include/Vector3D.h File Reference

This file is the main header for 3d vector operations. More...

#include <math.h>
#include <immintrin.h>
#include "Vector3D.hpp"

Go to the source code of this file.

Defines
#define	VECTOR3D_DOTP_MASK   0x71
#define	VECTOR3D_ROT1_MASK   0xC9
#define	VECTOR3D_ROT2_MASK   0xD2
Typedefs
typedef align16 __m128	Vector3D__
struct {
float   x
float   y
float   z
float   _
}	Vector3D_v
struct {
float   r
float   phi
float   z
float   _
}	Vector3D_c
struct {
float   r
float   phi
float   theta
float   _
}	Vector3D_s
union {
align16 Vector3D__   _
align16 Vector3D_v   v
align16 Vector3D_c   c
align16 Vector3D_s   s
}	Vector3D_t
Functions
__forceinline Vector3D_t	Vector3D ()
	vector zero initializer
__forceinline Vector3D_t	Vector3D (register float S0)
	vector float initializer
__forceinline Vector3D_t	Vector3D (register float x, register float y, register float z)
	cartesian vector initializer
__forceinline Vector3D_t	Vector3DC (register float r, register float phi, register float z)
	cylindrical vector initializer
__forceinline Vector3D_t	Vector3DS (register float r, register float phi, register float theta)
	spherical vector initializer
__forceinline Vector3D_t	add (register Vector3D_t L0, register Vector3D_t R0)
	vector addition
__forceinline void	add_ (register Vector3D_t &L0, register Vector3D_t R0)
	vector addition-assignment (L0 += R0)
__forceinline Vector3D_t	sub (register Vector3D_t L0, register Vector3D_t R0)
	vector subtraction
__forceinline void	sub_ (register Vector3D_t &L0, register Vector3D_t R0)
	vector subtraction-assignment (L0 -= R0)
__forceinline Vector3D_t	mul (register Vector3D_t L0, register float R0)
	scalar vector multiplication
__forceinline void	mul_ (register Vector3D_t &L0, register float R0)
	scalar vector multiplication-assignment (L0 *= R0)
__forceinline Vector3D_t	div (register Vector3D_t L0, register float R0)
	scalar vector division
__forceinline void	div_ (register Vector3D_t &L0, register float R0)
	scalar vector division-assignment (L0 /= R0)
__forceinline float	dot (register Vector3D_t L0, register Vector3D_t R0)
	the cartesian dot (or scalar) product resp. the inner product of the euclidean vector space
__forceinline Vector3D_t	cross (register Vector3D_t L0, register Vector3D_t R0)
	the cartesian cross product
__forceinline void	cross_ (register Vector3D_t &L0, register Vector3D_t R0)
	the self-assigning cartesian cross product (L0 x= R0)
__forceinline float	triple (register Vector3D_t L0, register Vector3D_t M0, register Vector3D_t R0)
	the cartesian vector-valued vector triple product
__forceinline float	abs (register Vector3D_t V0)
	the cartesian absolute value resp. length of a vector
__forceinline float	absC (register Vector3D_t V0)
	the cylindrical absolute value resp. length of a vector
__forceinline float	absS (register Vector3D_t V0)
	the spherical absolute value resp. length of a vector
__forceinline Vector3D_t	unit (register Vector3D_t V0)
	the cartesian unit vector
__forceinline void	unit_ (register Vector3D_t &V0)
	self-assign the cartesian unit vector: V0 /= abs(V0)
__forceinline Vector3D_t	unitC (register Vector3D_t V0)
	the cylindrical unit vector
__forceinline void	unitC_ (register Vector3D_t &V0)
	self-assign the cylindrical unit vector: V0 = ( V0.c.r/abs(V0) , 0.0f , V0.c.z/abs(V0) )
__forceinline Vector3D_t	unitS (register Vector3D_t V0)
	the sherical unit vector
__forceinline void	unitS_ (register Vector3D_t &V0)
	self-assign the spherical unit vector: V0 = ( 1.0f , V0.s.phi , V0.s.theta )
__forceinline Vector3D_t	v2c (register Vector3D_t V0)
	convert cartesian coordinates to cylindrical coordinates
__forceinline void	v2c_ (register Vector3D_t &V0)
	convert cartesian coordinates to cylindrical coordinates (self-assigned)
__forceinline Vector3D_t	v2s (register Vector3D_t V0)
	convert cartesian coordinates to spherical coordinates
__forceinline void	v2s_ (register Vector3D_t &V0)
	convert cartesian coordinates to spherical coordinates (self-assigned)
__forceinline Vector3D_t	c2v (register Vector3D_t V0)
	convert cylindrical coordinates to cartesian coordinates
__forceinline void	c2v_ (register Vector3D_t &V0)
	convert cylindrical coordinates to cartesian coordinates (self-assigned)
__forceinline Vector3D_t	c2s (register Vector3D_t V0)
	convert cylindrical coordinates to spherical coordinates
__forceinline void	c2s_ (register Vector3D_t &V0)
	convert cylindrical coordinates to spherical coordinates (self-assigned)
__forceinline Vector3D_t	s2v (register Vector3D_t V0)
	convert spherical coordinates to cartesian coordinates
__forceinline void	s2v_ (register Vector3D_t &V0)
	convert spherical coordinates to cartesian coordinates (self-assigned)
__forceinline Vector3D_t	s2c (register Vector3D_t V0)
	convert spherical coordinates to cylindrical coordinates
__forceinline void	s2c_ (register Vector3D_t &V0)
	convert spherical coordinates to cylindrical coordinates (self-assigned)

