An axis aligned cage. More...
#include <cage.h>
Inheritance diagram for Cage:
Public Member Functions | |
| Cage () | |
| Empty. | |
| Cage (const Box &, const double &, bool=false) | |
| Create a cage. More... | |
| ~Cage () | |
| Empty. | |
| Vector & | operator[] (int) |
| Returns either end vertex of the box. | |
| Vector | operator[] (int) const |
| Overloaded. | |
| double | R (const Vector &) const |
| Computes the squared Euclidean distance between the cage and a point. More... | |
| double | Signed (const Vector &) const |
| Computes the signed distance between the cage and a point. More... | |
| Box | GetBox () const |
| Compute the bounding box. | |
| Mesh | GetMesh (int=8) const |
| Compute the mesh of the cage. More... | |
Protected Attributes | |
| bool | rounded = false |
| Thickness. More... | |
 Protected Attributes inherited from Box | |
| Vector | a |
| Lower vertex. | |
| Vector | b |
| Upper vertex. | |
Friends | |
| std::ostream & | operator<< (std::ostream &, const Cage &) |
| Overloaded. More... | |
Additional Inherited Members | |
| Protected Member Functions inherited from Box | |
| Box () | |
| Empty. | |
| Box (const double &) | |
| Create a cube centered at the origin and of given half side length. More... | |
| Box (const Vector &) | |
| Create an empty box given one vertex. More... | |
| Box (const Vector &, const Vector &) | |
| Create a box given two opposite corners. More... | |
| Box (const Vector &, const double &) | |
| Create a box given a center point and the half side length. More... | |
| Box (const Vector &, const double &, const double &, const double &) | |
| Create a box given a center point and its width, length, and height. More... | |
| Box (const double &, const double &, const double &) | |
| Create a box given its sizes. More... | |
| Box (const Vector *, int) | |
| Creates the bounding box of a set of points. More... | |
| Box (const QVector< Vector > &) | |
| Creates the bounding box of a set of points. More... | |
| Box (const Box &, const Box &) | |
| Create a box embedding two boxes. More... | |
| Box (const Box &, const Frame &) | |
| Creates an axis aligned bounding box from a box and a frame. More... | |
| Box (const Box &, const FrameScaled &) | |
| Creates an axis aligned bounding box from a box and a frame. More... | |
| Box (const Box &, const Matrix &) | |
| Creates an axis aligned bounding box from a box and a transformation matrix. More... | |
| ~Box () | |
| Empty. | |
| Vector & | operator[] (int) |
| Returns either end vertex of the box. | |
| Vector | operator[] (int) const |
| Overloaded. | |
| Vector | Center () const |
| Returns the center of the box. | |
| Vector | Vertex (int) const |
| Returns the k-th vertex of the box. More... | |
| Vector | Vertex (int, int, int, int, int, int) const |
| Compute the coordinates of a grid aligned point. More... | |
| Segment | Edge (int) const |
| Compute the k-th edge segment of the box. More... | |
| Plane | Face (int) const |
| Compute the k-th plane of the box. More... | |
| Vector | Size () const |
| Compute the size (width, length and height) of a box. More... | |
| Vector | Diagonal () const |
| Returns the diagonal of the box. | |
| double | Radius () const |
| Returns the radius of the box, i.e. the length of the half diagonal of the box. | |
| double | R (const Vector &) const |
| Computes the squared Euclidean distance between the box and a point. More... | |
| double | Signed (const Vector &) const |
| Computes the signed distance between the box and a point. More... | |
| Vector | Normal (const Vector &) const |
| Computes the normal vector between a point and a box. More... | |
| double | R (const Box &) const |
| Compute the squared Euclidean distance between two boxes. More... | |
| double | RInfinity (const Box &) const |
| Compute the maximum distance between two boxes. More... | |
| int | Intersect (const Ray &) const |
| Check the intersection between a box and a ray. More... | |
| int | Intersect (const Ray &, double &, double &) const |
| Computes the intersection between a box and a ray. More... | |
| int | Intersect (const Ray &, double &) const |
| Compute the first positive intersection between the box and a ray. More... | |
| int | Intersect (const Ray &, double &, double &, Vector &, Vector &) const |
| Compute the intersection between an axis aligned box and a ray. More... | |
| int | Intersect (const Ray &, double &, Vector &) const |
| Compute the first positive intersection between the box and a ray. More... | |
| int | Intersect (const Vector &, const Vector &) const |
| Check if a segment intersects an axis aligned box. More... | |
| bool | Intersect (const Box &) const |
