Cone Class Reference

Cones defined as truncated cones. More...

#include <cone.h>

Inheritance diagram for Cone:

Public Member Functions
	Cone ()
	Empty.
	Cone (const Vector &, const Vector &, const double &, const double &=0.0)
	Creates a cone characterized by its end-vertices and radii.
	Cone (const double &, const double &, const double &)
	Creates a vertical cone characterized height and radii.
	~Cone ()
	Empty.
constexpr double	Radius (int) const
	Gets either end-radius of the cone.
int	Intersect (const Ray &, double &, double &) const
	Compute the intersections between the cone and a ray.
int	Intersect (const Ray &, double &, double &, Vector &, Vector &) const
	Compute the intersections between the cone and a ray.
int	Intersect (const Ray &, double &, Vector &) const
	Compute the first positive intersection between the cone and a ray.
bool	Inside (const Vector &) const
	Check if a point is inside or outside the cone.
double	R (const Vector &) const
	Compute the distance between a point and the cone.
double	Signed (const Vector &) const
	Compute the signed distance between a point and the cone.
Vector	Normal (const Vector &) const
	Computes the vector distance between the cone and a point.
void	Rotate (const Matrix &)
	Rotates the cone.
void	Translate (const Vector &)
	Translates the cone.
void	Scale (const double &)
	Uniformly scales the cone.
double	Area () const
	Compute the total surface area of the cone.
double	Volume () const
	Compute the volume of the cone.
Vector	RandomInside (Random &=Random::R239) const
	Generate a random vector inside the cone.
Box	GetBox () const
	Compute the axis-aligned bounding box of the cone.
Vector	Vertex (int) const
	Return one of the end vertexes of the axis.
Public Member Functions inherited from Axis
	Axis ()
	Empty.
	Axis (const Vector &, const Vector &)
	Creates an axis given end vertices.
	~Axis ()
	Empty.
void	Rotate (const Matrix &)
	Rotates an axis.
void	Translate (const Vector &)
	Translates an axis.
void	Scale (const double &)
	Uniformly scales an axis.
void	Scale (const Vector &)
	Scales an axis.
Quadric	Equation (const Ray &) const
	Compute the polynomial equation of the Euclidean distance between a ray and the axis.
Vector	Vertex (int) const
	Return one of the end vertexes of the axis.
Vector	Point (const double &) const
	Compute a point on the axis.
Vector	GetAxis () const
	Returns the normalized axis vector.
double	Length () const
	Return the axis length.
Vector	Symmetric (const Vector &) const
	Symmetric point.
Sphere	Symmetric (const Sphere &) const
	Symmetric sphere.
Vector	Normal (const Vector &) const
	Compute the normal vector between a point and its projection onto the edge.
double	R (const Vector &) const
	Compute the squared distance to the segment.
double	R (const Axis &) const
	Compute the squared distance between two axes.
double	R (const Vector &, double &) const
	Compute the squared distance to the axis.
Matrix	GetFrame () const
	Compute an orthonormal frame attached to the axis.
Vector2	Radial (const Vector &) const
	Compute the radial coordinates of a point.

Static Public Member Functions
static Vector	RandomDirection (const Vector &, const double &, Random &=Random::R239)
	Generate a random direction.
Static Public Member Functions inherited from Axis
static Matrix	GetFrame (const Vector &)
	Compute an orthonormal frame attached to the axis.
static Vector	BoxVector (const Vector &)
	Compute the box vector extent of a unit circle with a given axis.

Static Public Attributes
static const double	epsilon = 1.0e-4
	Epsilon value.
static const Cone	Unit
	Unit vertical cone.
Static Public Attributes inherited from Axis
static const Axis	Z
	Axes from origin, identical to Axis(Vector::Null,Vector::X) ...

