Geometry

The geometry classes use the vector classes. In this document, `vector', `point' and `centre' imply objects of type `Vector'.

Input/output

Surface class

type_name
parameters

type_name	parameters
plane	normal_vector (n) family_parameter (f=n.r : r = point_in_plane)
cylinder	point_on_axis axis_vector radius
cone	point_on_axis axis_vector half_angle (radians)
general_cone	point_on_axis axis_vector half_angle (radians) radius_at_point_on_axis
sphere	centre radius
ellipsoid	centre radius_1 radius_2 ... radius_N
general_ellipsoid	centre axis_vector_1 axis_vector_2 ... axis_vector_N radius_1 radius_2 ... radius_N

Programming

Class `Line'

Class `Surface'

Class `Plane'

Class `Cylinder'

Class `Cone'

Class `Gencone'

Class `Sphere'

Class `Ellipsoid'

Class `Genellipsoid'

Class `Surface_function'

Class `Outside'

Class `Surface_subset'

Class `Surface_intersection'

Class `Surface_union'

Fitting surfaces to data

Point

• Find the average of a set of points and weights:

     Vector average(
        const Array& v, // array of position vectors
        const Array& w // array of weights
     )
     

Plane

• Fit a (hyper)plane to weighted {r,f} data:

     Plane best_fitting_plane(
        const Array& r, // Array of position Vectors
        const Vector& f, // Array of function values
        const Vector& w // Array of weights
     )
     

  Returns a plane whose normal has no components if it fails.

Sphere

• Fit a sphere to a weighted set of points r:

     Sphere best_fitting_sphere(
        const Array& r, // Array of position Vectors
        const Vector& w // Array of weights
     )
     

  Returns a sphere whose centre has no components if it fails.

Ellipsoid

• Fit an ellipsoid to a weighted set of points r:

     Ellipsoid best_fitting_ellipsoid(
        const Array& r, // Array of position Vectors
        const Vector& w // Array of weights
     )
     

  Returns an ellipsoid whose centre has no components if it fails.
• Fit an ellipsoid to a weighted set of points r given the centre:

     Ellipsoid best_fitting_ellipsoid(
        const Vector& c, // centre
        const Array& r, // Array of position Vectors
        const Vector& w // Array of weights
     )
     

  Returns an ellipsoid whose centre has no components if it fails.