/*
算出AB和CD二線的交點
AB的直線參數式為(xa,ya)+t(xb-xa,yb-ya)
CD的直線參數式為(xc,yc)+k(xd-xc,yd-yc)
交點P(xp,yp)的k如下
k=((yb-ya)*(xc-xa)-(yc-ya)*(xb-xa))/((yd-yc)*(xb-xa)-(yb-ya)*(xd-xc))
xp=xc+k*(xd-xc)
yp=yc+k*(yd-yc)
*/
void TSIP(double xa,double ya,double xb,double yb,double xc,double yc,double xd,double yd,double *px,double *py){
double k=((yb-ya)*(xc-xa)-(yc-ya)*(xb-xa))/((yd-yc)*(xb-xa)-(yb-ya)*(xd-xc));
*px=xc+k*(xd-xc);
*py=yc+k*(yd-yc);
printf("P=(%.2f,%.2f)\n",*px,*py);
}
/*
算出過Ic和AB垂直的直線交點Hc
Ic在AB上的垂足Hc
AB的直線參數式為(xa,ya)+k(xb-xa,yb-ya)
IcHc的直線參數式為(xic,yic)+t(yb-ya,xa-xb)
當k=((xa-xb)*(xa-xic)-(yb-ya)*(ya-yic))/((yb-ya)*(yb-ya)+(xa-xb)*(xa-xb))
xhc=xa+k*(xb-xa)
yhc=ya+k*(yb-ya)
*/
void IcABHc(double xa,double ya,double xb,double yb,double xic,double yic,double *px,double *py){
double k=((xa-xb)*(xa-xic)-(yb-ya)*(ya-yic))/((yb-ya)*(yb-ya)+(xa-xb)*(xa-xb));
double xhc=xa+k*(xb-xa);
double yhc=ya+k*(yb-ya);
*px=xhc;
*py=yhc;
}
/*
繪出三角形ABC的角C對的旁切圓
三角形ABC A(xa,ya), B(xb,yb), C(xc,yc)
Q為角A的外角平分線在CB邊的交點,
(xq,yq)=(xb,yb)+c*(xb-xc,yb-yc)/(b-c)
R為角B的外角平分線在CA邊的交點,
(xr,yr)=(xa,ya)+c*(xa-xc,ya-yc)/(a-c)
Ic為AQ和BR的交點，角C所對的旁心
Ic在AB上的垂足Hc，即切點
AB的直線參數式為(xa,ya)+k(xb-xa,yb-ya)
IcHc的直線參數式為(xic,yic)+t(yb-ya,xa-xb)
當k=((xa-xb)*(xa-xic)-(yb-ya)*(ya-yic))/((yb-ya)*(yb-ya)+(xa-xb)*(xa-xb))
xhc=xa+k*(xb-xa)
yhc=ya+k*(yb-ya)
Ic在CB上的垂足Hcb，即切點
CB的直線參數式為(xc,yc)+k(xb-xc,yb-yc)
IcHcb的直線參數式為(xic,yic)+t(yb-yc,xc-xb)
當k=((xc-xb)*(xc-xic)-(yb-yc)*(yc-yic))/((yb-yc)*(yb-yc)+(xc-xb)*(xc-xb))
xhcb=xc+k*(xb-xc)
yhcb=yc+k*(yb-yc)
Ic在CA上的垂足Hca，即切點
CA的直線參數式為(xc,yc)+k(xa-xc,ya-yc)
IcHca的直線參數式為(xic,yic)+t(ya-yc,xc-xa)
當k=((xc-xa)*(xc-xic)-(ya-yc)*(yc-yic))/((ya-yc)*(ya-yc)+(xc-xa)*(xc-xa))
xhca=xc+k*(xa-xc)
yhca=yc+k*(ya-yc)
*/
void SideCircle(double xa,double ya,double xb,double yb,double xc,double yc,Image *pim,char *cst){
pim->strokeColor(cst);
double c=pow(pow(xa-xb,2)+pow(ya-yb,2),0.5);
double b=pow(pow(xa-xc,2)+pow(ya-yc,2),0.5);
double a=pow(pow(xb-xc,2)+pow(yb-yc,2),0.5);
double xq=xb+c*(xb-xc)/(b-c);
double yq=yb+c*(yb-yc)/(b-c);
pim->draw(DrawableText(xq, yq, "Q"));
pim->draw( DrawableLine(xb,yb,xq,yq));
pim->draw( DrawableLine(xa,ya,xq,yq));
double xr=xa+c*(xa-xc)/(a-c);
double yr=ya+c*(ya-yc)/(a-c);
pim->draw(DrawableText(xr, yr, "R"));
pim->draw( DrawableLine(xa,ya,xr,yr));
pim->draw( DrawableLine(xb,yb,xr,yr));
double xic,yic,xhc,yhc;
TSIP(xa,ya,xq,yq,xb,yb,xr,yr,&xic,&yic);
pim->draw(DrawableText(xic, yic, "Ic"));
IcABHc(xa,ya,xb,yb,xic,yic,&xhc,&yhc);
pim->draw(DrawableText(xhc, yhc, "H"));
pim->draw(DrawableCircle(xic,yic,xhc,yhc));
IcABHc(xa,ya,xc,yc,xic,yic,&xhc,&yhc);
pim->draw(DrawableText(xhc, yhc, "H"));
pim->draw(DrawableCircle(xic,yic,xhc,yhc));
pim->draw(DrawableLine(xa,ya,xhc,yhc));
IcABHc(xc,yc,xb,yb,xic,yic,&xhc,&yhc);
pim->draw(DrawableText(xhc, yhc, "H"));
pim->draw(DrawableCircle(xic,yic,xhc,yhc));
pim->draw(DrawableLine(xb,yb,xhc,yhc));
pim->draw(DrawableLine(xa,ya,xic,yic));
pim->draw(DrawableLine(xb,yb,xic,yic));
pim->draw(DrawableLine(xc,yc,xic,yic));
}