Smoothing the Glow: Interpolating Antenna Patterns

Picture this: you’ve measured your Yagi antenna at twenty-degree intervals, capturing signal strength readings that look like a jagged mountain range when plotted. But your 3D-printed lantern needs smooth, flowing curves that capture the antenna’s radiation pattern without the harsh edges of discrete measurements.

This is where linear interpolation becomes your artistic ally. Between any two measured points, we can estimate intermediate values by drawing a straight line and reading off coordinates. It’s the computational equivalent of “connect the dots,” but with mathematical precision.

Tcl approaches this with characteristic directness:

proc interpolate {x1 y1 x2 y2 x} {
    set slope [expr {($y2 - $y1) / ($x2 - $x1)}]
    return [expr {$y1 + $slope * ($x - $x1)}]
}

set signal_15 [interpolate 0 -6.2 20 -3.1 15]
puts "Signal at 15°: $signal_15 dBm"

Python offers the same logic with modern syntax sugar:

def interpolate(x1, y1, x2, y2, x):
    slope = (y2 - y1) / (x2 - x1)
    return y1 + slope * (x - x1)

signal_15 = interpolate(0, -6.2, 20, -3.1, 15)
print(f"Signal at 15°: {signal_15:.1f} dBm")

Both give us about -3.9 dBm at the 15-degree mark—three-quarters of the way between our measurements, as expected. The beauty lies in simplicity: linear interpolation assumes the antenna’s behaviour changes steadily between measurement points, which works brilliantly for most RF patterns.

Of course, real antenna lobes aren’t perfectly linear. For those subtle curves that make your lantern glow authentically, you might graduate to cubic splines or Bezier interpolation. But linear interpolation remains the workhorse—fast, predictable, and surprisingly effective at turning your scattered RF measurements into the smooth, printable curves that will cast beautiful shadows on your workshop wall.