curvature.js

#!/usr/local/bin/spn

# Playing around with differential geometry is fun!

let derivative = function derivative(fn) {
	return function(x0) {
		let f = fn;
		let dx = 1.0e-5;
		let x = x0 + dx;
		let y0 = f(x0), y = f(x);
		return (y - y0) / dx;
	};
};

let curvature = function curvature(f, x1) {
	let x2 = x1 + 1.0e-5;
	let y1 = f(x1), y2 = f(x2);
	let fprime = derivative(f);
	let dy1 = fprime(x1), dy2 = fprime(x2);
	let xc = ((y1 - y2) * dy1 * dy2 + x1 * dy2 - x2 * dy1) / (dy2 - dy1);
	let yc = y1 - (xc - x1) / dy1;
	let c = 1.0 / hypot(xc - x1, yc - y1);
	return c;
};

let circle = function circle(x) {
	return sqrt(1.0 - x * x);
};

let functions = {
	{ "sin",    sin,    M_PI_2 },
	{ "cosh",   cosh,   0.0    },
	{ "circle", circle, 0.35   },
	{ "exp",    exp,    1.0    }
};

foreach(functions, function(k, v) {
	printf("curvature of %s(%.5f)\t= %.5f\n", v[0], v[2], curvature(v[1], v[2]));
});