Vec3D Functions

API functions that utilize the vec3d class are grouped here. For details of the class, including member functions, see vec3d. Click here to return to the main page. More...

Classes
class	vec3d

Functions
vec3d	operator+ (const vec3d &a, const vec3d &b)
vec3d	operator- (const vec3d &a, const vec3d &b)
vec3d	operator* (const vec3d &a, double b)
vec3d	operator* (const vec3d &a, const vec3d &b)
vec3d	operator/ (const vec3d &a, double b)
vec3d &	vec3d::set_vec (const std::vector< double > &a)
vec3d &	vec3d::set_refx (const vec3d &a)
vec3d &	vec3d::set_refy (const vec3d &a)
vec3d &	vec3d::set_refz (const vec3d &a)
void	vec3d::offset_i (double offset, int idir)
double	vec3d::magsq () const
int	vec3d::major_comp () const
int	vec3d::minor_comp () const
bool	vec3d::isnan () const
bool	vec3d::isinf () const
bool	vec3d::isfinite () const
void	vec3d::print (const char *label="") const
double	dist (const vec3d &a, const vec3d &b)
double	dist_squared (const vec3d &a, const vec3d &b)
double	dot (const vec3d &a, const vec3d &b)
vec3d	cross (const vec3d &a, const vec3d &b)
double	angle (const vec3d &a, const vec3d &b)
double	signed_angle (const vec3d &a, const vec3d &b, const vec3d &ref)
double	cos_angle (const vec3d &a, const vec3d &b)
vec3d	RotateArbAxis (const vec3d &p, double theta, const vec3d &r)
string	std::to_string (const vec3d &v)
void	FitPlane (const std::vector< vec3d > &pts, vec3d &cen, vec3d &norm)
vec3d	compsum (const std::vector< vec3d > &x)

Detailed Description

---

Class Documentation

vec3d

class vec3d

vec3d is typically used to describe coordinate points and vectors in 3D space. All 3 elements in the vector are of type double.

Definition at line 237 of file Vec3d.h.

