# 3D Curve Length

• Apr 11th 2010, 07:47 AM
CrashDummy11
3D Curve Length
Can anyone help me calculate the length of a 3D curve? I need to know the length from 0 degrees to 800 degrees of a curve in the form:

x(t)=(R-r)cos(t)+rcos(((R-r)/R)t)
y(t)=(R-r)sin(t)-rsin(((R-r)/R)t)
z(t)=at

I have specific values that I am using for R, r, and a. The curve is called a Hypocycloid.
• Apr 11th 2010, 09:38 AM
HallsofIvy
Quote:

Originally Posted by CrashDummy11
Can anyone help me calculate the length of a 3D curve? I need to know the length from 0 degrees to 800 degrees of a curve in the form:

x(t)=(R-r)cos(t)+rcos(((R-r)/R)t)
y(t)=(R-r)sin(t)-rsin(((R-r)/R)t)
z(t)=at

I have specific values that I am using for R, r, and a. The curve is called a Hypocycloid.

For any curve given by x(t), y(t), and z(t), the arclength is given by $\displaystyle \int_{t_0}^{t_1} \sqrt{(x')^2+ (y')^2+ (z')^2}dt$.
• Apr 11th 2010, 10:17 AM
CrashDummy11
I tried that but everytime I tried to evaluate the integral for an interval beyond 0-1 it came up as invalid. Any ideas?