Optimizing Horizontal and Vertical Alignment Calculations inside Browser-Based Engines

Highway alignments require precise coordinate and elevation calculations. Traditionally, these calculations are performed on desktop CAD packages or backend servers due to the complexity of curve math. However, modern JavaScript engines allow us to run these computations client-side in the browser, eliminating the need for server uploads and improving data privacy.

Doing this efficiently requires optimizing our code for speed. Below, we discuss the mathematical principles and optimizations used to build our client-side alignment tools.

1. Geometric Formulas for Alignment Interpolation

For vertical curves, we use parabolic transitions. Given PVI stations (Sv), elevations (Zv), and curve lengths (L), the elevation y at any station x within the curve is calculated as:

Where G1 and G2 are the incoming and outgoing slopes, and BVC is the Beginning of Vertical Curve.

2. JavaScript Interpolation Optimization

The interpolation engine must process thousands of station requests in milliseconds. We use binary search to quickly locate alignment segments:

function findSegment(points, targetStation) {
  let low = 0;
  let high = points.length - 1;
  
  while (low <= high) {
    let mid = Math.floor((low + high) / 2);
    let p = points[mid];
    
    if (mid < points.length - 1 && targetStation >= p.station && targetStation <= points[mid + 1].station) {
      return [p, points[mid + 1]];
    }
    
    if (targetStation < p.station) {
      high = mid - 1;
    } else {
      low = mid + 1;
    }
  }
  return null;
}

This binary search optimization reduces time complexity from O(N) to O(log N), enabling the browser to process coordinate interpolations instantly.