define ACCURACY_DOUBLE 0.0000001
/*
--- Eventuellement définition d'un booléen
*/
#ifndef Boolean
#define Boolean char
#endif
#ifndef False
#define False 0
#endif
#ifndef True
#define True 1
#endif
#ifndef PI
#ifndef M_PI
#define PI 3.14159265358979323846
#else
#define PI M_PI
#endif
#endif
/*
--- Variable globale pour les tris
*/
static GeoPt Pt_Ref ;
/*
===================================================================
====
===================================================================
====
ROUTINES A USAGE INTERNE
===================================================================
====
===================================================================
====
*/
/*
* C o m p u t e s _ C e n t e r _ A n d _ R a d i u s _ O f _ T r i a n g l e
*
* Algorithm taken from comp.graphics.algorithm
*
*
* The circumscribing circle of a triangle is computed with the following
* formulae :
* Let the three given points be a, b, c. Use _0 and _1 to represent
* x and y coordinates. The coordinates of the center p=(p_0,p_1) of
* the circle determined by a, b, and c are:
*
* A = b_0 - a_0
* B = b_1 - a_1
* C = c_0 - a_0
* D = c_1 - a_1
*
* E = A*(a_0 + b_0) + B*(a_1 + b_1)
* F = C*(a_0 + c_0) + D*(a_1 + c_1)
*
* G = 2.0*(A*(c_1 - b_1)-B*(c_0 - b_0))
*
* p_0 = (D*E - B*F) / G
* p_1 = (A*F - C*E) / G
*
* If G is zero then the three points are collinear and no finite-radius
* circle through them exists. Otherwise, the radius of the circle is:
*
* r^2 = (a_0 - p_0)^2 + (a_1 - p_1)^2
*
*
* Reference:
*
* [O' Rourke (C)] p. 201. Simplified by Jim Ward.
*
*/
static int Computes_Center_And_Radius_Of_Triangle ( GeoPt *Pt1, GeoPt *Pt2,
GeoPt *Pt3, GeoPt *Center,
double *R)
{
double x1, y1, x2, y2, x3, y3 ;
double xlk,ylk,xmk,ymk,det,rlksq,rmksq,xcc,ycc;
x1 = Pt1->X ;
y1 = Pt1->Y ;
x2 = Pt2->X ;
y2 = Pt2->Y ;
x3 = Pt3->X ;
y3 = Pt3->Y ;
xlk = x2 - x1;
ylk = y2 - y1;
xmk = x3 - x1;
ymk = y3 - y1;
det = (xlk*(y3 - y2)) - (ylk*(x3 - x2));
if( det == 0.0 ) /* two points needed at least */
return ERROR ;
else
{
det = 2.0 * det ;
rlksq = (xlk * (x1+x2)) + (ylk * (y1+y2)) ;
rmksq = (xmk * (x1+x3)) + (ymk * (y1+y3)) ;
xcc = ((rlksq*ymk) - (rmksq*ylk)) / det ;
ycc = ((xlk*rmksq) - (xmk*rlksq)) / det ;
Center->X = xcc ;
Center->Y = ycc ;
/* to get the radius, use the next equation */
*R = ((x1 - xcc)*(x1 - xcc)) + ((y1-ycc)*(y1-ycc)) ;
return SUCCESS ;
}
}
/*
******
******
****** ROUTINES DE MATHS, MAIS ADAPTEES
******
******
*/
/*
* T h e t a
*
* Based on the routine in Sedgewick (p. 353)
*
*/
static double Theta ( GeoPt Pt1, GeoPt Pt2 )
{
double t, dx, dy, ax, ay, x1, y1, x2, y2 ;
x1 = Pt1.X ;
y1 = Pt1.Y ;
x2 = Pt2.X ;
y2 = Pt2.Y ;
dx = x2 - x1 ;
dy = y2 - y1 ;
ax = fabs(dx);
ay = fabs(dy);
if ( (ax+ay) == 0.0 )
t = 0.0 ;
else
t = dy / (ax+ay) ;
if ( dx < 0 )
t = 2.0 - t ;
else
if ( dy < 0 )
t = 4.0 + t ;
t = t * 90.0 ;
return (t);
}
/*
* A n g l e O f V i e w
*
*
*/
