DIFFERENTIAL GEOMETRY OF CURVES 83
Figure P3.2
a
b
c
Q
C
B
P
A
O
ρ
ρ
ρ
ρ
ρ
- Plot the curvature and torsion of the Viviani’s curve (intersection of a cylinder and a sphere).
- Write a procedure to create Frenet-Frame (defined by the tangent, normal and bi-normal) at any given point
of a 3-D curve. Also write a procedure to calculate curvature and torsion of the curve at a given point. Any
symbolic math package like Maple, Mathematica may be used for the purpose. It would be helpful to
incorporate plotting in the procedure. - Given three points A,B and C on a curve with position veotors a,b and c, respectively (Figure P3.2),
determine the radius of curvature ρ using vector algebra.