Common Tangents

Raw Download Revise
import geometry;

import patterns;

size(9cm,0);

line[] tan2cir(circle c1, circle c2){ line[] lines;

  if ( c1.C == c2.C && c1.r == c2.r ) { label( "Ups, circles are equal!", c1.C ); }

  if ( c1.C != c2.C ) {

  line[] n = { line(c1.C, c2.C) + unit(c2.C-c1.C) * dir(90) * c1.r, line(c1.C, c2.C) + unit(c1.C-c2.C) * dir(90) * c1.r };

  lines.append( n );

  if ( c1.r != c2.r ) { lines = tangents( circle( c1.C, c1.r ), scale( c2.r / (c2.r - c1.r), c2.C) * c1.C ); }

  lines.append( tangents( circle( c1.C, c1.r ), scale( c2.r / (c2.r + c1.r), c2.C) * c1.C ) ); }

  return lines;

}

/*

// Код для проверки работоспособности

real r = 3, R = 8, L = r + R + 4;

// real L = 0; // для совпадения центров окружностей

point O1 = (2,3), O2 = O1 + L * dir( 120 );

circle c1 = circle( O1, r );

circle c2 = circle( O2, R );

line[] out = tan2cir( c1, c2 );

draw( c1^^c2 );

draw( out );

label( "number of tangents is " + string( out.length ), c1.C, S ); // Размер массива касательных

// Нерабочий код

line[] tan2cir(circle c1, circle c2){ line[] lines;

  if ( c1.C == c2.C && c1.r == c2.r ) { label( "Ups, circles are equal!", c1.C ); }

  else { lines = { line(c1.C, c2.C) + unit(c2.C-c1.C) * dir(90) * c1.r, line(c1.C, c2.C) + unit(c1.C-c2.C) * dir(90) * c1.r };

  if ( c1.r != c2.r ) { lines = tangents( circle( c1.C, c1.r ), scale( c2.r / (c2.r - c1.r), c2.C) * c1.C ); }

  lines.append( tangents( circle( c1.C, c1.r ), scale( c2.r / (c2.r + c1.r), c2.C) * c1.C ) ); }

  return lines;

}

// Старый код, для сравнения прогресса

line[] tan2cir(point O1, real r1, point O2, real r2){

  line[] lines;

  circle c1 = circle( O1, r1 );

  if ( r1 == r2 ) {

    line per = parallel(O1, dir(90) * line(O1, O2) );

    lines.push( parallel( intersectionpoints( c1, per )[0], line(O1, O2) ) );

    lines.push( parallel( intersectionpoints( c1, per )[1], line(O1, O2) ) );

  } else {

    point A = (O2 + (O1 - O2) * ( r2 / (r2 - r1) ) );

    lines.push( tangents(c1, A)[0] );

    lines.push( tangents(c1, A)[1] );

  }

  point B = (O2 - O1) * r1 / (r1 + r2);

  line[] tang = tangents( c1, B );

  for ( int i = 0; i < tang.length; ++i ) { lines.push( tang[i] ); }

  return lines;

}

*/