)
}
}
)
(
}
{
)
)
(
)
(
(
{
}
)
(
)
}
)
)
{
(
(
)
)
}
)
(
}

Line to Line Intersection

  1. // line to line intersection https://en.wikipedia.org/wiki/Line%E2%80%93line_intersection
  2. function lineIntersection(p1, p2, p3, p4) {
  3.   let ip = { x: 0, y: 0 };
  4.   // rare case where I use `_` in a non-constant variable name
  5.   // to make this easy to read to with the wikipedia info
  6.   const x4_x3 = p4.x - p3.x;
  7.   const y4_y3 = p4.y - p3.y;
  8.   const x2_x1 = p2.x - p1.x;
  9.   const y2_y1 = p2.y - p1.y;
  10.   const x1_x3 = p1.x - p3.x;
  11.   const y1_y3 = p1.y - p3.y;
  12.   let nx, ny, dn;
  13.  
  14.   nx = x4_x3 * y1_y3 - y4_y3 * x1_x3;
  15.   ny = x2_x1 * y1_y3 - y2_y1 * x1_x3;
  16.   dn = y4_y3 * x2_x1 - x4_x3 * y2_y1;
  17.  
  18.   nx /= dn;
  19.   ny /= dn;
  20.  
  21.   // has intersection
  22.   if (nx >= 0 && nx <= 1 && ny >= 0 && ny <= 1) {
  23.     ny = p1.y + nx * y2_y1;
  24.     nx = p1.x + nx * x2_x1;
  25.     ip.x = nx;
  26.     ip.y = ny;
  27.   } else {
  28.     // no intersection
  29.     ip = null;
  30.   }
  31.   return ip;
  32. }
  33.  
  34. const el = document.body.appendChild(
  35.   document.createElement('div'));
  36.  
  37. // hard coding line values for simplicity and ease of understanding
  38. el.innerHTML = `
  39.   <svg width="100%" height="100%" viewBox="0 0 550 496">
  40.     <path id='path' d="M 10 10 L 300 300 M 100 10 L 160 320" stroke="black" fill='none' vector-effect="non-scaling-stroke"/>
  41.     <rect id="intersecton" x="0" y="0" width="10" height="10" fill="red" />
  42.   </svg>
  43.   <style>
  44.     svg, div, body, html {
  45.       overflow: visible; 
  46.       height: 100%; 
  47.       width: 100%;
  48.       margin: 0; padding: 0;
  49.     }
  50.   </style>
  51. `;
  52.  
  53. const loc = lineIntersection(
  54.   {x: 10, y: 10}, {x: 300, y:300},
  55.   {x: 100, y: 10}, {x: 160, y:320}
  56. );
  57.  
  58. // subtract half the size of the rect from both axis to center it
  59. intersecton.x.baseVal.value = loc.x - 5;
  60.  
  61. // @NOTE: using the `id` global `window.intersection` 
  62. // is just good for demos - little risky for real stuff 
  63. // since it lends itself to easy collision
  64. window.intersecton.y.baseVal.value = loc.y - 5;

Line to line intersection rendered with SVG.

snippet.zone ~ 2021-22 /// {s/z}