A line-swept-sphere. More...

#include <capsule.h>

Inheritance diagram for Capsule:

Public Member Functions
	Capsule ()
	Empty.

	Capsule (const Vector &, const Vector &, const double &)
	Creates a capsule.

	~Capsule ()
	Empty.

bool	Inside (const Vector &) const
	Check if a point is inside the capsule.

double	R (const Vector &) const
	Computes the squared distance between a point and the capsule.

double	Signed (const Vector &) const
	Computes the signed distance between a point and the capsule.

bool	Intersect (const Ray &) const
	Check the intersection between a capsule and a ray.

int	Intersect (const Ray &, double &, double &) const
	Compute the intersections between a capsule and a ray.

int	Intersect (const Ray &, double &, double &, Vector &, Vector &) const
	Compute the intersections between a capsule and a ray.

int	Intersect (const Ray &, double &, Vector &) const
	Compute the first positive intersection between a capsule and a ray.

double	R (const Capsule &, double &, double &) const
	Computes the squared distance between two capsules.

bool	Intersect (const Capsule &, double &, double &) const
	Check if two capsules intersect.

Capsule	Rotated (const Matrix &) const
	Return a capsule rotated by a given matrix.

Capsule	Translated (const Vector &) const
	Return a capsule translated by a given vector.

Capsule	Scaled (const double &) const
	Return a scaled capsule.

Capsule	Transformed (const Frame &) const
	Return a capsule transformed by a frame.

Box	GetBox () const
	Computes the tight bounding box of the capsule.

double	Volume () const
	Compute the volume.

double	Area () const
	Compute the surface area.

double	Radius () const
	Gets the radius of a cylinder.

Static Public Attributes
static const Capsule	Unit
	Unit vertical capsule.

Friends
std::ostream &	operator<< (std::ostream &s, const Capsule &c)
	Overloaded.

Additional Inherited Members
Protected Member Functions inherited from Cylinder
	Cylinder ()
	Empty.

	Cylinder (const Vector &, const Vector &, const double &)
	Creates a cylinder.

	Cylinder (const double &, const double &, const double &=1.0)
	Creates a vertical cylinder.

	Cylinder (const Vector &, const double &, const double &=1.0)
	Creates a vertical cylinder.

	Cylinder (const Circle &, const double &, bool=false)
	Create a vertical cylinder as an extruded circle.

	Cylinder (const Box &, const Axis &)
	Creates the boudning cylinder embedding a box rotated around an axis.

	~Cylinder ()
	Empty.

double	Radius () const
	Gets the radius of a cylinder.

int	Intersect (const Ray &, double &, double &) const
	Compute the intersection between a cylinder and a ray.

int	Intersect (const Ray &, double &, double &, Vector &, Vector &) const
	Compute the intersections between a cylinder and a ray.

int	Intersect (const Ray &, double &, Vector &) const
	Compute the first positive intersection between a cylinder and a ray.

bool	Intersect (const Ray &) const
	Check the intersection between a cylinder and a ray.

bool	Inside (const Vector &) const
	Check if a point is inside or outside the cylinder.

double	Volume () const
	Computes the volume of a cylinder.

double	Area () const
	Computes the surface area of a cylinder.

void	Scale (const double &)
	Uniformly scales a cylinder.

Cylinder	Transformed (const FrameScaled &) const
	Transformed cylinder.

Vector	RandomInside (Random &=Random::R239) const
	Generate a random vector inside the cylinder.

Box	GetBox () const
	Computes the axis-aligned bounding box of a cylinder.

Cylinder	Rotated (const Matrix &) const
	Return a cylinder rotated by a given matrix.

Cylinder	Translated (const Vector &) const
	Return a cylinder translated by a given vector.

Cylinder	Scaled (const double &) const
	Return a scaled cylinder.

double	R (const Vector &) const
	Squared distance between a point and the cylinder.

double	R (const Vector &, double &) const
	Computes the squared distance between a point and the cylinder.

double	Signed (const Vector &) const
	Signed Euclidean distance between a point and a cylinder.

Vector	Normal (const Vector &) const
	Compute the normal vector to a cylinder.

Vector	SignedNormal (const Vector &) const
	Compute the normal vector to the surface of the cylinder.

Vector	Vertex (int) const
	Return one of the end vertexes of the axis.

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

	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 Protected Member Functions inherited from Cylinder
static Vector2	Cast (const Vector &)
	Computes the inverse mapping of a point.

Static Protected 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.

Protected Attributes inherited from Cylinder
double	r = 1.0
	Radius.