Public Member Functions
	vec3d (double xx, double yy, double zz)
	vec3d (const threed_point_type &a)
	vec3d (const double a[3])
	vec3d (const float a[3])
	vec3d (const std::vector< double > &a)
vec3d &	operator= (const vec2d &a)
vec3d &	operator= (double a)
vec3d &	operator= (const threed_point_type &a)
double &	operator[] (int i)
const double &	operator[] (int i) const
vec2d	as_vec2d_xy ()
vec3d &	set_xyz (double xx, double yy, double zz)
vec3d &	set_vec (const std::vector< double > &a)
vec3d &	set_arr (const double a[])
vec3d &	set_arr (const float a[])
vec3d &	set_x (double xx)
vec3d &	set_y (double yy)
vec3d &	set_z (double zz)
vec3d &	set_refx (const vec3d &a)
vec3d &	set_refy (const vec3d &a)
vec3d &	set_refz (const vec3d &a)
void	get_pnt (double pnt[3]) const
void	get_pnt (float pnt[3]) const
void	get_pnt (threed_point_type &pnt) const
double	x () const
double	y () const
double	z () const
double *	data ()
void	Transform (const Matrix4d &m)
void	FlipNormal ()
void	rotate_x (double theta)
void	rotate_y (double theta)
void	rotate_z (double theta)
void	scale_x (double scale)
void	scale_y (double scale)
void	scale_z (double scale)
void	offset_x (double offset)
void	offset_y (double offset)
void	offset_z (double offset)
void	offset_i (double offset, int idir)
vec3d	reflect_xy () const
vec3d	reflect_xz () const
vec3d	reflect_yz () const
vec3d	swap_xy () const
vec3d	swap_xz () const
vec3d	swap_yz () const
vec3d &	operator+= (const vec3d &b)
vec3d &	operator-= (const vec3d &b)
vec3d &	operator*= (double b)
vec3d &	operator+= (double b[])
vec3d &	operator-= (double b[])
vec3d &	operator+= (float b[])
vec3d &	operator-= (float b[])
double	mag () const
double	magsq () const
void	normalize ()
int	major_comp () const
int	minor_comp () const
bool	isnan () const
bool	isinf () const
bool	isfinite () const
void	print (const char *label="") const
Public Attributes
double	v [3]
Friends
vec3d	operator+ (const vec3d &a, const vec3d &b)
vec3d	operator- (const vec3d &a, const vec3d &b)
vec3d	operator* (const vec3d &a, double b)
vec3d	operator* (double b, const vec3d &a)
vec3d	operator* (const vec3d &a, const vec3d &b)
vec3d	operator/ (const vec3d &a, double b)
vec3d	operator- (const vec3d &in)
bool	operator== (const vec3d &a, const vec3d &b)
bool	operator!= (const vec3d &a, const vec3d &b)
double	dist (const vec3d &a, const vec3d &b)
double	dist_squared (const vec3d &a, const vec3d &b)
double	dot (const vec3d &a, const vec3d &b)
vec3d	cross (const vec3d &a, const vec3d &b)
double	angle (const vec3d &a, const vec3d &b)
double	signed_angle (const vec3d &a, const vec3d &b, const vec3d &ref)
double	cos_angle (const vec3d &a, const vec3d &b)
double	radius_of_circle (const vec3d &p1, const vec3d &p2, const vec3d &p3)
void	center_of_circle (const vec3d &p1, const vec3d &p2, const vec3d &p3, vec3d &center)
bool	triangle_plane_intersect_test (const vec3d &org, const vec3d &norm, const vec3d &p1, const vec3d &p2, const vec3d &p3)
double	triangle_plane_minimum_dist (const vec3d &org, const vec3d &norm, const vec3d &p1, const vec3d &p2, const vec3d &p3, vec3d &pa, vec3d &pb)
double	triangle_plane_maximum_dist (const vec3d &org, const vec3d &norm, const vec3d &p1, const vec3d &p2, const vec3d &p3, vec3d &pa, vec3d &pb)
bool	plane_plane_intersection (const vec3d &p0, const vec3d &n0, const vec3d &p1, const vec3d &n1, vec3d &p, vec3d &v)
double	angle_pnt_2_plane (const vec3d &ptplane, vec3d norm, const vec3d &ptaxis, vec3d axis, const vec3d &pt, int ccw, vec3d &prot)
void	angle_pnt_2_plane (const vec3d &ptplane, vec3d norm, const vec3d &ptaxis, vec3d axis, const vec3d &pt, int ccw, vec3d &prot1, vec3d &prot2, double &theta1, double &theta2)
double	signed_dist_pnt_2_plane (const vec3d &org, const vec3d &norm, const vec3d &pnt)
double	dist_pnt_2_plane (const vec3d &org, const vec3d &norm, const vec3d &pnt)
double	dist_pnt_2_line (const vec3d &line_pt1, const vec3d &line_pt2, const vec3d &pnt)
double	dist_pnt_2_ray (const vec3d &line_pt1, const vec3d &dir_unit_vec, const vec3d &pnt)
vec3d	proj_u_on_v (const vec3d &u, const vec3d &v)
vec3d	proj_pnt_on_line_seg (const vec3d &line_pt1, const vec3d &line_pt2, const vec3d &pnt)
vec3d	proj_pnt_on_ray (const vec3d &line_pt1, const vec3d &line_dir, const vec3d &pnt)
vec3d	proj_pnt_on_ray (const vec3d &line_pt1, const vec3d &line_dir, const vec3d &pnt, double &t)
vec3d	proj_pnt_on_line (const vec3d &line_pt1, const vec3d &line_pt2, const vec3d &pnt)
vec3d	proj_pnt_to_plane (const vec3d &org, const vec3d &plane_ln1, const vec3d &plane_ln2, const vec3d &pnt)
vec3d	proj_vec_to_plane (const vec3d &vec, const vec3d &norm)
int	tri_seg_intersect (const vec3d &A, const vec3d &B, const vec3d &C, const vec3d &D, const vec3d &E, double &u, double &w, double &t)
int	tri_ray_intersect (const vec3d &A, const vec3d &B, const vec3d &C, const vec3d &D, const vec3d &E, double &u, double &w, double &t)
int	plane_ray_intersect (const vec3d &A, const vec3d &B, const vec3d &C, const vec3d &D, const vec3d &E, double &t)
int	plane_ray_intersect (const vec3d &orig, const vec3d &norm, const vec3d &D, const vec3d &E, double &t)
int	ray_ray_intersect (const vec3d &A, const vec3d &B, const vec3d &C, const vec3d &D, vec3d &int_pnt1, vec3d &int_pnt2)
double	tetra_volume (const vec3d &A, const vec3d &B, const vec3d &C)
double	area (const vec3d &A, const vec3d &B, const vec3d &C)
double	poly_area (const std::vector< vec3d > &pnt_vec)
double	dist3D_Segment_to_Segment (const vec3d &S1P0, const vec3d &S1P1, const vec3d &S2P0, const vec3d &S2P1)
double	dist3D_Segment_to_Segment (const vec3d &S1P0, const vec3d &S1P1, const vec3d &S2P0, const vec3d &S2P1, double *Lt, vec3d *Ln, double *St, vec3d *Sn)
double	nearSegSeg (const vec3d &L0, const vec3d &L1, const vec3d &S0, const vec3d &S1, double *Lt, vec3d *Ln, double *St, vec3d *Sn)
double	pointLineDistSquared (const vec3d &p, const vec3d &lp0, const vec3d &lp1, double &t, vec3d &pon)
double	pointSegDistSquared (const vec3d &p, const vec3d &sp0, const vec3d &sp1, double &t, vec3d &pon)
vec3d	point_on_line (const vec3d &lp0, const vec3d &lp1, const double &t)
vec2d	MapToPlane (const vec3d &p, const vec3d &planeOrig, const vec3d &planeVec1, const vec3d &planeVec2)
vec3d	MapFromPlane (const vec2d &uw, const vec3d &planeOrig, const vec3d &planeVec1, const vec3d &planeVec2)
int	plane_half_space (const vec3d &planeOrig, const vec3d &planeNorm, const vec3d &pnt)
bool	line_line_intersect (const vec3d &p1, const vec3d &p2, const vec3d &p3, const vec3d &p4, double *s, double *t)
vec3d	RotateArbAxis (const vec3d &p, double theta, const vec3d &r)
bool	PtInTri (const vec3d &v0, const vec3d &v1, const vec3d &v2, const vec3d &p)
vec3d	BarycentricWeights (const vec3d &v0, const vec3d &v1, const vec3d &v2, const vec3d &p)
void	BilinearWeights (const vec3d &p0, const vec3d &p1, const vec3d &p, std::vector< double > &weights)
double	tri_tri_min_dist (const vec3d &v0, const vec3d &v1, const vec3d &v2, const vec3d &v3, const vec3d &v4, const vec3d &v5, vec3d &p1, vec3d &p2)
double	pnt_tri_min_dist (const vec3d &v0, const vec3d &v1, const vec3d &v2, const vec3d &pnt, vec3d &pnearest)
vec3d	slerp (const vec3d &a, const vec3d &b, const double &t)
void	printpt (const vec3d &v)
vec3d	ToSpherical (const vec3d &v)
vec3d	ToSpherical2 (const vec3d &v, const vec3d &vdet)
vec3d	ToCartesian (const vec3d &v)
void	FitPlane (const std::vector< vec3d > &pts, vec3d &cen, vec3d &norm)

