\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)

CGAL 4.3 - 3D Convex Hulls

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IsStronglyConvexTraits_3 Concept Reference
Concepts

## Definition

Requirements of the traits class used by the function `CGAL::is_strongly_convex_3()`, which is used for postcondition checking by `CGAL::convex_hull_3()`.

Has Models:

  `CGAL::Convex_hull_traits_3<R>`

  All models of `Kernel`

See Also
  `ConvexHullTraits_3`
  `CGAL::is_strongly_convex_3()`

## Types
typedef unspecified_type | Plane_3
| a 3D plane
typedef unspecified_type | Point_3
| a 3D point
typedef unspecified_type | Ray_3
| a 3D ray
typedef unspecified_type | Triangle_3
| a 3D triangle
typedef unspecified_type | Construct_ray_3
| Function object type that provides `Ray_3 operator()(Point_3 p, Point_3 q)`, which constructs and returns the ray based at point `p` and passing though `q`.
typedef unspecified_type | Construct_triangle_3
| Function object type that provides `Triangle_3 operator()(Point_3 p, Point_3 q, Point_3 r)`, which constructs and returns the triangle with vertices `p`, `q`, and `r`.
typedef unspecified_type | Coplanar_3
| Predicate object type that provides `bool operator()(Point_3 p, Point_3 q, Point_3 r, Point_3 s)`, which determines if points `p`, `q`, `r`, and `s` are coplanar.
typedef unspecified_type | Do_intersect_3
| Function object type that provides `CGAL::Object operator()(Triangle_3 t, Ray_3 r)`, which returns `true` iff `t` and `r` intersect.
typedef unspecified_type | Has_on_positive_side_3
| Predicate object type that provides `bool operator()(Plane_3 h, Point_3 q)`, which determines of the point `q` is on the positive side of the halfspace `h`.
typedef unspecified_type | Oriented_side_3
| Predicate object type that provides `Oriented_side operator()(Plane_3 p, Point_3 q)`, which determines the position of point `q` relative to plane `p`.

## Creation
Only a copy constructor is required.
| IsStronglyConvexTraits_3 (IsStronglyConvexTraits_3 &t)

## Operations
For each of the above function and predicate object types, `Func_obj_type`, a function must exist with the name `func_obj_type_object` that creates an instance of the function or predicate object type. For example:
Construct_ray_3 | construct_ray_3_object ()