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// // // // $B:BI87O$,2hLL:BI87O(B($B:8>e$,(B(0,0))$B$G$"$k$3$H$KCm0U$9$k(B // public final class Point { double x,y; // 10^-5$B0J2<$O(B0$B$H8+$J$9!%(B static final double EPS=10e-5; Point(double x,double y){ this.x=x; this.y=y; } public double getX() { return x;} public double getY() { return y;} public String toString(){ return "Point("+x+","+y+")"; } public double length(){ return Math.sqrt(x*x+y*y); } public double distance(Point p){ double dx=x-p.getX(),dy=y-p.getY(); return Math.sqrt(dx*dx+dy*dy); } public Point plus(Point p){ return new Point(x+p.getX(),y+p.getY()); } public Point minus(Point p){ return new Point(x-p.getX(),y-p.getY()); } public Point times(double r){ return new Point(x*r,y*r); } // $B%Y%/%?!<$ND9$5$r(B newLength$B$K@55,2=$9$k!%(B public Point normal(double newLength){ double ratio=newLength/length(); return new Point(x*ratio,y*ratio); } // 2$B$D$NE@$NJ,3dE@$rJV$9!%(B // ratio$B$,(B0$B$N;~$O85$NE@!%(B1$B$N;~$OAj<j$NE@(B public Point inter(Point p,double ratio){ return times(1-ratio).plus(p.times(ratio)); } // $B%Y%/%H%k$N(B90$BEY2sE>(B public Point rot90(){ return new Point(y,-x); } // $B%Y%/%H%k$N(B270$BEY2sE>(B public Point rot270(){ return new Point(-y,x); } // $B<+J,$H%Y%/%?!<(Bp$B$NFb@Q(B(inner product) public double product(Point p){ return x*p.x+y*p.y; } // $B<+J,$+$i%Y%/%?!<(Bp$B$r8+$?3QEY$N(B cos public double cosTheta(Point p){ return product(p)/(p.length()*length()); } // $B<+J,$+$i%Y%/%?!<(Bp$B$r8+$?3QEY$N(B sin public double cosTheta(Point p){ return rot270().cosTheta(p); } // $B<+J,$+$i%Y%/%?!<(B p $B$r8+$?3QEY(B public double theta(Point p){ return Math.atan2(sinTheta(p),cosTheta(p)); } // $BD>@~(B p0-p1, p2-p3 $B$N8rE@(B // x = p0.x+t*(p1.x-p0.x) = p2.x+s*(p3.x-p2.x) // y = p0.y+t*(p1.y-p0.y) = p2.y+s*(p3.y-p2.y) public static Point cross(Point p0,Point p1,Point p2,Point p3){ double dy10=p1.y-p0.y,dx10=p1.x-p0.x; double d=dy10*(p3.x-p2.x)-dx10*(p3.y-p2.y); // $B9TNs<0$,>.$5$$$H$-$O(B null $B$rJV$9!%(B if(Math.abs(d)<EPS) return null; double s=(dy10*(p0.x-p2.x)-dx10*(p0.y-p2.y))/d; return p2.inter(p3,s); } }
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