Why Orthogonal Wire Routing Is a Topology Guarantee, Not Just a Visual Preference

TLDR

Constraining wire paths to 90° orthogonal (Manhattan) horizontal and vertical segments during drawing seems like a visual layout choice. In reality, it is a structural topology guarantee: it reduces port connection checks from complex $O(N \times M)$ line-segment distance calculations to exact axis-aligned bounding box (AABB) endpoint intersections. Enforcing orthogonality at draw time makes netlist generation, BOM extraction, and CAD file exports fast and reliable.

Routing Model	Connectivity Math Complexity	Endpoint Port Verification	Netlist Reliability
Free-Form Diagonal	$O(N \times M)$ Parametric segment math	Precision drift $\rightarrow$ False negatives	High ambiguity
Orthogonal (Manhattan)	$O(1)$ AABB Endpoint Intersection	Exact coordinate matching	100% Deterministic

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Problem statement: the ambiguity of free-form diagonal wires

In diagramming applications, allowing free-form diagonal wires ($M\,x_1,y_1\,L\,x_2,y_2$) feels like the most flexible UX choice.

However, arbitrary diagonal paths push immense geometric complexity downstream into topology analysis.

Verifying whether a diagonal wire connects to a component pin requires testing whether a line segment intersects a pin's circular hit radius. Due to floating-point coordinate drift in draw loops, a wire that visually appears attached to a pin may miss it by 0.0001 units, causing netlist generators to report false disconnected nets.

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Technical failure mode: parametric distance calculations

To resolve visual disconnection, developers often widen pin snap thresholds.

Widening thresholds creates a secondary defect: false positive connections, where wires passing near a component pin are incorrectly registered as connected pins in exported BOM netlists.

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The fix & architecture: dominant axis locking at draw time

Enforce orthogonal constraints at segment creation by locking cursor movement to the dominant axis:

// Enforce orthogonal (Manhattan) routing on drag segment
function commitOrthogonalSegment(lastPt, cursorX, cursorY) {
  const dx = Math.abs(cursorX - lastPt.x);
  const dy = Math.abs(cursorY - lastPt.y);
// Lock segment to dominant axis   return dx > dy     ? { x: cursorX, y: lastPt.y } // Horizontal segment     : { x: lastPt.x, y: cursorY }; // Vertical segment }

Exact AABB endpoint connectivity check

With orthogonal segments guaranteed, pin connectivity simplifies to two exact coordinate range checks:

// O(1) Endpoint Connectivity Check
function isWireConnectedToPort(wireEndpoint, portBbox, epsilon = 2) {
  return (
    wireEndpoint.x >= portBbox.x - epsilon &&
    wireEndpoint.x <= portBbox.x + portBbox.w + epsilon &&
    wireEndpoint.y >= portBbox.y - epsilon &&
    wireEndpoint.y <= portBbox.y + portBbox.h + epsilon
  );
}

Degenerate zero-length segment removal

When moving attached components, recalculating orthogonal bend points can create zero-length segments ($x_1=x_2$ and $y_1=y_2$). Prune degenerate points after endpoint updates:

function pruneDegenerateWirePoints(points) {
  return points.filter((pt, i) => {
    if (i === 0) return true;
    const prev = points[i - 1];
    return Math.hypot(pt.x - prev.x, pt.y - prev.y) > 0.001;
  });
}

Rule of thumb: Enforce orthogonal Manhattan constraints at wire creation to simplify downstream topology analysis into $O(1)$ axis-aligned bounding box checks.