How to make a function of the distance between the curves?
Need to find the shortest distance between two curves by the method of gradient descent:
x^2+y^2-2*x+4*y+3 = 0 and x = (cosϕ)^3 − 1, y = 2 + (sinϕ)^3
The crux of the matter is that I can't be a function of the distance between points on these lines to minimize. Tell me how to do it? Thanks in advance
There is a formula for the distance between two points: sqrt((x2-x1)^2+(y2-y1)^2)
That's it, substitute x and y from the first and second equations, and in the first have to Express x through y.
Get a function of the distance between two arbitrary points of the curves: d = f(x; f) >= 0