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pari_precision=$precision
pari_header=$pari_header\
\
{\
line(p1,p2)=\
if(#p2==2,\
a=p2[2]-p1[2];b=p1[1]-p2[1];c=p2[1]*p1[2]-p1[1]*p2[2];\
return([0,0,0,a,b,c]));\
if(#p2==3,\
return([0,0,0,-p2[2],p2[1],p2[2]*p1[1]-p2[1]*p1[2]]),\
return([0,0,0,p2[4],p2[5],-(p2[4]*p1[1] + p2[5]*p1[2])]));\
}\
{\
ray(p1,p2)=line(p1,p2)\
}\
{\
midperpendicular(p1,p2)=\
x1=p1[1];y1=p1[2];x2=p2[1];y2=p2[2];\
a=x1-x2;b=y1-y2;c=(x2^2+y2^2-x1^2-y1^2)/2;\
xm=(x1+x2)/2;ym=(y1+y2)/2;xd=x2-x1;yd=y2-y1;\
return([0,0,0,a,b,c]);\
}\
\
{\
perpendicular(p1,p2)=\
x1=p1[1];y1=p1[2];\
if(#p2==6,a=-p2[5];b=p2[4],a=p2[1];b=p2[2]);\
c=-(a*p1[1]+b*p1[2]);\
return([0,0,0,a,b,c]);\
}\
\
{\
bissector(p1,p2,p3)=\
v1=p1-p2; v2=p3-p2;\
v1=v1/sqrt(norml2(v1)) ; v2=v2/sqrt(norml2(v1)) ;\
return(midperpendicular(p2+v1,p2+v2));\
}\
\
{\
circle(p1,p2)=\
circ=(x-p1[1])^2 +(y-p1[2])^2 ;\
if (#p2==2, diff=p2-p1;\
c=circ-(diff[1]^2+diff[2]^2),\
c=circ-(p2)^2);\
return([polcoeff(c,2,x),polcoeff(c,2,y),polcoeff(polcoeff(c,1,x),1,y),polcoeff(polcoeff(c,1,x),0,y),polcoeff(polcoeff(c,0,x),1,y),polcoeff(polcoeff(c,0,x),0,y)])\
}\
\
{\
segment(p1,p2)=\
if( #p2==2, return(sqrt(norml2(p2-p1))),return(p2));\
}\
\
\\compute the middle of 2 points\
{\
middle(x1,y1,x2,y2)=\
x=(x1+x2)/2;y=(y1+y2)/2;\
return([x,y]);\
}\
\\ compute the line through 2 points ax+by+c=0 segment,x1,y1,x2,y2\
{\
segment(p1,p2)=\
x1=p1[1];y1=p1[2];x2=p2[1];y2=p2[2];\
a=y2-y1;b=x1-x2;c=x2*y1-x1*y2;cnorm=max(abs(a),max(abs(b),abs(c)));\
a=a/cnorm;b=b/cnorm;c=c/cnorm;\
return([a,b,c,x1,y1,x2,y2]);\
}\
ray(p1,p2)=\
x1=p1[1];y1=p1[2];x2=p2[1];y2=p2[2];\
a=y2-y1;b=x1-x2;c=x2*y1-x1*y2;cnorm=max(abs(a),max(abs(b),abs(c)));\
a=a/cnorm;b=b/cnorm;c=c/cnorm;\
return([a,b,c,x1,y1]);\
}\
\
\\ compute the mid-perpendicular line of 2 points\
{\
midper(p1,p2)=\
x1=p1[1];y1=p1[2];x2=p2[1];y2=p2[2];\
a=x1-x2;b=y1-y2;c=(x2^2+y2^2-x1^2-y1^2)/2;cnorm=max(abs(a),max(abs(b),abs(c)));\
a=a/cnorm;b=b/cnorm;c=c/cnorm;\
xm=(x1+x2)/2;ym=(y1+y2)/2;xd=x2-x1;yd=y2-y1;\
return([a,b,c,xm+yd,ym-xd,xm-yd,ym+xd]);\
}\
\
{\
barycenter(p1,p2,t)=\
x1=p1[1];y1=p1[2];x2=p2[1];y2=p2[2] ; t1=t[1]; t2=t[2];\
