A 3D Plane of equation a*x + b*y + c*z + d = 0. More...

#include <easy3d/core/plane.h>

Public Types
typedef Vec< 2, FT >	Point2
	The type of the 2D point.

typedef Vec< 3, FT >	Point3
	The type of the 3D point.

typedef Vec< 3, FT >	Vector3
	The type of the 3D vector.

typedef GenericLine< 3, FT >	Line3
	The type of the 3D line.

typedef GenericPlane< FT >	thisclass
	The type of this class.

Public Member Functions
	GenericPlane (const Point3 &p1, const Point3 &p2, const Point3 &p3)
	Constructs a plane from three points `p1`, `p2`, and `p3`.

	GenericPlane (const Point3 &p, const Vector3 &n)
	Constructs a plane from a point `p` and the plane normal `n`.

	GenericPlane (FT a, FT b, FT c, FT d)
	Constructs a plane from its equation parameters `a`, `b`, `c`, and `d`.

	GenericPlane ()=default
	Default constructor.

FT	a () const
	Returns plane equation parameter `a`.

FT	b () const
	Returns plane equation parameter `b`.

FT	c () const
	Returns plane equation parameter `c`.

FT	d () const
	Returns plane equation parameter `d`.

FT &	operator[] (size_t idx)
	Returns the `idx_th` parameter of the plane equation.

const FT &	operator[] (size_t idx) const
	Returns the `idx_th` const parameter of the plane equation (const version).

Vector3	normal () const
	Returns the normal of the plane.

Point3	point () const
	Returns a point lying on this plane.

Vector3	base1 () const
	Returns the first ortho-base defined on this plane.

Vector3	base2 () const
	Returns the second ortho-base defined on this plane.

Point2	to_2d (const Point3 &p) const
	Converts a 3D point into a 2D point relative to the local coordinate system defined by the three orthogonal vectors base1(), base2(), and normal().

Point3	to_3d (const Point2 &p) const
	Converts a 2D point in the local coordinate system defined by the three orthogonal vectors base1(), base2(), and normal() into the 3D space.

Point3	projection (const Point3 &p) const
	The projection of a point `p` on this plane.

FT	value (const Point3 &p) const
	Evaluates the plane (i.e., computes the value of a * x + b * y + c * z + d) for the given point `p`.

FT	squared_distance (const Point3 &p) const
	Computes the squared distance of a point `p` to this plane.

bool	intersect (const Line3 &line, Point3 &p) const
	Tests if a `line` intersects with this plane (both line and the plane are unlimited).

bool	intersect (const Line3 &line) const
	Tests if a `line` intersects with this plane (both line and the plane are unlimited).

bool	intersect (const Point3 &s, const Point3 &t, Point3 &p) const
	Tests if a `line` segment (given by its two end points `s` and `t`) intersects with this plane.

bool	intersect (const Point3 &s, const Point3 &t) const
	Tests if a `line` segment (given by its two end points `s` and `t`) intersects with this plane.

bool	intersect (const thisclass &another, Line3 &line) const
	Tests if this plane intersects with `another` plane.

bool	intersect (const thisclass &another) const
	Tests if this plane intersects with `another` plane.

int	orient (const Point3 &p) const
	Determines the relative orientation of a point with respect to this plane.

const FT *	data () const
	Returns the constant memory address of the coefficients.

FT *	data ()
	Returns the memory address of the coefficients.

	operator const FT * () const
	Conversion operator returning the constant memory address of the coefficients. This is very convenient to pass a plane as a parameter to functions.

	operator FT * ()
	Conversion operator returning the memory address of the coefficients. This is very convenient to pass a plane as a parameter to functions.

Detailed Description

template<typename FT>
class easy3d::GenericPlane< FT >

A 3D Plane of equation a*x + b*y + c*z + d = 0.

Template Parameters

FT	The scalar type for plane coefficients.

Constructor & Destructor Documentation

◆ GenericPlane() [1/3]

template<typename FT>

GenericPlane	(	const Point3 &	p1,
		const Point3 &	p2,
		const Point3 &	p3 )

Constructs a plane from three points p1, p2, and p3.