static double AngleOfView ( GeoPt ViewPt, GeoPt Pt1, GeoPt Pt2 )
{
double a1, b1, a2, b2, a, b, t, cosinus ;
a1 = Pt1.X - ViewPt.X ;
a2 = Pt1.Y - ViewPt.Y ;
b1 = Pt2.X - ViewPt.X ;
b2 = Pt2.Y - ViewPt.Y ;
a = sqrt ( (a1*a1) + (a2*a2) );
b = sqrt ( (b1*b1) + (b2*b2) );
if ( (a == 0.0) || (b == 0.0) )
return (0.0) ;
cosinus = (a1*b1+a2*b2) / (a*b) ;
t = acos ( cosinus );
t = t * 180.0 / PI ;
return (t);
}
/*
* C o m p a r e _ T h e t a
*
*/
static int Compare_Theta(const void *F1, const void *F2)
{
double dx, dy, d1, d2, t1, t2 ;
IndexedGeoPt *FF1 = (IndexedGeoPt *)(F1) ;
IndexedGeoPt *FF2 = (IndexedGeoPt *)(F2) ;
t1 = Theta ( Pt_Ref, *(FF1->Pt) ) ;
t2 = Theta ( Pt_Ref, *(FF2->Pt) ) ;
if ( t1 < t2 )
return (-1) ;
else
if ( t1 > t2 )
return (1) ;
else
{
dx = FF1->Pt->X - Pt_Ref.X ;
dy = FF1->Pt->Y - Pt_Ref.Y ;
d1 = sqrt( (dx*dx) + (dy*dy) );
dx = FF2->Pt->X - Pt_Ref.X ;
dy = FF2->Pt->Y - Pt_Ref.Y ;
d2 = sqrt( (dx*dx) + (dy*dy) );
if ( d1 < d2 )
return (-1) ;
else
if ( d1 > d2 )
return (1) ;
else
return (0);
}
}
/*
* W r a p (Graham scan)
* (Finds the convex enveloppe of the points)
*/
static int Wrap ( GeoPt *Pts, int N_Pts, int *N_CPts, IndexedGeoPt **IPts )
{
int i, j, imin, M ;
GeoPt *tt=(GeoPt *)NULL ;
double Th, theta, v, x1, y1, x2, y2 ;
Boolean New = False ;
*N_CPts = 0 ;
if ( *IPts != (IndexedGeoPt *)NULL )
free ( *IPts );
*IPts = (IndexedGeoPt *)NULL ;
/*
--- First initializations and tests
*/
if ( N_Pts < 3 )
return SUCCESS ;
*IPts = (IndexedGeoPt *) calloc ( (N_Pts+2), sizeof(IndexedGeoPt) );
if ( *IPts == (IndexedGeoPt *)NULL )
return ERROR ;
/*
--- Transfers data from buffer to buffer and computes the minimum (lower Y and upper X)
*/
imin = 0 ;
for ( i = 0 ; i < N_Pts ; i++ )
{
(*IPts)[i].Pt = &(Pts[i]) ;
(*IPts)[i].num = i ;
if ( i > 0 )
{
x1 = (*IPts)[imin].Pt->X ;
y1 = (*IPts)[imin].Pt->Y ;
x2 = (*IPts)[i].Pt->X ;
y2 = (*IPts)[i].Pt->Y ;
if ( y2 <= y1 )
{
if ( (y2 < y1) ||
((fabs(y2 -y1) < ACCURACY_DOUBLE) && (x2 > x1)) )
imin = i ;
}
}
}
if ( N_Pts == 3 )
{
*N_CPts = 3 ;
return SUCCESS ;
}
/*
--- Then reorder array by arranging with the angle from that right-lower point
*/
Pt_Ref.X = (*IPts)[imin].Pt->X ;
Pt_Ref.Y = (*IPts)[imin].Pt->Y ;
qsort ( (*IPts), N_Pts, sizeof(IndexedGeoPt), Compare_Theta );
(*IPts)[N_Pts].Pt = (*IPts)[0].Pt ;
(*IPts)[N_Pts].num = N_Pts ;
/*
--- Then wraps up in order to find convex enveloppe
*/
imin = 0 ;
Th = 0.0 ;
for ( M = 0 ; M < N_Pts ; M++ )
{
tt = (*IPts)[M].Pt ;
j = (*IPts)[M].num ;
(*IPts)[M].Pt = (*IPts)[imin].Pt ;
(*IPts)[M].num = (*IPts)[imin].num ;
(*IPts)[imin].Pt = tt ;
(*IPts)[imin].num = j ;
imin = N_Pts ;
v = Th ;
Th = 360.0 ;
New = False ;
for ( i = (M+1) ; i <= N_Pts ; i++ )
{
theta = Theta ( *((*IPts)[M].Pt), *((*IPts)[i].Pt)) ;
if ( (theta > v) && (theta < Th) )
{
imin = i ;
New = True ;
Th = theta ;
}
}
if ( ! New )
break ;
}
if ( M <= 2 )
{
if ( (*IPts) != (IndexedGeoPt *)NULL )
free ( *IPts );
