Cable net generation of a deployable offset parabolic reflector using quasi-geodesic curves

Designing an offset cable net in parabolic reflectors introduces several complexities compared to prime focus configurations. This study aims to develop a versatile cable net generation algorithm capable of adapting to the reflector's dimensions and the curvature of the paraboloid surface. In this regard, we propose a methodology that leverages specific paraboloid surface curves known as quasi-geodesic curves. Similar to geodesic curves on a sphere, quasi-geodesic curves visually resemble proper geodesic shapes but may follow distinct mathematical principles. We introduce two types of quasi-geodesic curves: primary curves that intersect the center point of the cable net and secondary curves that pass through any two points on the net. We present various solutions accommodating different cable net layouts and introduce a quality index based on an equilateral triangle cable net. Finally, we compare the quasi-geodesic-type cable net with the isogrid-type cable net to highlight tension distribution and surface accuracy improvements.