How to animate the Problem of Apollonius?

LostPhasma

Hi! I'm totally new to Processing, I hope to get your support!

Basically, I'd like to recreate this:

From Wikipedia: In Euclidean plane geometry, Apollonius's problem is to construct circles that are tangent to three given circles in a plane. Three given circles generically have eight different circles that are tangent to them.

My aim is to make the three main circles move inside the window with a random pattern, maintaining tangent the 8 others circles.

I found this code that represent a particular case , in which a circle degenerated into a line: https://gist.github.com/FreedomGrenade/4afcff17982c7299e683

Can you help me?

KevinWorkman

What have you tried so far? Where exactly are you stuck? What exactly are you confused about?

quark

There are plenty of solvers online - this Java solution is easy to understand and can be easily adapted for Processing.

LostPhasma

Just asking if someone has did this before, I'm new to this program. I'm taking some class at the University, I only know basic functions.

I would like to know if exists a simple way to create tangent circles to three main circles, I don't know how to do it!

quark

I would like to know if exists a simple way to create tangent circles to three main circles, I don't know how to do it!

and there we hit the problem. What is simple to one person is not for another.

For me the answer is yes, there is a simple solution based on modifying the code in the link I provided. Obviously that is not the case for you.

The difficulty of this problem is in three parts.

1) Understanding the algebraic method used to find the 8 solution circles.

2) Converting the algebraic solution to some source code

3) Creating a Processing sketch to show the solutions.

Just asking if someone has did this before

I suspect that is has but who knows. Do you want a full code solution? If so I could run one up for you although you will learn more if you do it yourself.