*IPts = (IndexedGeoPt *)NULL ;
*N_CPts = 0 ;
return SUCCESS ;
}
/*
--- Eliminates copy of first point (made to stop the above algorithm)
*/
for ( i = M ; i <= N_Pts ; i++ )
if ( (*IPts)[i].num == (*IPts)[0].num )
{
if ( i != N_Pts )
{
for ( j = (i+1) ; j <= N_Pts ; j++ )
{
(*IPts)[j-1].Pt = (*IPts)[j].Pt ;
(*IPts)[j-1].num = (*IPts)[j].num ;
}
}
break ;
}
*N_CPts = M ;
return SUCCESS ;
}
/*
* I s _ I n Circle
*
* Tests whether a point lies inside the circumscribing circle of a triangle
*
* There are 2 versions of this :
* 1) It saves memory and takes the 3 points defining the triangle
* 2) It saves computing time, and takes only the center of the triangle
* and the radius
*
*/
#ifndef OPTIMIZED_MEMORY
static int Is_InCircle ( GeoPt *Center, double Radius, GeoPt *Pt )
{
double d ;
d = ((Pt->X - Center->X)*(Pt->X - Center->X)) + ((Pt->Y - Center->Y)*(Pt->Y - Center->Y)) ;
if ( d > (Radius+ACCURACY_DOUBLE) )
return 0 ;
else
return 1 ;
}
#else
static int Is_InCircle( GeoPt *Pt1, GeoPt *Pt2, GeoPt *Pt3, GeoPt *Pt)
{
GeoPt Center ;
double d, Radius ;
if ( Computes_Center_And_Radius_Of_Triangle ( Pt1, Pt2, Pt3, &Center, &Radius) ==
ERROR )
return 0 ;
else
{
d = ((Pt->X - Center.X)*(Pt->X - Center.X)) + ((Pt->Y - Center.Y)*(Pt->Y - Center.Y)) ;
if ( d > (Radius+ACCURACY_DOUBLE) )
return 0 ;
else
return 1 ;
}
}
#endif
/*
* A l l o c a t e s _ T r i a n g l e
*
*/
static Triangle *Allocates_Triangle ( void )
{
Triangle *elt = (Triangle *)NULL ;
elt = (Triangle *)calloc ( 1, sizeof(Triangle));
if ( elt != (Triangle *)NULL )
{
elt->previous = (Triangle *)NULL ;
elt->next = (Triangle *)NULL ;
}
return elt ;
}
/*
* I n i t _ T r i a n g u l a t i o n
*
*/
static int Init_Triangulation ( IndexedGeoPt *IPts, int N_Cpts, int *N_Triangles,
Triangle **First, Triangle **Last )
{
int i, s = SUCCESS ;
Triangle *elt = (Triangle *)NULL ;
*N_Triangles = N_Cpts - 2 ;
*Last = (Triangle *)NULL ;
for ( i = 1 ; i < (N_Cpts-1) ; i++ )
{
/* Allocates memory */
elt = Allocates_Triangle ();
if ( elt == (Triangle *)NULL )
{
s = ERROR ;
continue ;
}
/* Stores summits */
elt->S1 = IPts[0].num ;
elt->S2 = IPts[i].num ;
elt->S3 = IPts[i+1].num ;
/* Eventually computes center and radius of circumscribing triangle */
#ifndef OPTIMIZED_MEMORY
Computes_Center_And_Radius_Of_Triangle ( IPts[0].Pt, IPts[i].Pt, IPts[i+1].Pt,
&elt->Center, &(elt->R) );
#endif
/* Updates the list */
elt->next = (Triangle *)NULL ;
if ( i == 1 )
{
elt->previous = (Triangle *)NULL ;
*First = elt ;
}
else
{
elt->previous = *Last ;
elt->previous->next = elt ;
}
*Last = elt ;
}
return s ;
}
/*
* F i n d s _ E n c l o s i n g _ P o l y g o n _ F o r _ A d d i t i o n
*
*/
static int Finds_Enclosing_Polygon_For_Addition ( int num, GeoPt *Pts,
IndexedGeoPt **IPts, int *NPtsPoly,
int *N_Triangles, Triangle **First, Triangle **Last )
{
int i, j, N=0, local = 0, n ;
Boolean WithS1, WithS2, WithS3 ;
Triangle *elt=(Triangle *)NULL, *next =(Triangle *)NULL ;