Member Function Documentation

data()

double * vec3d::data ( )

inline

Definition at line 601 of file Vec3d.h.

FlipNormal()

void vec3d::FlipNormal ( )

inline

Definition at line 612 of file Vec3d.h.

get_pnt() [1/2]

void vec3d::get_pnt ( double pnt[3] ) const

inline

Definition at line 490 of file Vec3d.h.

get_pnt() [2/2]

void vec3d::get_pnt ( float pnt[3] ) const

inline

Definition at line 496 of file Vec3d.h.

mag()

double vec3d::mag

(

)

const

Get the magnitude of a vec3d

//==== Test Vec3d ====//
vec3d a();                                // Default Constructor
 
//==== Test Mag ====//
a.set_xyz( 1.0, 2.0, 3.0 );
 
if ( abs( a.mag() - sqrt( 14 ) ) > 1e-6 )                        { Print( "---> Error: Vec3d Mag " ); }

Returns

Magnitude

normalize()

void vec3d::normalize

(

)

Normalize the vec3d

//==== Test Vec3d ====//
vec3d a(), b(), c();                                // Default Constructor
 
//==== Test Cross ====//
a.set_xyz( 4.0, 0.0, 0.0 );
b.set_xyz( 0.0, 3.0, 0.0 );
 
c = cross( a, b );
 
c.normalize();

offset_x()

void vec3d::offset_x ( double offset )

inline

Offset the X coordinate of the vec3d

//==== Test Vec3d ====//
vec3d a();                                // Default Constructor
 
//===== Test Offset ====//
a.set_xyz( 2.0, 2.0, 2.0 );
 
a.offset_x( 10.0 );

Parameters

[in]

offset

Offset for the X value

Definition at line 830 of file Vec3d.h.

offset_y()

void vec3d::offset_y ( double offset )

inline

Offset the Y coordinate of the vec3d

//==== Test Vec3d ====//
vec3d a();                                // Default Constructor
 
//===== Test Offset ====//
a.set_xyz( 2.0, 2.0, 2.0 );
 
a.offset_y( 10.0 );

Parameters

[in]

offset

Offset for the Y value

Definition at line 862 of file Vec3d.h.

offset_z()

void vec3d::offset_z ( double offset )

inline

Offset the Z coordinate of the vec3d

//==== Test Vec3d ====//
vec3d a();                                // Default Constructor
 
//===== Test Offset ====//
a.set_xyz( 2.0, 2.0, 2.0 );
 
a.offset_z( 10.0 );

Parameters

[in]

offset

Offset for the Z value

Definition at line 894 of file Vec3d.h.

operator[]() [1/2]

double & vec3d::operator[] ( int i )

inline

Definition at line 266 of file Vec3d.h.

operator[]() [2/2]

const double & vec3d::operator[] ( int i ) const

inline

Definition at line 270 of file Vec3d.h.

reflect_xy()

vec3d vec3d::reflect_xy ( ) const

inline

Reflect the vec3d across the XY plane

//==== Test Vec3d ====//
vec3d a(), b();                                // Default Constructor
 
//===== Test Reflect ====//
a.set_xyz( 1.0, 2.0, 3.0 );
 
b = a.reflect_xy();

Returns

Reflected vec3d

Definition at line 955 of file Vec3d.h.

reflect_xz()

vec3d vec3d::reflect_xz ( ) const

inline

Reflect the vec3d across the XZ plane

//==== Test Vec3d ====//
vec3d a(), b();                                // Default Constructor
 
//===== Test Reflect ====//
a.set_xyz( 1.0, 2.0, 3.0 );
 
b = a.reflect_xz();

Returns

Reflected vec3d

Definition at line 988 of file Vec3d.h.

reflect_yz()

vec3d vec3d::reflect_yz ( ) const

inline

Reflect the vec3d across the YZ plane

//==== Test Vec3d ====//
vec3d a(), b();                                // Default Constructor
 
//===== Test Reflect ====//
a.set_xyz( 1.0, 2.0, 3.0 );
 
b = a.reflect_yz();

Returns

Reflected vec3d

Definition at line 1021 of file Vec3d.h.

rotate_x()

void vec3d::rotate_x

(

double

theta

)

Rotate the vec3d about the X axis.