Parameters

p1	The first point.
p2	The second point.
p3	The third point.

◆ GenericPlane() [2/3]

template<typename FT>

GenericPlane	(	const Point3 &	p,
		const Vector3 &	n )

Constructs a plane from a point p and the plane normal n.

Parameters

p	The point on the plane.
n	The normal vector of the plane.

◆ GenericPlane() [3/3]

template<typename FT>

GenericPlane	(	FT	a,
		FT	b,
		FT	c,
		FT	d )

inline

Constructs a plane from its equation parameters a, b, c, and d.

Parameters

a	The coefficient for x.
b	The coefficient for y.
c	The coefficient for z.
d	The constant term.

Member Function Documentation

◆ a()

template<typename FT>

FT a ( ) const

inline

Returns plane equation parameter a.

Returns: The coefficient a.

◆ b()

template<typename FT>

FT b ( ) const

inline

Returns plane equation parameter b.

Returns: The coefficient b.

◆ base1()

template<typename FT>

GenericPlane< FT >::Vector3 base1 ( ) const

Returns the first ortho-base defined on this plane.

Returns: The first ortho-base vector.

◆ base2()

template<typename FT>

GenericPlane< FT >::Vector3 base2 ( ) const

Returns the second ortho-base defined on this plane.

Returns: The second ortho-base vector.

◆ c()

template<typename FT>

FT c ( ) const

inline

Returns plane equation parameter c.

Returns: The coefficient c.

◆ d()

template<typename FT>

FT d ( ) const

inline

Returns plane equation parameter d.

Returns: The coefficient d.

◆ data() [1/2]

template<typename FT>

FT * data ( )

inline

Returns the memory address of the coefficients.

Returns: The memory address of the coefficients.

◆ data() [2/2]

template<typename FT>

const FT * data ( ) const

inline

Returns the constant memory address of the coefficients.

Returns: The constant memory address of the coefficients.

◆ intersect() [1/6]

template<typename FT>

bool intersect ( const Line3 & line ) const

Tests if a line intersects with this plane (both line and the plane are unlimited).

Parameters

line	The line to test.

Returns: true if they intersect, false otherwise (the line is parallel to this plane).

◆ intersect() [2/6]

template<typename FT>

bool intersect	(	const Line3 &	line,
		Point3 &	p ) const

Tests if a line intersects with this plane (both line and the plane are unlimited).

Parameters

line	The line to test.
p	The intersection point if they intersect.

Returns: true if they intersect, false otherwise (the line is parallel to this plane).

◆ intersect() [3/6]

template<typename FT>

bool intersect	(	const Point3 &	s,
		const Point3 &	t ) const

Tests if a line segment (given by its two end points s and t) intersects with this plane.

Parameters

s	The start point of the line segment.
t	The end point of the line segment.

Returns: true if they intersect, false otherwise (the two end points of the line segment lie on the same side of the plane).

◆ intersect() [4/6]

template<typename FT>

bool intersect	(	const Point3 &	s,
		const Point3 &	t,
		Point3 &	p ) const

Tests if a line segment (given by its two end points s and t) intersects with this plane.

Parameters

s	The start point of the line segment.
t	The end point of the line segment.
p	The intersection point if they intersect.

Returns: true if they intersect, false otherwise (the two end points of the line segment lie on the same side of the plane).

◆ intersect() [5/6]

template<typename FT>

bool intersect ( const thisclass & another ) const

Tests if this plane intersects with another plane.

Parameters

another The other plane to test.

Returns: true if they intersect, false otherwise (the two planes are parallel).

◆ intersect() [6/6]

template<typename FT>

bool intersect	(	const thisclass &	another,
		Line3 &	line ) const

Tests if this plane intersects with another plane.

Parameters

another	The other plane to test.
line	The intersecting line if they intersect.

Returns: true if they intersect, false otherwise (the two planes are parallel).

◆ normal()

template<typename FT>

GenericPlane< FT >::Vector3 normal ( ) const

Returns the normal of the plane.

Returns: The normal vector of the plane.

◆ operator const FT *()

template<typename FT>

operator const FT * ( ) const

inline

Conversion operator returning the constant memory address of the coefficients. This is very convenient to pass a plane as a parameter to functions.