IndexedGeoPt *tmp=(IndexedGeoPt *)NULL ;
if ( *IPts == (IndexedGeoPt *)NULL )
local = 1 ;
/*
--- Eliminates triangles where the point is inside, storing summits for the polygon
computation
*/
elt = *First ;
while ( elt != (Triangle *)NULL )
{
next = elt->next ;
if ( (local) && (next == (Triangle *)NULL) )
*Last = elt ;
/* Tests whether point is inside circle */
#ifndef OPTIMIZED_MEMORY
if ( Is_InCircle ( &elt->Center, elt->R, &Pts[num] ) == 1 )
#else
if ( Is_InCircle ( &Pts[elt->S1], &Pts[elt->S2], &Pts[elt->S3], &Pts[num] ) )
#endif
{
WithS1 = False ;
WithS2 = False ;
WithS3 = False ;
n = 0 ;
/* Stores summits if necessary */
for ( j = 0 ; j < N ; j++ )
{
if ( (! WithS1) && ((*IPts)[j].num == elt->S1) )
{
WithS1 = True ;
n = n + 1 ;
}
if ( (! WithS2) && ((*IPts)[j].num == elt->S2) )
{
WithS2 = True ;
n = n + 1 ;
}
if ( (! WithS3) && ((*IPts)[j].num == elt->S3) )
{
WithS3 = True ;
n = n + 1 ;
}
if ( (WithS1) && (WithS2) && (WithS3) )
break ;
}
if ( n != 3 )
{
if ( local )
{
tmp = (IndexedGeoPt *)realloc ( *IPts,
(((3-n)+N)*sizeof(IndexedGeoPt)) );
if ( tmp == (IndexedGeoPt *)NULL )
{
return ERROR ;
}
*IPts = tmp ;
}
if ( ! WithS1 )
{
(*IPts)[N].num = elt->S1 ;
N = N + 1 ;
}
if ( ! WithS2 )
{
(*IPts)[N].num = elt->S2 ;
N = N + 1 ;
}
if ( ! WithS3 )
{
(*IPts)[N].num = elt->S3 ;
N = N + 1 ;
}
}
if ( elt->previous != (Triangle *)NULL )
elt->previous->next = next ;
else
*First = next ;
if ( next != (Triangle *)NULL )
next->previous = elt->previous ;
else
*Last = elt->previous ;
free ( elt ) ;
/* Updates values and starts again */
*N_Triangles = *N_Triangles - 1 ;
}
elt = next ;
}
if ( N == 0 )
{
if ( *N_Triangles == 0 )
{
*First = (Triangle *)NULL ;
*Last = (Triangle *)NULL ;
}
*NPtsPoly = 0 ;
return ERROR ;
}
/*
--- Now stores the addresses of points
*/
for ( i = 0 ; i < N ; i++ )
(*IPts)[i].Pt = &(Pts[(*IPts)[i].num]) ;
/*
--- Now orders the polygon by angle around the main point
*/
Pt_Ref.X = Pts[num].X ;
Pt_Ref.Y = Pts[num].Y ;
qsort ( *IPts, N, sizeof(IndexedGeoPt), Compare_Theta );
*NPtsPoly = N ;
return SUCCESS ;
}
/*
* F i n d s _ E n c l o s i n g _ P o l y g o n _ F o r _ D e l e t i o n
*
*/
static int Finds_Enclosing_Polygon_For_Deletion ( int num, GeoPt *Pts,
IndexedGeoPt **IPts, int *NPtsPoly,
int *N_Triangles, Triangle **First, Triangle **Last )
{
int i, j, N=0, n ;
Boolean WithS1, WithS2, WithS3, HasWithS1, HasWithS2, HasWithS3 ;
Triangle *elt=(Triangle *)NULL, *next =(Triangle *)NULL ;
IndexedGeoPt *tmp=(IndexedGeoPt *)NULL ;
/*
--- Eliminates triangles where the point is inside, storing summits for the polygon
computation
*/
elt = *First ;
while ( elt != (Triangle *)NULL )
{
next = elt->next ;
if ( next == (Triangle *)NULL )
*Last = elt ;
/* Tests whether triangle is the one which should be removed */
if ( (elt->S1 == num) || (elt->S2 == num) || (elt->S3 == num) )
{
WithS1 = False ;
WithS2 = False ;
WithS3 = False ;
