Spirograph
Time limit8sMemory limit512 MB
For each test case, compute the total arc length of a hypotrochoid traced by a pinhole in a circle of radius Q rolling inside a fixed circle of radius P, with pinhole offset R.
- Level
Hard8 of 10
- Topics
- Math, Geometry, Simulation
- Solved
- No attempts yet
Problem
Some of you may have seen an instrument like the one in the figure below.
Figure 1: Spirograph
There is a fixed circle (labeled A in the figure) and a smaller interior circle with several pinholes (labeled B). Put a pen tip through one of the pinholes, then roll circle B without slipping around the inside of circle A, and you can draw curves like the one below. Such curves are called hypotrochoids.
Figure 2: An example hypotrochoid
Given the radius of the fixed circle A, the radius of the interior circle B, and the distance between the center of B and the pinhole used, write a program that computes the length of the hypotrochoid.
Input
The input consists of multiple test cases. Each test case is described by a single line containing three integers P, Q, R in that order, where P is the radius of the fixed circle A, Q is the radius of the interior circle B, and R is the distance between the center of circle B and the pinhole. You can assume that 0 ≤ R < Q < P ≤ 1000. P, Q, and R are separated by a single space, and no other spaces appear in the input.
The end of input is indicated by a line with P = Q = R = 0.
Output
For each test case, output the length of the hypotrochoid curve. The error must be within 10-2 (= 0.01).