Practical informations Practical informations Send source code to: - - PowerPoint PPT Presentation

Practical informations Practical informations

• Send source code to:

christophe.leblanc@ulg.ac.be p g

2D and 3D curves: curvature 2D and 3D curves: curvature

• Compute the curvatures of two curves:

– 2D: (Semi) circle of radius r=1 ( )

r u / 1 ) ( = κ

– 3D: Helix of radius r=10

) ( ) 1 ² /( ) ( + = r r u κ ) 1 /( ) ( + r r u κ

2D and 3D curves: curvature 2D and 3D curves: curvature

• For doing the calculations, you will need the following

member functions of npoint3:

– double norm(void) const – double dotprod(const npoint3 other) const – Overloading of operators +, -, *, /

2D and 3D curves: curvature 2D and 3D curves: curvature

• For doing the calculations, you will need the following

member functions of npoint3:

– double norm(void) const – double dotprod(const npoint3 other) const – Overloading of operators +, -, *, /

• Warning: need to convert

Warning: need to convert npoint <-> npoint3

Homogeneous coordinates (4D) Euclidean coordinates (3D) coordinates (4D) coordinates (3D)

2D and 3D curves: curvature 2D and 3D curves: curvature

• For doing the calculations, you will need the following

member functions of Vector:

• A vector in homogeneous coordinates has weight

w = 0

– double Norm(void) const – double operator * (const Vector &V) const

• A point in homogeneous coordinates equal to an

– void Cross(Vector &V1, Vector &V2)

euclidean point has weight w = 1

2D and 3D curves: curvature 2D and 3D curves: curvature

• ADVICE : try to be organized by implementing

new functions in the main.cc file

– first and second derivatives. Tangent – Tangent. – Normal. – Derivative of the tangent.