The Geometry API is provided by the Geometry concept detailed below.

Geometry concept

Introduction

The Geometry concept provides an abstraction layer to manipulate the geometry of the real datastructures. For example the Point type of the CGAL Surface_mesh datastructure is different from the Point type of the AIF datastructure. So we need this abstraction layer to define a common interface that is supported by all datastructures. This allow to write an algorithm in a generic way.

The interface implementing the Geometry concept for a datastructure is defined by the specialization of the FEVV::Geometry_traits< > class for this datastructure. The various Geometry_traits specializations are defined in the Wrappings/Geometry_traits_....h files.

Notations

G A FEVV::Geometry_traits< > type.
gt An object of type G.
p,q, r Objects of type Point.
x, y, z Objects of type Scalar.
v, u Objects of type Vector.

Associated types

Type	Reference	Description
`G::Scalar`	Affine coordinates	A type used to represent the coordinate of a `Point`.
`G::Point`	Point of affine space	The type "aggregating" `Scalar` coordinates.
`G::Vector`	Affine "substraction"	The type of an element of the associated vector space.

Valid expressions

Expression	Returns	Description
`Point(x, y, z)`	`Point`	Constructor of the `Point` defined its respective given coordinates.
`q(p)`	`Point`	`Point` copy constructor.
`q = p`	`Point`	`Point` assignement operator.
`ORIGIN`	`Point`	The point at the origin.
`gt.get_x(p)`	`Scalar`	Returns the 1st coordinate of point `p`.
`gt.get_y(p)`	`Scalar`	Returns the 2nd coordinate of point `p`.
`gt.get_z(p)`	`Scalar`	Returns the 3rd coordinate of point `p`.
`Vector(x, y, z)`	`Vector`	Constructor of the `Vector` defined its respective given coordinates.
`u(v)`	`Vector`	`Vector` copy constructor.
`u = v`	`Vector`	`Vector` assignement operator.
`NULL_VECTOR`	`Vector`	The zero length vector.
`v[0]`	`Scalar`	Returns the 1st coordinate of vector `v` (read only).
`v[1]`	`Scalar`	Returns the 2nd coordinate of vector `v` (read only).
`v[2]`	`Scalar`	Returns the 3rd coordinate of vector `v` (read only).
`gt.normalize(v)`	`Vector`	Returns the normalization of vector 'v'.
`gt.length2(v)`	`Scalar`	Returns the square of the length of vector `v`.
`gt.length(v)`	`Scalar`	Returns the length of vector `v`.
`gt.length(p, q)`	`Scalar`	Returns the distance between points `p` and `q`.
`gt.normal(p, q, r)`	`Vector`	Returns a vector that is normal to the plane passing through points `p`, `q` and `r`.
`gt.unit_normal(p, q, r)`	`Vector`	Returns a unit vector that is normal to the plane passing through points `p`, `q` and `r`.
`gt.add_v(u, v)`	`Vector`	Returns the sum of vectors `u` and `v`.
`gt.add_pv(p, v)`	`Point`	Returns the sum of point `p` and vector `v`.
`gt.sub_v(u, v)`	`Vector`	Returns the sum of vector `u` and the opposite of vector `v`.
`gt.sub_pv(p, v)`	`Point`	Returns the sum of point `p` and the opposite of vector `v`.
`gt.sub_p(p, q)`	`Vector`	Returns the vector from point `q` to point `p`.
`gt.scalar_mult(v, s)`	`Vector`	Returns the multiplication of vector `v` by scalar `s`.
`gt.dot_product(u, v)`	`Scalar`	Returns the dot product of vectors `u` and `v`.
`gt.cross_product(u, v)`	`Vector`	Returns the cross product of vectors `u` and `v`.

Notes:

the concept checking test GeometryConceptCheck.h illustrate all above expressions
the current implementation misses to enable the following expressions
- p + q which returns a Point
- p - q which returns a Vector
- p + v which returns a Point
because they are not supported by the Point and Vector types of all datastructures.