---

Detailed Description

This file is the main header for 3d vector operations.

Version:

0.1b

Author:

Hans-Christian Ahlswede

This file is the header which defines data types and declares functions for 3d vector operations such as addition/subtraction, multiplication/division dot/cross/triple-product, absolute values, normalization and angular functions.

Warning:

using the compiler flags -O1 and sse-intrinsics results in slower code, choose -Os or at least -O2 if sse is enabled.

---

Function Documentation

__forceinline float abs

(

register Vector3D_t

V0 )

the cartesian absolute value resp. length of a vector

Parameters:

V0	the vector in cartesian coordinates

Returns:

the (scalar) value: sqrt(<V0,V0>) resp. sqrt(V0.V0)

__forceinline float absC

(

register Vector3D_t

V0 )

the cylindrical absolute value resp. length of a vector

Parameters:

V0	the vector in cylindrical coordinates

Returns:

the (scalar) value: sqrt(V0.c.r^2 + V0.c.z^2)

Warning:

not yet implemented

__forceinline float absS

(

register Vector3D_t

V0 )

the spherical absolute value resp. length of a vector

Parameters:

V0	the vector in spherical coordinates

Returns:

the (scalar) value: V0.s.r

Warning:

not yet implemented

__forceinline Vector3D_t add	(	register Vector3D_t	L0,
		register Vector3D_t	R0
	)

vector addition

Parameters:

L0	the left hand sided operand
R0	the right hand sided operand

Returns:

the sum vector: L0 + R0

__forceinline void add_	(	register Vector3D_t &	L0,
		register Vector3D_t	R0
	)

vector addition-assignment (L0 += R0)

Parameters:

L0	the left hand sided operand, this parameter will also hold the result
R0	the right hand sided operand

__forceinline Vector3D_t c2s

(

register Vector3D_t

V0 )

convert cylindrical coordinates to spherical coordinates

Parameters:

V0	the vector in cylindrical coordinates

Returns:

the vector in spherical coordinates

Warning:

not yet implemented

__forceinline void c2s_

(

register Vector3D_t &

V0 )

convert cylindrical coordinates to spherical coordinates (self-assigned)

Parameters:

V0	the vector in cylindrical coordinates

Warning:

not yet implemented

__forceinline Vector3D_t c2v

(

register Vector3D_t

V0 )

convert cylindrical coordinates to cartesian coordinates

Parameters:

V0	the vector in cylindrical coordinates

Returns:

the vector in cartesian coordinates

Warning:

not yet implemented

__forceinline void c2v_

(

register Vector3D_t &

V0 )

convert cylindrical coordinates to cartesian coordinates (self-assigned)

