Cylinder Class Reference

A cylinder characterized by its end vertices and radius. More...

#include <cylinder.h>

Inheritance diagram for Cylinder:

Public Member Functions
	Cylinder ()
	Empty.
	Cylinder (const Vector &, const Vector &, const double &)
	Creates a cylinder. More...
	Cylinder (const double &, const double &, const double &=1.0)
	Creates a vertical cylinder. More...
	Cylinder (const Box &, const Axis &)
	Creates the boudning cylinder embedding a box rotated around an axis. More...
	~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. More...
int	Intersect (const Ray &, double &, double &, Vector &, Vector &) const
	Compute the intersections between a cylinder and a ray. More...
int	Intersect (const Ray &, double &, Vector &) const
	Compute the first positive intersection between a cylinder and a ray. More...
bool	Intersect (const Ray &) const
	Check the intersection between a cylinder and a ray. More...
bool	Inside (const Vector &) const
	Check if a point is inside or outside the cylinder. More...
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. More...
Cylinder	Transformed (const FrameScaled &) const
	Transformed cylinder. More...
Vector	RandomInside (Random &=Random::R239) const
	Generate a random vector inside the cylinder. More...
Box	GetBox () const
	Computes the axis-aligned bounding box of a cylinder. More...
Cylinder	Rotated (const Matrix &) const
	Return a cylinder rotated by a given matrix. More...
Cylinder	Translated (const Vector &) const
	Return a cylinder translated by a given vector. More...
Cylinder	Scaled (const double &) const
	Return a scaled cylinder. More...
double	R (const Vector &) const
	Squared distance between a point and the cylinder. More...
double	R (const Vector &, double &) const
	Computes the squared distance between a point and the cylinder. More...
double	Signed (const Vector &) const
	Signed Euclidean distance between a point and a cylinder. More...
Vector	Normal (const Vector &) const
	Compute the normal vector to a cylinder skeleton. More...
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. More...
	~Axis ()
	Empty.
void	Rotate (const Matrix &)
	Rotates an axis. More...
void	Translate (const Vector &)
	Translates an axis. More...
void	Scale (const double &)
	Uniformly scales an axis. More...
void	Scale (const Vector &)
	Scales an axis. More...
Quadric	Equation (const Ray &) const
	Compute the polynomial equation of the Euclidean distance between a ray and the axis. More...
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. More...
Sphere	Symmetric (const Sphere &) const
	Symmetric sphere. More...
Vector	Normal (const Vector &) const
	Compute the normal vector between a point and its projection onto the edge. More...
double	R (const Vector &) const
	Compute the squared distance to the segment. More...
double	R (const Axis &) const
	Compute the squared distance between two axes. More...
double	R (const Vector &, double &) const
	Compute the squared distance to the axis. More...
Matrix	GetFrame () const
	Compute an orthonormal frame attached to the axis. More...

Static Public Member Functions
static int	Cast (const Vector &, double &, double &)
	Computes the inverse mapping of a point. More...
Static Public Member Functions inherited from Axis
static Matrix	GetFrame (const Vector &)
	Compute an orthonormal frame attached to the axis. More...
static Vector	BoxVector (const Vector &)
	Compute the box vector extent of a unit circle with a given axis. More...

Static Public Attributes
static const double	epsilon = 1.0e-4
	Epsilon value for intersection tests.
static const Cylinder	Unit
	Unit vertical cylinder.

Protected Attributes
double	r = 1.0
	Radius.
Protected Attributes inherited from Axis
Vector	b = Vector::Z
	End vertices of the axis.
Vector	axis = Vector::Z
	Normalized axis vector.
double	length = 1.0
	Length of the axis.

Friends
std::ostream &	operator<< (std::ostream &, const Cylinder &)
	Overloaded. More...

Additional Inherited Members
Protected Member Functions inherited from Axis
double	Radial (const Vector &, Vector &, Vector &) const
	Compute the radial coordinates of a point. More...
Vector2	Radial (const Vector &) const
	Compute the radial coordinates of a point. More...

Detailed Description

A cylinder characterized by its end vertices and radius.

Note that only the radius is stored, the squared radius value is computed on the fly whenever needed.

Constructor & Destructor Documentation

Cylinder() [1/3]

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

explicit

Creates a cylinder.

Parameters

a,b	End vertices of the axis.
r	Radius of the cylinder.

Cylinder() [2/3]

Cylinder::Cylinder ( const double &  a, const double &  b, const double &  r = 1.0  )

explicit

Creates a vertical cylinder.

Parameters

a,b	Height of apexes.
r	Radius.

Cylinder() [3/3]

Cylinder::Cylinder ( const Box &  box, const Axis &  ax  )

explicit

Creates the boudning cylinder embedding a box rotated around an axis.

