二维的三角形网格剖分程序 easymesh.docx
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二维的三角形网格剖分程序 easymesh.docx
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二维的三角形网格剖分程序easymesh
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%Author:
BojanNICENO%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%niceno@univ.trieste.it%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%*/
#defineGRAPHICSOFF
#include
#include
#include
#include
#ifndefmax
#definemax(a,b)(((a)>(b))?
(a):
(b))
#endif
#ifndefmin
#definemin(a,b)(((a)<(b))?
(a):
(b))
#endif
#ifndefPI
#definePI3.14159265359
#endif
#defineSMALL1e-30
#defineGREAT1e+30
#defineON0
#defineOFF-1/*elementisswitchedoff*/
#defineWAIT-2/*nodeiswaiting(itisacornernode)*/
#defineA3
#defineD4
#defineW5
#defineMAX_NODES3000
/*-----------------------------+
|definitionsforthechains|
+-----------------------------*/
#defineCLOSED0
#defineOPEN1
#defineINSIDE2
structele
{
inti,j,k;
intei,ej,ek;
intsi,sj,sk;
intmark;/*isitoff(ONorOFF)*/
intstate;/*isit(D)one,(A)ctiveor(W)aiting*/
intmaterial;
doublexv,yv,xin,yin,R,r,Det;
intnew_numb;/*usedforrenumeration*/
}
elem[MAX_NODES*2];
structsid
{
intea,eb;/*leftandrightelement*/
inta,b,c,d;/*left,right,startandendpoint*/
intmark;/*isitoff,isontheboundary*/
doubles;
intnew_numb;/*usedforrenumeration*/
}
side[MAX_NODES*3];
/*sid.ea/eb/a/b/c/d/mark/s/*/
structnod
{
doublex,y,F;
doublesumx,sumy;
intNne;
intmark;/*isitoff*/
intnext;/*nextnodeintheboundarychain*/
intchain;/*onwhichchainsisthenode*/
intinserted;
intnew_numb;/*usedforrenumeration*/
}
node[MAX_NODES],point[MAX_NODES/2];
structseg
{intn0,n1;
intN;intchain;intbound;intmark;}
*segment;
structchai
{ints0,s1,type;}
*chain;
intNe,Nn,Ns,Nc;/*numberof:
elements,nodes,sides*/
intugly;/*moralibitiglobalna?
?
?
*/
/*=========================================================================*/
doublearea(structnod*na,structnod*nb,structnod*nc)
{
return0.5*(((*nb).x-(*na).x)*((*nc).y-(*na).y)
-((*nb).y-(*na).y)*((*nc).x-(*na).x));
}
/*-------------------------------------------------------------------------*/
/*=========================================================================*/
doubledist(structnod*na,structnod*nb)
{
returnsqrt(((*nb).x-(*na).x)*((*nb).x-(*na).x)
+((*nb).y-(*na).y)*((*nb).y-(*na).y));
}
/*-------------------------------------------------------------------------*/
/*=========================================================================*/
in_elem(structnod*n)
{
inte;
for(e=0;e ? */ { if(area(n,&node[elem[e].i],&node[elem[e].j])>=0.0 &&area(n,&node[elem[e].j],&node[elem[e].k])>=0.0 &&area(n,&node[elem[e].k],&node[elem[e].i])>=0.0) break; } returne; } /*-in_elem-----------------------------------------------------------------*/ /*=========================================================================*/ bowyer(intn,intspac) { inte,i,s,swap; structnodvor; do { swap=0; for(s=0;s if(side[s].mark==0) /*if(! ((node[side[s].c].inserted>1&&node[side[s].d].bound==OFF&&side[s].s<(node[side[s].c].F+node[side[s].d].F))|| (node[side[s].d].inserted>1&&node[side[s].c].bound==OFF&&side[s].s<(node[side[s].c].F+node[side[s].d].F))))*/ { if(side[s].a==n) {e=side[s].eb; if(e! =OFF) {vor.x=elem[e].xv; vor.y=elem[e].yv; if(dist(&vor,&node[n]) {swap_side(s);swap=1;}}} elseif(side[s].b==n) {e=side[s].ea; if(e! =OFF) {vor.x=elem[e].xv; vor.y=elem[e].yv; if(dist(&vor,&node[n]) {swap_side(s);swap=1;}}} } } while(swap==1); } /*-bowyer------------------------------------------------------------------*/ /*=========================================================================*/ circles(inte) /*---------------------------------------------------+ |Thisfunctioncalculatesradiiofinscribedand| |circumscribedcircleforagivenelement(inte)| +---------------------------------------------------*/ { doublex,y,xi,yi,xj,yj,xk,yk,xij,yij,xjk,yjk,num,den; doublesi,sj,sk,O; xi=node[elem[e].i].x;yi=node[elem[e].i].y; xj=node[elem[e].j].x;yj=node[elem[e].j].y; xk=node[elem[e].k].x;yk=node[elem[e].k].y; xij=0.5*(xi+xj);yij=0.5*(yi+yj); xjk=0.5*(xj+xk);yjk=0.5*(yj+yk); num=(xij-xjk)*(xj-xi)+(yij-yjk)*(yj-yi); den=(xj-xi)*(yk-yj)-(xk-xj)*(yj-yi); if(den>0) { elem[e].xv=x=xjk+num/den*(yk-yj); elem[e].yv=y=yjk-num/den*(xk-xj); elem[e].R=sqrt((xi-x)*(xi-x)+(yi-y)*(yi-y)); } si=side[elem[e].si].s; sj=side[elem[e].sj].s; sk=side[elem[e].sk].s; O=si+sj+sk; elem[e].Det=xi*(yj-yk)-xj*(yi-yk)+xk*(yi-yj); elem[e].xin=(xi*si+xj*sj+xk*sk)/O; elem[e].yin=(yi*si+yj*sj+yk*sk)/O; elem[e].r=elem[e].Det/O; } /*-circles-----------------------------------------------------------------*/ /*=========================================================================*/ spacing(inte,intn) /*----------------------------------------------------------------+ |Thisfunctioncalculatesthevalueofthespacingfunctionin| |anewnode'n'whichisinsertedinelement'e'byalinear| |approximationfromthevaluesofthespacingfunctioninthe| |elementsnodes.| +----------------------------------------------------------------*/ { doubledxji,dxki,dyji,dyki,dx_i,dy_i,det,a,b; dxji=node[elem[e].j].x-node[elem[e].i].x; dyji=node[elem[e].j].y-node[elem[e].i].y; dxki=node[elem[e].k].x-node[elem[e].i].x; dyki=node[elem[e].k].y-node[elem[e].i].y; dx_i=node[n].x-node[elem[e].i].x; dy_i=node[n].y-node[elem[e].i].y; det=dxji*dyki-dxki*dyji; a=(+dyki*dx_i-dxki*dy_i)/det; b=(-dyji*dx_i+dxji*dy_i)/det; node[n].F=node[elem[e].i].F+ a*(node[elem[e].j].F-node[elem[e].i].F)+ b*(node[elem[e].k].F-node[elem[e].i].F); } /*-spacing-----------------------------------------------------------------*/ /*=========================================================================*/ insert_node(doublex,doubley,intspac, intprev_n,intprev_s_mark,intmark,intnext_s_mark,intnext_n) { inti,j,k,en,n,e,ei,ej,ek,s,si,sj,sk; doublesx,sy; Nn++;/*onenewnode*/ node[Nn-1].x=x; node[Nn-1].y=y; node[Nn-1].mark=mark; /*findtheelementwhichcontainsnewnode*/ e=in_elem(&node[Nn-1]); /*calculatethespacingfunctioninthenewnode*/ if(spac==ON) spacing(e,Nn-1); i=elem[e].i;j=elem[e].j;k=elem[e].k; ei=elem[e].ei;ej=elem[e].ej;ek=elem[e].ek; si=elem[e].si;sj=elem[e].sj;sk=elem[e].sk; Ne+=2; Ns+=3; /*---------------+ |newelements| +---------------*/ elem[Ne-2].i=Nn-1;elem[Ne-2].j=k;elem[Ne-2].k=i; elem[Ne-1].i=Nn-1;elem[Ne-1].j=i;elem[Ne-1].k=j; elem[Ne-2].ei=ej;elem[Ne-2].ej=Ne-1;elem[Ne-2].ek=e; elem[Ne-1].ei=ek;elem[Ne-1].ej=e;elem[Ne-1].ek=Ne-2; elem[Ne-2].si=sj;elem[Ne-2].sj=Ns-2;elem[Ne-2].sk=Ns-3; elem[Ne-1].si=sk;elem[Ne-1].sj=Ns-1;elem[Ne-1].sk=Ns-2; /*------------+ |newsides| +------------*/ side[Ns-3].c=k;side[Ns-3].d=Nn-1;/*c-d*/ side[Ns-3].a=j;side[Ns-3].b=i;/*a-b*/ side[Ns-3].ea=e;side[Ns-3].eb=Ne-2; side[Ns-2].c=i;side[Ns-2].d=Nn-1;/*c-d*/ side[Ns-2].a=k;side[Ns-2].b=j;/*a-b*/ side[Ns-2].ea=Ne-2;side[Ns-2].eb=Ne-1; side[Ns-1].c=j;side[Ns-1].d=Nn-1;/*c-d*/ side[Ns-1].a=i;side[Ns-1].b=k;/*a-b*/ side[Ns-1].ea=Ne-1;side[Ns-1].eb=e; for(s=1;s<=3;s++) {sx=node[side[Ns-s].c].x-node[side[Ns-s].d].x; sy=node[side[Ns-s].c].y-node[side[Ns-s].d].y; side[Ns-s].s=sqrt(sx*sx+sy*sy);} elem[e].i=Nn-1; elem[e].ej=Ne-2; elem[e].ek=Ne-1; elem[e].sj=Ns-3; elem[e].sk=Ns-1; if(side[si].a==i){side[si].a=Nn-1;side[si].ea=e;} if(side[si].b==i){side[si].b=Nn-1;side[si].eb=e;} if(side[sj].a==j){side[sj].a=Nn-1;side[sj].ea=Ne-2;} if(side[sj].b==j){side[sj].b=Nn-1;side[sj].eb=Ne-2;} if(side[sk].a==k){side[sk].a=Nn-1;side[sk].ea=Ne-1;} if(side[sk].b==k){side[sk].b=Nn-1;side[sk].eb=Ne-1;} if(ej! =-1) {if(elem[ej].ei==e)
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