Computer Aided Engineering Design

DIFFERENTIAL GEOMETRY OF CURVES 83

Figure P3.2

a

b

c

Q

C

B

P

A

O

ρ

ρ

ρ

ρ

ρ

12. Plot the curvature and torsion of the Viviani’s curve (intersection of a cylinder and a sphere).


13. 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.


14. 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.