Parameters

box	The box.
ax	The axis.

Member Function Documentation

Cast()

int Cylinder::Cast ( const Vector &  p, double &  u, double &  v  )

static

Computes the inverse mapping of a point.

Projects the point onto the z-axis unit cylinder, uv-coordinates are set to unit interval [0,1].

Parameters

p	point
u,v	inverse mapping coordinates

GetBox()

Box Cylinder::GetBox

(

)

const

Computes the axis-aligned bounding box of a cylinder.

See also

Circle::GetBox()

Inside()

bool Cylinder::Inside

(

const Vector &

p

)

const

Check if a point is inside or outside the cylinder.

Parameters

p

Point.

Intersect() [1/4]

bool Cylinder::Intersect

(

const Ray &

ray

)

const

Check the intersection between a cylinder and a ray.

Parameters

ray

The ray.

Intersect() [2/4]

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

Compute the intersection between a cylinder and a ray.

Intersections are sorted according to intersection depth.

Parameters

ray	The ray.
ta,tb	Intersection depths.

Intersect() [3/4]

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

Compute the intersections between a cylinder and a ray.

Intersections are sorted according to intersection depth.

Parameters

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

Intersect() [4/4]

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

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

Parameters

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

Normal()

Vector Cylinder::Normal

(

const Vector &

p

)

const

Compute the normal vector to a cylinder skeleton.

Project the point in space onto the axis of the cylinder. If projection lies inside the segment, then return the normal to the segment minus the right radius direction, otherwise perform computations for the end caps.

Parameters

p

Point.

R() [1/2]

double Cylinder::R

(

const Vector &

p

)

const

Squared distance between a point and the cylinder.

From 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.

Cost in worst case: 11 +, 9 *, 1 sqrt, 3 if.

Parameters

p

Point.

double Cylinder::R(const Vector& p) const
{
Vector n = p - a;  // Cost: 3+
double s = axis*n; // Cost: 3* 2+
double ra = n*n;   // Cost: 3* 2+
 
// Vertex A
if (s < 0.0)
{
double z = s*s;    // Cost: 1*
double u = ra - z; // Cost: 1+
// Inside disc at vertex A
if (u < r*r)       // Cost: 1?
{
return z;
}
// Circle A
else
{
u = sqrt(u);    // Cost: 1 sqrt
u -= r;         // Cost: 1+
return z + u*u; // Cost: 1* 1+
}
}
else
{
// Vertex B
if (s > length)
{
double z = s - length; // 1+
z *= z;                // 1*
double u = ra - s*s;   // 1+ 1*
// Inside disc at vertex B
if (u < r*r)
{
return z;
}
// Circle A
else
{
u = sqrt(u);     // 1 sqrt
u -= r;          // 1+
return z + u*u;  // 1* 1+
}
}
// Cylinder
else
{
double z = s*s;    // 1*
double u = ra - z; // 1+
if (u < r*r)
{
return 0;
}
else
{
u = sqrt(u);   // 1 sqrt
u -= r;        // 1+
return u*u;    // 1*
}
}
}
}

R() [2/2]

double Cylinder::R	(	const Vector &	p,
		double &	s
	)		const

Computes the squared distance between a point and the cylinder.

Parameters

p	Point.
s	Returned position of the projected point onto the axis of the cylinder.

See also

Cylinder::R(const Vector&);

RandomInside()

Vector Cylinder::RandomInside

(

Random &

random = Random::R239

)

const

Generate a random vector inside the cylinder.

Parameters

random

Random number generator.

Rotated()

Cylinder Cylinder::Rotated

(

const Matrix &

r

)

const

Return a cylinder rotated by a given matrix.

Parameters

r	Rotation matrix.

Scale()

void Cylinder::Scale

(

const double &

s

)

Uniformly scales a cylinder.

Parameters

s	Scaling factor.

Scaled()

Cylinder Cylinder::Scaled

(

const double &

s

)

const

Return a scaled cylinder.

Parameters

s	Scaling factor.

Signed()

double Cylinder::Signed

(

const Vector &

p

)

const

Signed Euclidean distance between a point and a cylinder.

Parameters

p

Point.

Transformed()

Cylinder Cylinder::Transformed

(

const FrameScaled &

frame

)

const

Transformed cylinder.

Parameters

frame

Frame.

Translated()

Cylinder Cylinder::Translated

(

const Vector &

t

)

const

Return a cylinder translated by a given vector.

Parameters

t	Translation vector.

Friends And Related Function Documentation

operator<<

std::ostream & operator<< ( std::ostream &  s, const Cylinder &  cylinder  )

friend

Overloaded.

Parameters

s	Stream.
cylinder	The cylinder.