Parameters:

V0	the vector in cylindrical coordinates

Warning:

not yet implemented

__forceinline Vector3D_t cross	(	register Vector3D_t	L0,
		register Vector3D_t	R0
	)

the cartesian cross product

Parameters:

L0	the left hand sided (vector) operand in cartesian coordinates
R0	the right hand sided (vector) operand in cartesian coordinates

Returns:

the vector: L0 x R0

__forceinline void cross_	(	register Vector3D_t &	L0,
		register Vector3D_t	R0
	)

the self-assigning cartesian cross product (L0 x= R0)

Parameters:

L0	the left hand sided (vector) operand in cartesian coordinates, this parameter will also hold the result
R0	the right hand sided (vector) operand in cartesian coordinates

__forceinline Vector3D_t div	(	register Vector3D_t	L0,
		register float	R0
	)

scalar vector division

Parameters:

L0	the left hand sided (vector) operand
R0	the right hand sided (scalar) operand

Returns:

the scalar divided vector: L0*R0

__forceinline void div_	(	register Vector3D_t &	L0,
		register float	R0
	)

scalar vector division-assignment (L0 /= R0)

Parameters:

L0	the left hand sided (vector) operand, this parameter will also hold the result
R0	the right hand sided (scalar) operand

__forceinline float dot	(	register Vector3D_t	L0,
		register Vector3D_t	R0
	)

the cartesian dot (or scalar) product resp. the inner product of the euclidean vector space

Parameters:

L0	the left hand sided (vector) operand in cartesian coordinates
R0	the right hand sided (vector) operand in cartesian coordinates

Returns:

the (scalar) value: L0.R0 resp. <L0,R0>

__forceinline Vector3D_t mul	(	register Vector3D_t	L0,
		register float	R0
	)

scalar vector multiplication

Parameters:

L0	the left hand sided (vector) operand
R0	the right hand sided (scalar) operand

Returns:

the scalar multiplied vector: L0*R0

__forceinline void mul_	(	register Vector3D_t &	L0,
		register float	R0
	)

scalar vector multiplication-assignment (L0 *= R0)

Parameters:

L0	the left hand sided (vector) operand, this parameter will also hold the result
R0	the right hand sided (scalar) operand

__forceinline Vector3D_t s2c

(

register Vector3D_t

V0 )

convert spherical coordinates to cylindrical coordinates

Parameters:

V0	the vector in spherical coordinates

Returns:

the vector in cylindrical coordinates

Warning:

not yet implemented

__forceinline void s2c_

(

register Vector3D_t &

V0 )

convert spherical coordinates to cylindrical coordinates (self-assigned)

Parameters:

V0	the vector in spherical coordinates

Warning:

not yet implemented

__forceinline Vector3D_t s2v

(

register Vector3D_t

V0 )

convert spherical coordinates to cartesian coordinates

Parameters:

V0	the vector in spherical coordinates

Returns:

the vector in cartesian coordinates

Warning:

not yet implemented

__forceinline void s2v_

(

register Vector3D_t &

V0 )

convert spherical coordinates to cartesian coordinates (self-assigned)

Parameters:

V0	the vector in spherical coordinates

Warning:

not yet implemented

__forceinline Vector3D_t sub	(	register Vector3D_t	L0,
		register Vector3D_t	R0
	)

vector subtraction

Parameters:

L0	the left hand sided operand
R0	the right hand sided operand

Returns:

the difference vector: L0 - R0

__forceinline void sub_	(	register Vector3D_t &	L0,
		register Vector3D_t	R0
	)

vector subtraction-assignment (L0 -= R0)

Parameters:

L0	the left hand sided operand, this parameter will also hold the result
R0	the right hand sided operand

__forceinline float triple	(	register Vector3D_t	L0,
		register Vector3D_t	M0,
		register Vector3D_t	R0
	)

the cartesian vector-valued vector triple product

Parameters:

L0	the left hand sided (vector) operand in cartesian coordinates
M0	the middle (vector) operand in cartesian coordinates
R0	the right hand sided (vector) operand in cartesian coordinates