//==== Test Vec3d ====//
vec3d a();                                // Default Constructor
float PI = 3.14;
 
a.set_xyz( 1.0, 0.0, 0.0 );
 
a.rotate_x( 0.5 * PI );

Parameters

[in]

theta

double Rotation angle in radians

rotate_y()

void vec3d::rotate_y

(

double

theta

)

Rotate the vec3d about the Y axis.

//==== Test Vec3d ====//
vec3d a();                                // Default Constructor
float PI = 3.14;
 
a.set_xyz( 1.0, 0.0, 0.0 );
 
a.rotate_y( 0.5 * PI );

Parameters

[in]

theta

double Rotation angle in radians

rotate_z()

void vec3d::rotate_z

(

double

theta

)

Rotate the vec3d about the Z axis.

//==== Test Vec3d ====//
vec3d a();                                // Default Constructor
float PI = 3.14;
 
a.set_xyz( 1.0, 0.0, 0.0 );
 
a.rotate_z( 0.5 * PI );

Parameters

[in]

theta

double Rotation angle in radians

scale_x()

void vec3d::scale_x ( double scale )

inline

Scale the X coordinate of the vec3d

//==== Test Vec3d ====//
vec3d a();                                // Default Constructor
 
//===== Test Scale ====//
a.set_xyz( 2.0, 2.0, 2.0 );
 
a.scale_x( 2.0 );

Parameters

[in]

scale

Scaling factor for the X value

Definition at line 733 of file Vec3d.h.

scale_y()

void vec3d::scale_y ( double scale )

inline

Scale the Y coordinate of the vec3d

//==== Test Vec3d ====//
vec3d a();                                // Default Constructor
 
//===== Test Scale ====//
a.set_xyz( 2.0, 2.0, 2.0 );
 
a.scale_y( 2.0 );

Parameters

[in]

scale

Scaling factor for the Y value

Definition at line 765 of file Vec3d.h.

scale_z()

void vec3d::scale_z ( double scale )

inline

Scale the Z coordinate of the vec3d

//==== Test Vec3d ====//
vec3d a();                                // Default Constructor
 
//===== Test Scale ====//
a.set_xyz( 2.0, 2.0, 2.0 );
 
a.scale_z( 2.0 );

Parameters

[in]

scale

Scaling factor for the Z value

Definition at line 797 of file Vec3d.h.

set_x()

vec3d & vec3d::set_x

(

double

xx

)

Set the X coordinate (index 0) of the vec3d

//==== Test Vec3d ====//
vec3d a();                                // Default Constructor
 
a.set_x( 2.0 );

Parameters

[in]

xx

New X value

Returns

Updated vec3d

set_xyz()

vec3d & vec3d::set_xyz	(	double	xx,
		double	yy,
		double	zz )

Set all three elements of the vec3d vector

//==== Test Vec3d ====//
vec3d a();                                // Default Constructor
 
a.set_xyz( 2.0, 4.0, 6.0 );

Parameters

[in]	xx	New X value
[in]	yy	New Y value
[in]	zz	New Z value

Returns

Updated vec3d

set_y()

vec3d & vec3d::set_y

(

double

yy

)

Set the Y coordinate (index 1) of the vec3d

//==== Test Vec3d ====//
vec3d a();                                // Default Constructor
 
a.set_y( 4.0 );

Parameters

[in]

yy

New Y value

Returns

Updated vec3d

set_z()

vec3d & vec3d::set_z

(

double

zz

)

Set the z coordinate (index 2) of the vec3d

//==== Test Vec3d ====//
vec3d a();                                // Default Constructor
 
a.set_z( 6.0 );

Parameters

[in]

zz

in double new z value

Returns

vec3d result

swap_xy()

vec3d vec3d::swap_xy ( ) const

inline

Definition at line 1027 of file Vec3d.h.

swap_xz()

vec3d vec3d::swap_xz ( ) const

inline

Definition at line 1031 of file Vec3d.h.

swap_yz()

vec3d vec3d::swap_yz ( ) const

inline

Definition at line 1035 of file Vec3d.h.

x()

double vec3d::x ( ) const

inline

Get the X coordinate (index 0) of the vec3d

vec3d a();                                // Default Constructor
 
a.set_xyz( 2.0, 4.0, 6.0 );
 
if ( abs( a.x() - 2.0 ) > 1e-12 )                    { Print( "ERROR: x" ); __failure++; }
 
if ( abs( a[0] - 2.0 ) > 1e-12 )                     { Print( "ERROR: x" ); __failure++; }

Returns

X value

Definition at line 531 of file Vec3d.h.