HasWithS1 = False ;
HasWithS2 = False ;
HasWithS3 = False ;
if ( num == elt->S1 )
WithS1 = True ;
else
if ( num == elt->S2 )
WithS2 = True ;
else
WithS3 = True ;
n = 0 ;
/* Stores summits if necessary */
if ( N > 0 )
{
for ( j = 0 ; j < N ; j++ )
{
if ( (! WithS1) && (! HasWithS1) && ((*IPts)[j].num == elt->S1) )
{
HasWithS1 = True ;
n = n + 1 ;
}
if ( (! WithS2) && (! HasWithS2) && ((*IPts)[j].num == elt->S2) )
{
HasWithS2 = True ;
n = n + 1 ;
}
if ( (! WithS3) && (! HasWithS3) && ((*IPts)[j].num == elt->S3) )
{
WithS3 = True ;
n = n + 1 ;
}
if ( n == 2 )
break ;
}
if ( n == 2 )
n = 0 ;
}
else
{
n = 2 ;
}
if ( n != 0 )
{
tmp = (IndexedGeoPt *)realloc ( *IPts, ((N+n)*sizeof(IndexedGeoPt)) );
if ( tmp == (IndexedGeoPt *)NULL )
{
free(*IPts);
*IPts = NULL ;
*NPtsPoly = 0 ;
return ERROR ;
}
*IPts = tmp ;
if ( (! WithS1) && (! HasWithS1) )
{
(*IPts)[N].num = elt->S1 ;
N = N + 1 ;
}
if ( (! WithS2) && (! HasWithS2) )
{
(*IPts)[N].num = elt->S2 ;
N = N + 1 ;
}
if ( (! WithS3) && (! HasWithS3) )
{
(*IPts)[N].num = elt->S3 ;
N = N + 1 ;
}
}
if ( elt->previous != (Triangle *)NULL )
elt->previous->next = next ;
else
*First = next ;
if ( next != (Triangle *)NULL )
next->previous = elt->previous ;
else
*Last = elt->previous ;
free ( elt ) ;
/* Updates values and starts again */
*N_Triangles = *N_Triangles - 1 ;
}
elt = next ;
}
if ( *N_Triangles == 0 )
{
*First = (Triangle *)NULL ;
*Last = (Triangle *)NULL ;
}
/*
--- Now orders the polygon
*/
if ( N == 0 )
{
*NPtsPoly = 0 ;
return SUCCESS ;
}
/* Stores the addresses of points */
for ( i = 0 ; i < N ; i++ )
(*IPts)[i].Pt = &(Pts[(*IPts)[i].num]) ;
/* Then reorder array by arranging with the angle from around the reference point */
Pt_Ref.X = Pts[num].X ;
Pt_Ref.Y = Pts[num].Y ;
qsort ( *IPts, N, sizeof(IndexedGeoPt), Compare_Theta );
*NPtsPoly = N ;
return SUCCESS ;
}
/*
* A d d s _ N e w _ T r i a n g l e s
*
*/
static int Adds_New_Triangles ( int num, GeoPt *Pt, IndexedGeoPt *IPts, int NPtsPoly,
int *N_Triangles, Triangle **First, Triangle **Last)
{
int i, no, s = SUCCESS ;
Triangle *elt = (Triangle *)NULL ;
/*
--- Loops through all points of the enclosing polygon to build triangles
*/
for ( i = 0 ; i < NPtsPoly ; i++ )
{
/* Allocates memory */
elt = Allocates_Triangle ();
if ( elt == (Triangle *)NULL )
{
s = ERROR ;
continue ;
}
/* Stores summits */
elt->S1 = num ;
elt->S2 = IPts[i].num ;
if ( i < (NPtsPoly-1) )
no = i + 1 ;
else
no = 0 ;
elt->S3 = IPts[no].num ;
/* Eventually computes center and radius of circumscribing triangle */
#ifndef OPTIMIZED_MEMORY
Computes_Center_And_Radius_Of_Triangle ( Pt, IPts[i].Pt, IPts[no].Pt, &elt->Center,
&(elt->R) );
#endif
/* Updates list of triangles */
elt->next = (Triangle *)NULL ;
if ( (*Last) != (Triangle *)NULL )
(*Last)->next = elt ;
else
*First = elt ;
elt->previous = *Last ;
*Last = elt ;
*N_Triangles = *N_Triangles + 1 ;
}
return s ;
}
/*
* R e b u i l d s _ N e w _ T r i a n g l e s