| Check if the box intersects another box. More... | |
| bool | Inside (const Box &) const |
| Check if an argument box is inside the box. More... | |
| bool | Inside (const Vector &) const |
| Check if a point is inside the box. More... | |
| Box | Intersection (const Box &) const |
| Computes the intersection between two boxes. More... | |
| int | Difference (const Box &, Box *) const |
| Computes the difference between two boxes. More... | |
| bool | Empty () const |
| Check if a box is empty. More... | |
| double | Volume () const |
| Compute the volume of a box. | |
| double | Area () const |
| Compute the surface area of a box. | |
| void | SetCubic () |
| Creates the tightest embedding cube from an arbitrarilly shaped box. More... | |
| void | SetInscribedCubic () |
| Creates the biggest cube iscribed in the box. More... | |
| Box | Cube () const |
| Return the tightest embedding cube from an arbitrarilly shaped box. More... | |
| void | Extend (const double &) |
| Extend the limits of the box by a given distance. More... | |
| Box | Extended (const double &) const |
| Extend the limits of the box by a given distance. More... | |
| void | Extend (const Vector &) |
| Extend the limits of the box given a point. More... | |
| void | SetParallelepipedic (const double &, int &, int &, int &) |
| Creates a parallelepipedic box whose dimensions are integer multiples of a given input reference size. More... | |
| void | SetParallelepipedic (int, int &, int &, int &) |
| Inflates a box so that its dimensions should be a fraction of its maximum side length. More... | |
| Box | Sub (int) const |
| Computes the sub-box in the n-th octant. More... | |
| int | Octant (const Vector &) const |
| Compute the octant index of a vertex with respect to the box center. More... | |
| void | Translate (const Vector &) |
| Translates a box. More... | |
| Box | Translated (const Vector &) const |
| Translated box. More... | |
| void | Scale (const double &) |
| Scales a box. More... | |
| void | Scale (const Vector &) |
| Scales a box. More... | |
| Box | Scaled (const Vector &) const |
| Scales a box and return the scaled box. More... | |
| Box | Offsetted (const Vector &) const |
| Offets a box. More... | |
| Box | Centered () const |
| Compute the box translated to origin. More... | |
| Box | Cut (const Vector &, const Vector &) const |
| Compute the minimal box embedding the box cut by half space. More... | |
| int | IntegerAxis () const |
| Compute the axis which has the greater length. | |
| Vector | RandomInside (Random &=Random::R239) const |
| Generate a random vector inside the box. More... | |
| Vector | RandomSurface (Random &=Random::R239) const |
| Generate a random vector on the surface of the box. More... | |
| QVector< Vector > | Poisson (const double &, int, Random &=Random::R239) const |
| Compute a Poisson sphere distribution inside a box. More... | |
| Static Protected Attributes inherited from Box | |
| static constexpr const double | epsilon = 1.0e-5 |
| Epsilon value used to check intersections and some round off errors and for ray intersection tests. | |
| static const Box | Infinity |
| Largest box. More... | |
| static const Box | Null |
| Null box, equivalent to: More... | |
| static const Box | Unit |
| Unit box. | |
| static const int | edge [24] |
| Edge vertex indexes. | |
| static const Vector | normal [6] |
| Face normals. | |
Detailed Description
An axis aligned cage.
Constructor & Destructor Documentation
◆ Cage()
|
explicit |
Create a cage.
- Parameters
-
box The box. e Thickness, the effective (stored) offset distance is half of the thickness. r Flag indicating whether the cage should be rounded or not.
Member Function Documentation
◆ GetMesh()
| Mesh Cage::GetMesh | ( | int | n = 8 | ) | const |
Compute the mesh of the cage.
- Parameters
-
n Discretization of the circle, should the cage be rounded (not used otherwise).
◆ R()
| double Cage::R | ( | const Vector & | p | ) | const |
Computes the squared Euclidean distance between the cage and a point.
- Parameters
-
p Point.
◆ Signed()
| double Cage::Signed | ( | const Vector & | p | ) | const |
Computes the signed distance between the cage and a point.
The computation relies on an eightfold planar symmetry; in the first octant, the cage portion is the union of three boxes.
If the cage is rounded, it also shows eightfold planar symmetry, but in this case we compute the distance to line segments, and then offset the distance by the thickness.
- Parameters
-
p Point.
Friends And Related Function Documentation
◆ operator<<
|
friend |
Overloaded.
- Parameters
-
s Stream. cage The cage.
Member Data Documentation
◆ rounded
|
protected |
Thickness.
Rounded flag.
