Catenary curve deformer

A catenary is the natural curve a flexible rope or chain hangs under its own weight when fixed at two points. Imagine a power line sagging between two towers - that’s a catenary!

It’s useful for creating realistic:

• Power lines: As mentioned above, catenaries are perfect for depicting power lines with a natural droop.
• Suspension bridges: The main cables of suspension bridges often follow a catenary shape.
• Hanging cloths and fabrics: Flags, tents, and draped curtains can all benefit from a catenary curve for a realistic drape.

This is a simple example of how we can apply catenary to a curve with VEX in Houdini:

Point.wrangle

int numvtx = primvertexcount(0, @primnum);
float cuv = vertexcurveparam(0, @vtxnum);
float curve_length = primintrinsic(0, "measuredperimeter", @primnum);
float x = fit01(cuv, -curve_length / 2, curve_length / 2);
float random_seed = chf("random");
float a = chf("A") + (rand(@primnum + random_seed) - 0.5) * chf("random_amplitude");
a = max(a, 0.1);
float gain = chf("gain");
float y = gain * (a * cosh(x / a) - a * cosh(curve_length / (2 * a))) * -1;

// Set point position
v@P.y -= y;