*
*/
static int Rebuilds_New_Triangles ( IndexedGeoPt *IPts, int NPtsPoly,
int *N_Triangles, Triangle **First, Triangle **Last )
{
int i, s = SUCCESS, N ;
Triangle *elt = (Triangle *)NULL ;
#ifndef OPTIMIZED_MEMORY
int no, n1 ;
double R=0.0, a1, a2, th, RMin ;
GeoPt C, GeoC, CMin ;
/* On initialise les GeoPt en warning */
CMin.X=0.0;
CMin.Y=0.0;
C.X=0.0;
C.Y=0.0;
#endif
if ( NPtsPoly <= 3 )
return SUCCESS ;
N = NPtsPoly ;
/*
--- Loops through all points of the enclosing polygon to build triangles
*/
#ifndef OPTIMIZED_MEMORY
/* Computes geometric center of polygon */
GeoC.X = 0.0 ;
GeoC.Y = 0.0 ;
for ( i = 0 ; i < N ; i++ )
{
GeoC.X = GeoC.X + IPts[i].Pt->X ;
GeoC.Y = GeoC.Y + IPts[i].Pt->Y ;
}
GeoC.X = GeoC.X / (double)N ;
GeoC.Y = GeoC.Y / (double)N ;
RMin = DBL_MAX ;
for ( i = 0 ; i < N ; i++ )
{
/* Computes indexes of summits of polygon */
if ( i < (N -1) )
no = i + 1 ;
else
no = 0 ;
if ( i < (N -2) )
n1 = i + 2 ;
else
if ( i == (N-2) )
n1 = 0 ;
else
n1 = 1 ;
/* Do not compute if angle is > PI */
a1 = AngleOfView ( GeoC, *(IPts[no].Pt), *(IPts[i].Pt) );
a2 = AngleOfView ( GeoC, *(IPts[no].Pt), *(IPts[n1].Pt) );
th = fabs(a1) + fabs(a2) ;
if ( th > PI )
continue ;
/* Computes the center and radius of circumscribing circle */
Computes_Center_And_Radius_Of_Triangle ( IPts[i].Pt, IPts[no].Pt, IPts[n1].Pt, &C, &R
);
if ( R < RMin )
{
RMin = R ;
CMin.X = C.X ;
CMin.Y = C.Y ;
}
}
#endif
for ( i = 1 ; i < (N-1) ; i++ )
{
/* Allocates memory */
elt = Allocates_Triangle ();
if ( elt == (Triangle *)NULL )
{
s = ERROR ;
continue ;
}
elt->S1 = IPts[0].num ;
elt->S2 = IPts[i].num ;
elt->S3 = IPts[i+1].num ;
#ifndef OPTIMIZED_MEMORY
elt->Center.X = CMin.X ;
elt->Center.Y = CMin.Y ;
elt->R = RMin ;
#endif
/* Updates list of triangles */
elt->next = (Triangle *)NULL ;
elt->previous = *Last ;
if ( *Last == (Triangle *)NULL )
*First = elt ;
(*Last)->next = elt ;
*Last = elt ;
*N_Triangles = *N_Triangles + 1 ;
}
return s ;
}
/*
* A d d s _ O n e _ P o i n t _ T o _ T r i a n g u l a t i o n
*
*/
static int Adds_One_Point_To_Triangulation ( int num, GeoPt *Pts, IndexedGeoPt **IPts,
int *N_Triangles, Triangle **First, Triangle **Last )
{
int N_PtsPoly = 0 ;
/*
--- First finds the enclosing polygon
*/
Finds_Enclosing_Polygon_For_Addition ( num, Pts, IPts, &N_PtsPoly,
N_Triangles, First, Last );
/*
--- Now adds the new triangles
*/
Adds_New_Triangles ( num, &Pts[num], *IPts, N_PtsPoly, N_Triangles, First, Last );
return SUCCESS ;
}
/*
===================================================================
====
===================================================================
====
ROUTINES A USAGE EXTERNE
===================================================================
====
===================================================================
====
*/
/*
* T r i a n g u l a t e
*
* First computes the convex enveloppe, then finds the firsts