y()

double vec3d::y ( ) const

inline

Get the Y coordinate (index 1) of the vec3d

vec3d a();                                // Default Constructor
 
a.set_xyz( 2.0, 4.0, 6.0 );
 
if ( abs( a.y() - 4.0 ) > 1e-12 )                    { Print( "ERROR: y" ); __failure++; }
 
if ( abs( a[1] - 4.0 ) > 1e-12 )                     { Print( "ERROR: y" ); __failure++; }

Returns

Y value

Definition at line 563 of file Vec3d.h.

z()

double vec3d::z ( ) const

inline

Get the Z coordinate (index 2) of the vec3d

vec3d a();                                // Default Constructor
 
a.set_xyz( 2.0, 4.0, 6.0 );
 
if ( abs( a.z() - 6.0 ) > 1e-12 )                    { Print( "ERROR: z" ); __failure++; }
 
if ( abs( a[2] - 6.0 ) > 1e-12 )                     { Print( "ERROR: z" ); __failure++; }

Returns

Z value

Definition at line 595 of file Vec3d.h.

Friends And Related Symbol Documentation

angle

double angle ( const vec3d & a, const vec3d & b )

friend

Calculate the angle between two vec3d inputs (dot product divided by their magnitudes multiplied)

//==== Test Vec3d ====//
vec3d a(), b();                                // Default Constructor
float PI = 3.14159265359;
 
//==== Test Angle ====//
a.set_xyz( 1.0, 1.0, 0.0 );
b.set_xyz( 1.0, 0.0, 0.0 );
 
if ( abs( angle( a, b ) - PI / 4 ) > 1e-6 )                    { Print( "---> Error: Vec3d Angle " ); }

Parameters

[in]	a	First vec3d
[in]	b	Second vec3d

Returns

Angle in Radians

cos_angle

double cos_angle ( const vec3d & a, const vec3d & b )

friend

Calculate the cosine of angle between two vec3d inputs

vec3d pnt = vec3d( 2, 4, 6);
 
vec3d line_pt1(), line_pt2();
 
line_pt1.set_z( 4 );
line_pt2.set_y( 3 );
 
vec3d p_ln1 = pnt - line_pt1;
 
vec3d ln2_ln1 = line_pt2 - line_pt1;
 
double numer =  cos_angle( p_ln1, ln2_ln1 ) * p_ln1.mag();

See also

angle

Parameters

[in]	a	First vec3d
[in]	b	Second vec3d

Returns

Angle in Radians

cross

vec3d cross ( const vec3d & a, const vec3d & b )

friend

Calculate the cross product between two vec3d inputs

//==== Test Vec3d ====//
vec3d a(), b(), c();                                // Default Constructor
 
//==== Test Cross ====//
a.set_xyz( 4.0, 0.0, 0.0 );
b.set_xyz( 0.0, 3.0, 0.0 );
 
c = cross( a, b );
 
c.normalize();

Parameters

[in]	a	First vec3d
[in]	b	Second vec3d

Returns

Cross product

dist

double dist ( const vec3d & a, const vec3d & b )

friend

Calculate the distance between two vec3d inputs

//==== Test Vec3d ====//
vec3d a(), b();                                // Default Constructor
 
//==== Test Dist ====//
a.set_xyz( 2.0, 2.0, 2.0 );
b.set_xyz( 3.0, 4.0, 5.0 );
 
double d = dist( a, b );
 
if ( abs( d - sqrt( 14 ) ) > 1e-6 )    { Print( "---> Error: Vec3d Dist " ); }

See also

dist_squared

Parameters

[in]	a	First vec3d
[in]	b	Second vec3d

Returns

Distance

dist_squared

double dist_squared ( const vec3d & a, const vec3d & b )

friend

Calculate distance squared between two vec3d inputs

//==== Test Vec3d ====//
vec3d a(), b();                                // Default Constructor
 
//==== Test Dist ====//
a.set_xyz( 2.0, 2.0, 2.0 );
b.set_xyz( 3.0, 4.0, 5.0 );
 
double d2 = dist_squared( a, b );
 
if ( abs( d2 - 14 ) > 1e-6 )    { Print( "---> Error: Vec3d Dist " ); }

See also

dist

Parameters

[in]	a	First vec3d
[in]	b	Second vec3d

Returns

Distance squared

dot

double dot ( const vec3d & a, const vec3d & b )

friend

Calculate the dot product between two vec3d inputs

//==== Test Vec3d ====//
vec3d a(), b();                                // Default Constructor
 
//==== Test Dot ====//
a.set_xyz( 1.0, 2.0, 3.0 );
b.set_xyz( 2.0, 3.0, 4.0 );
 
if ( abs( dot( a, b ) - 20 ) > 1e-6 )                            { Print( "---> Error: Vec3d Dot " ); }

Parameters

[in]	a	First vec3d
[in]	b	Second vec3d

Returns

Dot product

FitPlane

void FitPlane ( const std::vector< vec3d > & pts, vec3d & cen, vec3d & norm )

friend

Fit a plane through a set of points by least squares, reporting a point on the plane and its normal.

