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(Compiled with Asymptote version 1.87svn-r4652) |
size(10cm,0); picture pavehexagonal(int depth=1) { picture opic; path hexa=polygon(6); pair center; real a,ap,r,rp,r_d=180/pi; for(int j=0; j<depth; ++j) { for (int i=1; i<=6; ++i) { a=i*60-30; r=j*sqrt(3); center=r*(rotate(a)*(1,0)); filldraw(opic, shift(center)*hexa, j/depth*.8red+(1-j/depth)*.8*blue); //Uncomment to see centers of hexagons dot(opic, shift(center)*midpoint(point(hexa,0)--point(hexa,3))); //Uncomment to see circles passing by centers //draw(opic, scale(r)*unitcircle, j/depth*red+(1-j/depth)*blue); rp=r; ap=0; for (real k=0; k<j-1; ++k) { r=sqrt((1.5*(j-1 - k))^2 + 3/4*(j+1 + k)^2); ap+=r_d*acos((rp^2 + r^2 - 3)/(2*r*rp)); center=r*(rotate(a + ap)*(1,0)); filldraw(opic, shift(center)*hexa, j/depth*.8*red+(1-j/depth)*.8*blue); //Uncomment to see the centers of hexagons //dot(opic, shift(center)*midpoint(point(hexa,0)--point(hexa,3))); rp=r; //Uncomment to see circles passing by centers //draw(opic, scale(r)*unitcircle, j/depth*red+(1-j/depth)*blue); } } } return opic; } add(pavehexagonal(7));