* triangles from that enveloppe, then adds point by point
* to form a complete triangulation (incremental delete-and-build algorithm)
*
*/
int Triangulate ( GeoPt *Pts, int N_Pts,
Triangle **Triangles, int *N_Triangles )
{
int N_Cpts = 0, s=SUCCESS, i ;
IndexedGeoPt *IPts = (IndexedGeoPt *)NULL, *tmp=(IndexedGeoPt *)NULL ;
Boolean *Used = (Boolean *)NULL ;
Triangle *First = (Triangle *)NULL, *Last=(Triangle *)NULL ;
/*
--- Initializations
*/
*N_Triangles = 0 ;
/*
--- First finds the convex enveloppe of the points and keeps the index of the pts
*/
s = Wrap ( Pts, N_Pts, &N_Cpts, &IPts );
if ( (s == ERROR) || (N_Cpts == 0) )
return s ;
tmp = (IndexedGeoPt *) realloc ( IPts, ((N_Pts+3)*sizeof(IndexedGeoPt)) );
if ( tmp == (IndexedGeoPt *)NULL )
{
free(IPts);
return ERROR ;
}
IPts = tmp ;
/*
--- Now finds the first triangulation from this convex enveloppe
*/
s = Init_Triangulation ( IPts, N_Cpts, N_Triangles, &First, &Last );
if ( (s == ERROR) || (N_Triangles == 0) )
{
free ( IPts );
return s ;
}
/*
--- Now eliminates all the points that were used
*/
Used = (Boolean *) calloc ( N_Pts, sizeof(Boolean) );
if ( Used == (Boolean *)NULL )
{
free ( IPts );
return ERROR ;
}
for ( i = 0 ; i < N_Cpts ; i++ )
Used[IPts[i].num] = True ;
/*
--- And now adds point by point
*/
if ( s == SUCCESS )
for ( i = 0 ; i < N_Pts ; i++ )
{
if ( Used[i] )
continue ;
s = Adds_One_Point_To_Triangulation ( i, Pts, &IPts,
N_Triangles, &First, &Last );
if ( s == ERROR )
break ;
Used[i] = True ;
}
/*
--- Frees memory and returns
*/
free ( Used );
free ( IPts );
*Triangles = First ;
return s ;
}
/*
* R e m o v e s O n e P o i n t T o T r i a n g u l a t i o n
*
*/
int RemovesOnePointToTriangulation ( int num, GeoPt *Pts,
Triangle **Triangles, int *N_Triangles )
{
int N_PtsPoly = 0, s ;
IndexedGeoPt *IPts = (IndexedGeoPt *)NULL ;
Triangle *First = (Triangle *)NULL, *Last=(Triangle *)NULL ;
/*
--- First finds the enclosing polygon
*/
First = *Triangles ;
s = Finds_Enclosing_Polygon_For_Deletion ( num, Pts, &IPts, &N_PtsPoly,
N_Triangles, &First, &Last );
*Triangles = First ;
if ( s == ERROR )
return ERROR ;
/*
--- Now rebuild the triangles
*/
s = Rebuilds_New_Triangles ( IPts, N_PtsPoly, N_Triangles, &First, &Last );
free ( IPts );
/*
-- Now eliminates unnecessary triangles
*/
*Triangles = First ;
return s ;
}
/*
* A d d s O n e P o i n t T o T r i a n g u l a t i o n
*
*/
int AddsOnePointToTriangulation ( int num, GeoPt *Pts,
Triangle **Triangles, int *N_Triangles )
{
int s = SUCCESS ;
IndexedGeoPt *IPts = (IndexedGeoPt *)NULL ;
Triangle *First = (Triangle *)NULL, *Last=(Triangle *)NULL ;
/*
--- Now rebuild the triangles
*/
s = Adds_One_Point_To_Triangulation ( num, Pts, &IPts, N_Triangles,
&First, &Last );
*Triangles = First ;
/*
--- Frees memory and returns
*/
free ( IPts );
return s ;
} |
[C] Triangulation de Delaunay (méthode incrémentale Delete and Build)
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