Parameters

[in]	pts	vector<vec3d> Points to fit the plane through
[out]	cen	vec3d A point on the fitted plane
[out]	norm	vec3d Normal of the fitted plane

operator* [1/2]

vec3d operator* ( const vec3d & a, const vec3d & b )

friend

Scalar multiplication operator for a vec3d, performed by the multiplication of each vec3d component and the scalar

vec3d a();                                // Default Constructor
 
a.set_xyz( 1.0, 2.0, 3.0 );
 
double b = 1.5;
 
vec3d c = a * b;
 
Print( "a * b = ", false );
 
Print( c );

operator* [2/2]

vec3d operator* ( const vec3d & a, double b )

friend

Scalar multiplication operator for a vec3d, performed by the multiplication of each vec3d component and the scalar

vec3d a();                                // Default Constructor
 
a.set_xyz( 1.0, 2.0, 3.0 );
 
double b = 1.5;
 
vec3d c = a * b;
 
Print( "a * b = ", false );
 
Print( c );

operator+

vec3d operator+ ( const vec3d & a, const vec3d & b )

friend

Addition operator for two vec3d objects, performed by the addition of each corresponding component

vec3d a(), b();                                // Default Constructor
 
a.set_xyz( 1.0, 2.0, 3.0 );
b.set_xyz( 4.0, 5.0, 6.0 );
 
vec3d c = a + b;
 
Print( "a + b = ", false );
 
Print( c );

operator-

vec3d operator- ( const vec3d & a, const vec3d & b )

friend

Subtraction operator for two vec3d objects, performed by the subtraction of each corresponding component

vec3d a(), b();                                // Default Constructor
 
a.set_xyz( 1.0, 2.0, 3.0 );
b.set_xyz( 4.0, 5.0, 6.0 );
 
vec3d c = a - b;
 
Print( "a - b = ", false );
 
Print( c );

operator/

vec3d operator/ ( const vec3d & a, double b )

friend

Scalar division operator for a vec3d, performed by the division of of each vec3d component by the scalar

vec3d a();                                // Default Constructor
 
a.set_xyz( 1.0, 2.0, 3.0 );
 
double b = 1.5;
 
vec3d c = a / b;
 
Print( "a / b = ", false );
 
Print( c );

RotateArbAxis

vec3d RotateArbAxis ( const vec3d & p, double theta, const vec3d & r )

friend

Rotate a input point by specified angle around an arbitrary axis. Assume right hand coordinate system

//==== Test Vec3d ====//
vec3d a(), b(), c();                                // Default Constructor
float PI = 3.14;
 
//==== Test Rotate ====//
a.set_xyz( 1.0, 1.0, 0.0 );
b.set_xyz( 1.0, 0.0, 0.0 );
c.set_xyz( 0.0, 0.0, 1.0 );
 
c = RotateArbAxis( b, PI, a );

Parameters

[in]	p	Coordinate point to rotate
[in]	theta	Angle of rotation in Radians
[in]	r	Reference axis for rotation

Returns

Coordinates of rotated point

signed_angle

double signed_angle ( const vec3d & a, const vec3d & b, const vec3d & ref )

friend

Calculate the signed angle between two vec3d inputs (dot product divided by their magnitudes multiplied) and an input reference axis

//==== Test Vec3d ====//
vec3d a(), b(), c();                                // Default Constructor
float PI = 3.14159265359;
 
//==== Test Angle ====//
a.set_xyz( 1.0, 1.0, 0.0 );
b.set_xyz( 1.0, 0.0, 0.0 );
c.set_xyz( 0.0, 0.0, 1.0 );
 
if ( abs( signed_angle( a, b, c ) - -PI / 4 ) > 1e-6 )            { Print( "---> Error: Vec3d SignedAngle " ); }

Parameters

[in]	a	First vec3d
[in]	b	Second vec3d
[in]	ref	Reference axis

Returns

Angle in Radians

Member Data Documentation

v

double vec3d::v[3]

Definition at line 243 of file Vec3d.h.

Function Documentation

angle()

double angle	(	const vec3d &	a,
		const vec3d &	b )

Calculate the angle between two vec3d inputs (dot product divided by their magnitudes multiplied)

//==== Test Vec3d ====//
vec3d a(), b();                                // Default Constructor
float PI = 3.14159265359;
 
//==== Test Angle ====//
a.set_xyz( 1.0, 1.0, 0.0 );
b.set_xyz( 1.0, 0.0, 0.0 );
 
if ( abs( angle( a, b ) - PI / 4 ) > 1e-6 )                    { Print( "---> Error: Vec3d Angle " ); }

Parameters

[in]	a	First vec3d
[in]	b	Second vec3d

Returns

Angle in Radians

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compsum()

vec3d compsum

(

const std::vector< vec3d > &

x

)

Sum a vector of vec3d using compensated summation, which keeps the rounding error down over a long list.