Protected Attributes
double	rb = 0.0
	Radius of the cone at the first and second vertexes of the axis.
double	rlength = -1.0
	Internal parameter.
double	conelength = Math::Sqrt2
	Side length of the cone.
Vector2	side = Vector2(-1.0, 1.0) / Math::Sqrt2
	Vector representing the side.
Protected Attributes inherited from Axis
Vector	b = Vector::Z
	End vertexes of the axis.
Vector	axis = Vector::Z
	Normalized axis vector.
double	length = 1.0
	Length of the axis.

Friends
std::ostream &	operator<< (std::ostream &s, const Cone &cone)
	Overloaded.

Additional Inherited Members
Protected Member Functions inherited from Axis
double	Radial (const Vector &, Vector &, Vector &) const
	Compute the radial coordinates of a point.

Detailed Description

Cones defined as truncated cones.

Constructor & Destructor Documentation

Cone() [1/2]

Cone::Cone ( const Vector & a, const Vector & b, const double & ra, const double & rb = 0.0 )

explicit

Creates a cone characterized by its end-vertices and radii.

Parameters

a,b	End vertices of the axis.
ra,rb	Radii.

Cone() [2/2]

Cone::Cone ( const double & ab, const double & ra, const double & rb )

explicit

Creates a vertical cone characterized height and radii.

Parameters

ab	Height.
ra,rb	Radii.

Member Function Documentation

Area()

double Cone::Area

(

)

const

Compute the total surface area of the cone.

The total surface area is the sum of the area of the cap discs, and the lateral surface area.

Inside()

bool Cone::Inside

(

const Vector &

p

)

const

Check if a point is inside or outside the cone.

Parameters

p

Point.

Intersect() [1/3]

int Cone::Intersect	(	const Ray &	ray,
		double &	ta,
		double &	tb ) const

Compute the intersections between the cone and a ray.

Parameters

ray	The ray.
ta,tb	Intersection depths.

Intersect() [2/3]

int Cone::Intersect	(	const Ray &	ray,
		double &	ta,
		double &	tb,
		Vector &	na,
		Vector &	nb ) const

Compute the intersections between the cone and a ray.

Parameters

ray	The ray.
ta,tb	Intersection depths.
na,nb	Normals at intersection points.

Intersect() [3/3]

int Cone::Intersect	(	const Ray &	ray,
		double &	t,
		Vector &	n ) const

Compute the first positive intersection between the cone and a ray.

Parameters

ray	The ray.
t	Intersection depth.
n	Normal at intersection point.

Normal()

Vector Cone::Normal

(

const Vector &

p

)

const

Computes the vector distance between the cone and a point.

Parameters

p

Point.

R()

double Cone::R

(

const Vector &

p

)

const

Compute the distance between a point and the cone.

Details appear in A. Barbier and E. Galin. Fast distance Computation between a Point and Cylinders, Cones, Line-swept-Spheres and Cone-Spheres. Journal of Graphics Tools. 9(2), 11-19 (2004).

Parameters

p

Point.

RandomDirection()

Vector Cone::RandomDirection ( const Vector & axis, const double & alpha, Random & random = Random::R239 )

static

Generate a random direction.

Parameters

axis	Axis.
alpha	Angle.
random	Random number generator.

RandomInside()

Vector Cone::RandomInside

(

Random &

random = Random::R239

)

const

Generate a random vector inside the cone.

Parameters

random

Random number generator.

Rotate()

void Cone::Rotate

(

const Matrix &

r

)

Rotates the cone.

Parameters

r	Rotation matrix.

Scale()

void Cone::Scale

(

const double &

s

)

Uniformly scales the cone.

Parameters

s	Scaling factor.

Signed()

double Cone::Signed

(

const Vector &

p

)

const

Compute the signed distance between a point and the cone.

Parameters

p

Point.

Translate()

void Cone::Translate

(

const Vector &

t

)

Translates the cone.

Parameters

t	Translation vector.

Friends And Related Symbol Documentation

operator<<

std::ostream & operator<< ( std::ostream & s, const Cone & cone )

friend

Overloaded.

Parameters

s	Stream.
cone	The cone.