Returns: The constant memory address of the coefficients.

◆ operator FT *()

template<typename FT>

operator FT * ( )

inline

Conversion operator returning the memory address of the coefficients. This is very convenient to pass a plane as a parameter to functions.

Returns: The memory address of the coefficients.

◆ operator[]() [1/2]

template<typename FT>

FT & operator[] ( size_t idx )

inline

Returns the idx_th parameter of the plane equation.

Parameters

idx	The index of the parameter.

Returns: The idx_th parameter.

◆ operator[]() [2/2]

template<typename FT>

const FT & operator[] ( size_t idx ) const

inline

Returns the idx_th const parameter of the plane equation (const version).

Parameters

idx	The index of the parameter.

Returns: The idx_th const parameter.

◆ orient()

template<typename FT>

int orient ( const Point3 & p ) const

Determines the relative orientation of a point with respect to this plane.

Parameters

p	The point to test.

Returns: 1 if the point is on the positive side, -1 if on the negative side, 0 if on the plane.

◆ point()

template<typename FT>

GenericPlane< FT >::Point3 point ( ) const

Returns a point lying on this plane.

Note: It is a fixed point (anytime you call this function it returns the same point).

Returns: A point on the plane.

◆ projection()

template<typename FT>

GenericPlane< FT >::Point3 projection ( const Point3 & p ) const

The projection of a point p on this plane.

Parameters

p	The point to project.

Returns: The projected point on the plane.

◆ squared_distance()

template<typename FT>

FT squared_distance ( const Point3 & p ) const

Computes the squared distance of a point p to this plane.

Parameters

p	The point to compute the distance to.

Returns: The squared distance to the plane.

◆ to_2d()

template<typename FT>

GenericPlane< FT >::Point2 to_2d ( const Point3 & p ) const

Converts a 3D point into a 2D point relative to the local coordinate system defined by the three orthogonal vectors base1(), base2(), and normal().

Parameters

p	The 3D point to convert.

Returns: The corresponding 2D point.

Note: After 3D->2D and then 2D->3D conversion, the resulted 3D point remains unchanged ONLY IF the input point lies on the plane. In case the original 3D point does not lie on the plane, the resulted 3D point will have coordinates equal to the projection of the input point onto the plane.

◆ to_3d()

template<typename FT>

GenericPlane< FT >::Point3 to_3d ( const Point2 & p ) const

Converts a 2D point in the local coordinate system defined by the three orthogonal vectors base1(), base2(), and normal() into the 3D space.

Parameters

p	The 2D point to convert.

Returns: The corresponding 3D point.

Note: After 3D->2D and then 2D->3D conversion, the resulted 3D point remains unchanged ONLY IF the input point lies on the plane. In case the original 3D point does not lie on the plane, the resulted 3D point will have coordinates equal to the projection of the input point onto the plane.

◆ value()

template<typename FT>

FT value ( const Point3 & p ) const

inline

Evaluates the plane (i.e., computes the value of a * x + b * y + c * z + d) for the given point p.

Parameters

p	The point to evaluate.

Returns: The evaluated value.

The documentation for this class was generated from the following file:

G:/3_code/Easy3D/easy3d/core/plane.h

Public Types

Public Member Functions

Detailed Description

Constructor & Destructor Documentation

◆ GenericPlane() [1/3]

◆ GenericPlane() [2/3]

◆ GenericPlane() [3/3]

Member Function Documentation

◆ a()

◆ b()

◆ base1()

◆ base2()

◆ c()

◆ d()

◆ data() [1/2]

◆ data() [2/2]

◆ intersect() [1/6]

◆ intersect() [2/6]

◆ intersect() [3/6]

◆ intersect() [4/6]

◆ intersect() [5/6]

◆ intersect() [6/6]

◆ normal()

◆ operator const FT *()

◆ operator FT *()

◆ operator[]() [1/2]

◆ operator[]() [2/2]

◆ orient()

◆ point()

◆ projection()

◆ squared_distance()

◆ to_2d()

◆ to_3d()

◆ value()