Parameters

[in]

x

vector<vec3d> Points to sum

Returns

vec3d Sum of the points

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cos_angle()

double cos_angle	(	const vec3d &	a,
		const vec3d &	b )

Calculate the cosine of angle between two vec3d inputs

vec3d pnt = vec3d( 2, 4, 6);
 
vec3d line_pt1(), line_pt2();
 
line_pt1.set_z( 4 );
line_pt2.set_y( 3 );
 
vec3d p_ln1 = pnt - line_pt1;
 
vec3d ln2_ln1 = line_pt2 - line_pt1;
 
double numer =  cos_angle( p_ln1, ln2_ln1 ) * p_ln1.mag();

See also

angle

Parameters

[in]	a	First vec3d
[in]	b	Second vec3d

Returns

Angle in Radians

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cross()

vec3d cross	(	const vec3d &	a,
		const vec3d &	b )

Calculate the cross product between two vec3d inputs

//==== Test Vec3d ====//
vec3d a(), b(), c();                                // Default Constructor
 
//==== Test Cross ====//
a.set_xyz( 4.0, 0.0, 0.0 );
b.set_xyz( 0.0, 3.0, 0.0 );
 
c = cross( a, b );
 
c.normalize();

Parameters

[in]	a	First vec3d
[in]	b	Second vec3d

Returns

Cross product

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dist()

double dist	(	const vec3d &	a,
		const vec3d &	b )

Calculate the distance between two vec3d inputs

//==== Test Vec3d ====//
vec3d a(), b();                                // Default Constructor
 
//==== Test Dist ====//
a.set_xyz( 2.0, 2.0, 2.0 );
b.set_xyz( 3.0, 4.0, 5.0 );
 
double d = dist( a, b );
 
if ( abs( d - sqrt( 14 ) ) > 1e-6 )    { Print( "---> Error: Vec3d Dist " ); }

See also

dist_squared

Parameters

[in]	a	First vec3d
[in]	b	Second vec3d

Returns

Distance

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dist_squared()

double dist_squared	(	const vec3d &	a,
		const vec3d &	b )

Calculate distance squared between two vec3d inputs

//==== Test Vec3d ====//
vec3d a(), b();                                // Default Constructor
 
//==== Test Dist ====//
a.set_xyz( 2.0, 2.0, 2.0 );
b.set_xyz( 3.0, 4.0, 5.0 );
 
double d2 = dist_squared( a, b );
 
if ( abs( d2 - 14 ) > 1e-6 )    { Print( "---> Error: Vec3d Dist " ); }

See also

dist

Parameters

[in]	a	First vec3d
[in]	b	Second vec3d

Returns

Distance squared

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dot()

double dot	(	const vec3d &	a,
		const vec3d &	b )

Calculate the dot product between two vec3d inputs

//==== Test Vec3d ====//
vec3d a(), b();                                // Default Constructor
 
//==== Test Dot ====//
a.set_xyz( 1.0, 2.0, 3.0 );
b.set_xyz( 2.0, 3.0, 4.0 );
 
if ( abs( dot( a, b ) - 20 ) > 1e-6 )                            { Print( "---> Error: Vec3d Dot " ); }

Parameters

[in]	a	First vec3d
[in]	b	Second vec3d

Returns

Dot product

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FitPlane()

void FitPlane	(	const std::vector< vec3d > &	pts,
		vec3d &	cen,
		vec3d &	norm )

Fit a plane through a set of points by least squares, reporting a point on the plane and its normal.

Parameters

[in]	pts	vector<vec3d> Points to fit the plane through
[out]	cen	vec3d A point on the fitted plane
[out]	norm	vec3d Normal of the fitted plane

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isfinite()

bool vec3d::isfinite

(

)

const

Test whether every coordinate is finite – neither infinite nor NaN.

See also

isnan, isinf

Returns

bool True if all three coordinates are finite

isinf()

bool vec3d::isinf

(

)

const

Test whether any coordinate is infinite.

See also

isnan, isfinite

Returns

bool True if any coordinate is infinite

isnan()

bool vec3d::isnan

(

)

const

Test whether any coordinate is NaN.

See also

isinf, isfinite

Returns

bool True if any coordinate is NaN

magsq()

double vec3d::magsq

(

)

const

Get the square of the magnitude. Cheaper than mag, which has to take a square root, and enough on its own when magnitudes are only being compared.

See also

mag

Returns

double Squared magnitude

major_comp()

int vec3d::major_comp

(

)

const

Get the index of the largest coordinate: 0 for X, 1 for Y, 2 for Z.

See also

minor_comp

Returns

int Index of the largest coordinate

minor_comp()

int vec3d::minor_comp

(

)

const

Get the index of the smallest coordinate: 0 for X, 1 for Y, 2 for Z.

See also

major_comp

Returns

int Index of the smallest coordinate

offset_i()

void vec3d::offset_i ( double offset, int idir )

inline

Offset one coordinate, chosen by index: 0 for X, 1 for Y, 2 for Z. The indexed counterpart of offset_x, offset_y and offset_z.