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.

Static Protected Attributes inherited from Cylinder
static const double	epsilon = 1.0e-4
	Epsilon value for intersection tests.

static const Cylinder	Unit
	Unit vertical cylinder.

Static Protected Attributes inherited from Axis
static const Axis	Z
	Axes from origin, identical to Axis(Vector::Null,Vector::X) ...

Detailed Description

A line-swept-sphere.

Capsules, which are line-swept-spheres, make good bounding volumes. The function Intersect(const Capsule&, const Capsule&) implements an efficient algorithm to detect the intersection between two capsules.

Note that capsule-ray intersection member function assumes that the ray direction is normalized.

Constructor & Destructor Documentation

◆ Capsule()

Capsule::Capsule	(	const Vector &	a,
		const Vector &	b,
		const double &	r )

explicit

Creates a capsule.

Parameters

a,b	Vertexes
r	Radius.

Member Function Documentation

◆ GetBox()

Box Capsule::GetBox ( ) const

Computes the tight bounding box of the capsule.

See also: Circle::GetBox()

◆ Inside()

bool Capsule::Inside ( const Vector & p ) const

Check if a point is inside the capsule.

Parameters

p Point.

◆ Intersect() [1/5]

bool Capsule::Intersect	(	const Capsule &	cs,
		double &	u,
		double &	v ) const

Check if two capsules intersect.

The algorithm computes the squared distance and compares it with the squared sum of radii.

Parameters

cs	The other capsule.
u,v	The location of the closests points on the two capsules where minimum distance occurs.

See also: Capsule::R()

◆ Intersect() [2/5]

bool Capsule::Intersect ( const Ray & ray ) const

Check the intersection between a capsule and a ray.

Note the function assumes that the ray is normalized, i.e. has a unit direction vector.

Parameters

ray	The normalized ray.

◆ Intersect() [3/5]

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

Compute the intersections between a capsule and a ray.

Note that this member function assumes that the ray is normalized, i.e. has a unit direction vector.

Intersections are sorted according to intersection depth.

Parameters

ray	The normalized ray.
ta,tb	Intersection depths.

◆ Intersect() [4/5]

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

Compute the intersections between a capsule and a ray.

Intersections are sorted according to intersection depth.

Note that this function is not fully optimized, as it relies on the member functions Sphere::Intersect() and Cylinder::Intersect() to compute the intersection with the union of two spheres and a cylinder. Several enhancements could be made by inlining the functions with the corresponding code and removing redundant computations.

Parameters

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

◆ Intersect() [5/5]

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

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

Parameters

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

◆ R() [1/2]

double Capsule::R	(	const Capsule &	cs,
		double &	u,
		double &	v ) const

Computes the squared distance between two capsules.

Parameters

cs	The line-swept-sphere.
u,v	The location of the closests points on the segments of the capsules where minimum distance occurs.

◆ R() [2/2]

double Capsule::R ( const Vector & p ) const

Computes the squared distance between a point and the capsule.

Parameters

p Point.

◆ Rotated()

Capsule Capsule::Rotated ( const Matrix & r ) const

Return a capsule rotated by a given matrix.

Parameters

r	Rotation matrix.

◆ Scaled()

Capsule Capsule::Scaled ( const double & s ) const

Return a scaled capsule.

Parameters

s	Scaling factor.

◆ Signed()

double Capsule::Signed ( const Vector & p ) const

Computes the signed distance between a point and the capsule.

Parameters

p Point.

◆ Transformed()

Capsule Capsule::Transformed ( const Frame & frame ) const

Return a capsule transformed by a frame.

Parameters

frame The frame.

◆ Translated()

Capsule Capsule::Translated ( const Vector & t ) const

Return a capsule translated by a given vector.

Parameters

t	Translation vector.

Friends And Related Symbol Documentation

◆ operator<<

std::ostream & operator<<	(	std::ostream &	s,
		const Capsule &	c )

friend

Overloaded.

Parameters

s	Stream.
c	Capsule.

Public Member Functions

Static Public Attributes

Friends

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ Capsule()

Member Function Documentation

◆ GetBox()

◆ Inside()

◆ Intersect() [1/5]

◆ Intersect() [2/5]

◆ Intersect() [3/5]

◆ Intersect() [4/5]

◆ Intersect() [5/5]

◆ R() [1/2]

◆ R() [2/2]

◆ Rotated()

◆ Scaled()

◆ Signed()

◆ Transformed()

◆ Translated()

Friends And Related Symbol Documentation

◆ operator<<