Returns:

the vector: [L0,M0,R0] resp. <L0,M0 x R0> resp. L0.(M0 x R0)

__forceinline Vector3D_t unit

(

register Vector3D_t

V0 )

the cartesian unit vector

Parameters:

V0	the vector

Returns:

the unit vector: V0 / abs(V0)

__forceinline void unit_

(

register Vector3D_t &

V0 )

self-assign the cartesian unit vector: V0 /= abs(V0)

Parameters:

V0	the vector

__forceinline Vector3D_t unitC

(

register Vector3D_t

V0 )

the cylindrical unit vector

Parameters:

V0	the vector

Returns:

the unit vector: ( V0.c.r/abs(V0) , 0.0f , V0.c.z/abs(V0) )

Warning:

not yet implemented

__forceinline void unitC_

(

register Vector3D_t &

V0 )

self-assign the cylindrical unit vector: V0 = ( V0.c.r/abs(V0) , 0.0f , V0.c.z/abs(V0) )

Parameters:

V0	the vector

Warning:

not yet implemented

__forceinline Vector3D_t unitS

(

register Vector3D_t

V0 )

the sherical unit vector

Parameters:

V0	the vector

Returns:

the unit vector: ( 1.0f , V0.s.phi , V0.s.theta )

Warning:

not yet implemented

__forceinline void unitS_

(

register Vector3D_t &

V0 )

self-assign the spherical unit vector: V0 = ( 1.0f , V0.s.phi , V0.s.theta )

Parameters:

V0	the vector

Warning:

not yet implemented

__forceinline Vector3D_t v2c

(

register Vector3D_t

V0 )

convert cartesian coordinates to cylindrical coordinates

Parameters:

V0	the vector in cartesian coordinates

Returns:

the vector in cylindrical coordinates

Warning:

not yet implemented

__forceinline void v2c_

(

register Vector3D_t &

V0 )

convert cartesian coordinates to cylindrical coordinates (self-assigned)

Parameters:

V0	the vector in cartesian coordinates

Warning:

not yet implemented

__forceinline Vector3D_t v2s

(

register Vector3D_t

V0 )

convert cartesian coordinates to spherical coordinates

Parameters:

V0	the vector in cartesian coordinates

Returns:

the vector in spherical coordinates

Warning:

not yet implemented

__forceinline void v2s_

(

register Vector3D_t &

V0 )

convert cartesian coordinates to spherical coordinates (self-assigned)

Parameters:

V0	the vector in cartesian coordinates

Warning:

not yet implemented

__forceinline Vector3D_t Vector3D	(	register float	x,
		register float	y,
		register float	z
	)

cartesian vector initializer

Parameters:

x	initialization value for the x coordinate
y	initialization value for the y coordinate
z	initialization value for the z coordinate

Returns:

a cartesian vector where the element are initialized to the parameters x, y and z

__forceinline Vector3D_t Vector3D

(

)

vector zero initializer

Returns:

a vector where each element is initialized to 0.0f

__forceinline Vector3D_t Vector3D

(

register float

S0 )

vector float initializer

Parameters:

S0	initialization value

Returns:

a vector where each element is initialized to parameter S0

__forceinline Vector3D_t Vector3DC	(	register float	r,
		register float	phi,
		register float	z
	)

cylindrical vector initializer

Parameters:

r	initialization value for the r coordinate (radial coordinate)
phi	initialization value for the phi coordinate (polar coordinate)
z	initialization value for the z coordinate

Returns:

a cylindrical vector where the element are initialized to the parameters r, pi and z

Warning:

not yet implemented

__forceinline Vector3D_t Vector3DS	(	register float	r,
		register float	phi,
		register float	theta
	)

spherical vector initializer

Parameters:

r	initialization value for the r coordinate (radial coordinate)
phi	initialization value for the phi coordinate (polar coordinate)
theta	initialization value for the theta coordinate (azimuthal coordinate)

Returns:

a spherical vector where the element are initialized to the parameters r, phi and theta

Warning:

not yet implemented