See also

offset_x, offset_y, offset_z

Parameters

[in]	offset	double Amount to offset by
[in]	idir	int Coordinate index, 0 for X, 1 for Y, 2 for Z

Definition at line 922 of file Vec3d.h.

operator*() [1/2]

vec3d operator*	(	const vec3d &	a,
		const vec3d &	b )

Scalar multiplication operator for a vec3d, performed by the multiplication of each vec3d component and the scalar

vec3d a();                                // Default Constructor
 
a.set_xyz( 1.0, 2.0, 3.0 );
 
double b = 1.5;
 
vec3d c = a * b;
 
Print( "a * b = ", false );
 
Print( c );

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operator*() [2/2]

vec3d operator*	(	const vec3d &	a,
		double	b )

Scalar multiplication operator for a vec3d, performed by the multiplication of each vec3d component and the scalar

vec3d a();                                // Default Constructor
 
a.set_xyz( 1.0, 2.0, 3.0 );
 
double b = 1.5;
 
vec3d c = a * b;
 
Print( "a * b = ", false );
 
Print( c );

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operator+()

vec3d operator+	(	const vec3d &	a,
		const vec3d &	b )

Addition operator for two vec3d objects, performed by the addition of each corresponding component

vec3d a(), b();                                // Default Constructor
 
a.set_xyz( 1.0, 2.0, 3.0 );
b.set_xyz( 4.0, 5.0, 6.0 );
 
vec3d c = a + b;
 
Print( "a + b = ", false );
 
Print( c );

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operator-()

vec3d operator-	(	const vec3d &	a,
		const vec3d &	b )

Subtraction operator for two vec3d objects, performed by the subtraction of each corresponding component

vec3d a(), b();                                // Default Constructor
 
a.set_xyz( 1.0, 2.0, 3.0 );
b.set_xyz( 4.0, 5.0, 6.0 );
 
vec3d c = a - b;
 
Print( "a - b = ", false );
 
Print( c );

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operator/()

vec3d operator/	(	const vec3d &	a,
		double	b )

Scalar division operator for a vec3d, performed by the division of of each vec3d component by the scalar

vec3d a();                                // Default Constructor
 
a.set_xyz( 1.0, 2.0, 3.0 );
 
double b = 1.5;
 
vec3d c = a / b;
 
Print( "a / b = ", false );
 
Print( c );

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print()

void vec3d::print

(

const char *

label = ""

)

const

Print the vec3d to stdout, for debugging. Writes to the console rather than returning anything, so there is nothing for an example to check.

Parameters

[in]

label

string Label to print in front of the coordinates

RotateArbAxis()

vec3d RotateArbAxis	(	const vec3d &	p,
		double	theta,
		const vec3d &	r )

Rotate a input point by specified angle around an arbitrary axis. Assume right hand coordinate system

//==== Test Vec3d ====//
vec3d a(), b(), c();                                // Default Constructor
float PI = 3.14;
 
//==== Test Rotate ====//
a.set_xyz( 1.0, 1.0, 0.0 );
b.set_xyz( 1.0, 0.0, 0.0 );
c.set_xyz( 0.0, 0.0, 1.0 );
 
c = RotateArbAxis( b, PI, a );

Parameters

[in]	p	Coordinate point to rotate
[in]	theta	Angle of rotation in Radians
[in]	r	Reference axis for rotation

Returns

Coordinates of rotated point

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set_refx()

vec3d & vec3d::set_refx

(

const vec3d &

a

)

Set this vec3d to another reflected about the YZ plane, negating X.

See also

set_refy, set_refz, reflect_yz

Parameters

[in]

a

vec3d Point to reflect

Returns

vec3d Updated vec3d

set_refy()

vec3d & vec3d::set_refy

(

const vec3d &

a

)

Set this vec3d to another reflected about the XZ plane, negating Y.

See also

set_refx, set_refz, reflect_xz

Parameters

[in]

a

vec3d Point to reflect

Returns

vec3d Updated vec3d

set_refz()

vec3d & vec3d::set_refz

(

const vec3d &

a

)

Set this vec3d to another reflected about the XY plane, negating Z.

See also

set_refx, set_refy, reflect_xy

Parameters

[in]

a

vec3d Point to reflect

Returns

vec3d Updated vec3d

set_vec()

vec3d & vec3d::set_vec

(

const std::vector< double > &

a

)

Set all three coordinates from a vector of three doubles.

See also

set_xyz

Parameters

[in]

a

vector<double> Three coordinates, X, Y and Z

Returns

vec3d Updated vec3d

signed_angle()

double signed_angle	(	const vec3d &	a,
		const vec3d &	b,
		const vec3d &	ref )

Calculate the signed angle between two vec3d inputs (dot product divided by their magnitudes multiplied) and an input reference axis

//==== Test Vec3d ====//
vec3d a(), b(), c();                                // Default Constructor
float PI = 3.14159265359;
 
//==== Test Angle ====//
a.set_xyz( 1.0, 1.0, 0.0 );
b.set_xyz( 1.0, 0.0, 0.0 );
c.set_xyz( 0.0, 0.0, 1.0 );
 
if ( abs( signed_angle( a, b, c ) - -PI / 4 ) > 1e-6 )            { Print( "---> Error: Vec3d SignedAngle " ); }

Parameters

[in]	a	First vec3d
[in]	b	Second vec3d
[in]	ref	Reference axis

Returns

Angle in Radians

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to_string()

string std::to_string

(

const vec3d &

v

)

Format a vec3d as a string, for printing or writing to a file.

Parameters

[in]

v

vec3d Point to format

Returns

string The formatted point

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