if(t1+t2 == 0, return([]), x=(t1*x1+t2*x2)/(t1+t2);y=(t1*y1+t2*y2)/(t1+t2);\
return([x,y]));\
}\
\
\\ compute the intersection point of two lines\
{\
line_intersect(l1,l2)=\
a1=l1[1];b1=l1[2];c1=l1[3];a2=l2[1];b2=l2[2];c2=l2[3];\
det=a1*b2-a2*b1;\
if(abs(det)<compare_precision, return("error parallel"));\
x=-(c1*b2-b1*c2)/det;y=-(a1*c2-a2*c1)/det;\
return([x,y]);\
}\
\
\\ compute the foot point of perpendicular of a line through a point.\
{\
foot_perp(l1,p1)=\
a1=l1[1];b1=l1[2];c1=l1[3];x1=p[1];x2=p[2];c2=-b1*x1+a1*y1;\
det=(b1)^2+(a1)^2;\
x=(-c1*a1-c2*b1)/det;y=(a1*c2-b1*c1)/det;\
return([x,y]);\
}\
\
\\ internal computation, intersection point of a line and a circle\
{\
lc_int_(data)=\
a=data[1];b=data[2];c=data[3];xc=data[4];yc=data[5];r=data[6];\
if(abs(a)>abs(b),\
b=-b/a;c=-c/a;\
A=b^2+1;B=b*(c-xc)-yc;C=(c-xc)^2+yc^2-r^2;discr=B^2-A*C;\
if(discr<-(compare_precision^2), return("error no_intersection"));\
if(discr<0, discr=0);\
discr=sqrt(discr);y1=(-B+discr)/A;y2=(-B-discr)/A;\
x1=b*y1+c;x2=b*y2+c;\
,\
a=-a/b;c=-c/b;\
A=a^2+1;B=a*(c-yc)-xc;C=(c-yc)^2+xc^2-r^2;discr=B^2-A*C;\
if(discr<-(compare_precision^2), return("error no_intersection"));\
if(discr<0, discr=0);\
discr=sqrt(discr);x1=(-B+discr)/A;x2=(-B-discr)/A;\
y1=a*x1+c;y2=a*x2+c;\
);\
if(abs(x1)<range_limit && abs(y1)<range_limit && pointcheck([x1,y1])==0,\
out=[x1,y1], out=[]);\
if(abs(x2)<range_limit && abs(y2)<range_limit && \
pointcheck([x2,y2])==0 && max(abs(x1-x2),abs(y1-y2))>closeness,\
out=concat(out,[x2,y2]));\
if(out==[], return("error no_available"), return(out));\
}\
\
\\ compute the intersection point of a line and a circle\
{\
lc_intersect(l1,c2)=\
return(lc_int_(l1,c2));\
}\
\
\\ compute the intersection point of two circles\
{\
circle_intersect(c1,c2)=\
x1=c1[1];y1=c1[2];r1=c1[3];x2=c2[1];y2=c2[2];r2=c2[3];\
a=2*(x1-x2);b=2*(y1-y2);c=x2^2+y2^2-x1^2-y1^2+r1^2-r2^2;\
cnorm=max(abs(a),max(abs(b),abs(c)));\
return(lc_int_([a/cnorm,b/cnorm,c/cnorm,x1,y1,r1]));\
}\
\
\\ compute a circle of center p1 and through p2.\
{\
circle(p1,p2)=\
diff=p2-p1;\
radius=sqrt(diff[1]^2+diff[2]^2);\
cir=concat(p1,radius);
return(cir);\
}\
|
