renderstack::quaternion Class Reference

quaternion for 3d rotations and attitude

#include <quaternion.hpp>

Public Member Functions
	quaternion ()
	quaternion (float x_, float y_, float z_, float w_)
	quaternion (quaternion const &other)
	quaternion (matrix const &m)
	quaternion (vec3 const &axis, float half_a_sin, float half_a_cos)
vec3	hpb () const
vec3	view_axis () const
vec3	up_axis () const
vec3	right_axis () const
quaternion	operator* (quaternion const &other) const
quaternion &	operator*= (quaternion const &other)
Data Fields
float	x
float	y
float	z
float	w

---

Detailed Description

Definition at line 38 of file quaternion.hpp.

---

Constructor & Destructor Documentation

renderstack::quaternion::quaternion

(

)

[inline]

Definition at line 41 of file quaternion.hpp.

    :   x(0.0f)
    ,   y(0.0f)
    ,   z(0.0f)
    ,   w(1.0f)
    {
    }

renderstack::quaternion::quaternion	(	float	x_,
		float	y_,
		float	z_,
		float	w_
	)			[inline]

Definition at line 48 of file quaternion.hpp.

    :   x(x_)
    ,   y(y_)
    ,   z(z_)
    ,   w(w_)
    {
    }

renderstack::quaternion::quaternion

(

quaternion const &

other

)

[inline]

Definition at line 55 of file quaternion.hpp.

    :   x(other.x)
    ,   y(other.y)
    ,   z(other.z)
    ,   w(other.w)
    {
    }

renderstack::quaternion::quaternion

(

matrix const &

m

)

[explicit]

Definition at line 127 of file quaternion.cpp.

{
    /*  Check the sum of the diagonal  */ 
    float tr = mat.m[0][0] + mat.m[1][1] + mat.m[2][2];

    if(tr > RS_EPSILON /*1e-6f*/ )
    {
        /*  The sum is positive  */ 
        float s = sqrtf(tr + 1.0f);
        w = 0.5f * s;
        s = 0.5f / s;
        x = (mat.m[1][2] - mat.m[2][1]) * s;
        y = (mat.m[2][0] - mat.m[0][2]) * s;
        z = (mat.m[0][1] - mat.m[1][0]) * s;
    }
    else
    {
        /*  The sum is negative  */ 
        float *q[3] = {&y, &z, &x};
        int const n_index[3] = {1, 2, 0};
        int i = 0;
        if(mat.m[1][1] > mat.m[i][i]) i = 1;
        if(mat.m[2][2] > mat.m[i][i]) i = 2;
        int j = n_index[i];
        int k = n_index[j];

        float s = sqrtf(
            mat.m[i][i] - (mat.m[j][j] + mat.m[k][k]) + 1.0f
        );
        *q[i] = 0.5f * s;
        if(s != 0)
        {
            s = 0.5f / s;
        }
        *q[j] = (mat.m[i][j] + mat.m[j][i]) * s;
        *q[k] = (mat.m[i][k] + mat.m[k][i]) * s;
        w     = (mat.m[j][k] + mat.m[k][j]) * s;
    }
}

renderstack::quaternion::quaternion	(	vec3 const &	axis,
		float	half_a_sin,
		float	half_a_cos
	)			[inline]

Definition at line 63 of file quaternion.hpp.

    :   x(axis.x * half_a_sin)
    ,   y(axis.y * half_a_sin)
    ,   z(axis.z * half_a_sin)
    ,   w(half_a_cos)
    {
    }

---

Member Function Documentation

vec3 renderstack::quaternion::hpb

(

)

const

Definition at line 32 of file quaternion.cpp.

{
    float   sqx = x * x;
    float   sqy = y * y;
    float   sqz = z * z;

    float   singularity_test        = x * y + z * w;
    int     north_pole_singularity  = singularity_test >  (0.5f - RS_EPSILON);
    int     south_pole_singularity  = singularity_test < -(0.5f - RS_EPSILON);

    if(north_pole_singularity)
    {
        return vec3(
            -2.0f * atan2f(x, w),
            RS_HALF_PI,
            0.0f
        );
    }

    if(south_pole_singularity)
    {
        return vec3(
            2.0f * atan2f(x, w),
            RS_HALF_PI,
            0
        );
    }
    return vec3(
        -atan2f(2.0f * y * w - x * z, 1.0f - 2.0f * (sqy - sqz)),
         asinf (2.0f * x * y + z * w),
        -atan2f(2.0f * x * w - y * z, 1.0f - 2.0f * (sqx - sqz))
    );
}

vec3 renderstack::quaternion::view_axis

(

)

const

Definition at line 67 of file quaternion.cpp.

{
    float x2 = 2.0f * x;
    float y2 = 2.0f * y;
    float z2 = 2.0f * z;
    float xx = x * x2;
    float xz = x * z2;
    float yy = y * y2;
    float yz = y * z2;
    float wx = w * x2;
    float wy = w * y2;

    return vec3(
        xz + wy,
        yz - wx,
        1.0f - (xx + yy)
    );
}

vec3 renderstack::quaternion::up_axis

(

)

const

Definition at line 87 of file quaternion.cpp.

{
    float x2 = 2.0f * x;
    float y2 = 2.0f * y;
    float z2 = 2.0f * z;
    float xx = x * x2;
    float xy = x * y2;
    float yz = y * z2;
    float zz = y * z2;
    float wx = w * x2;
    float wz = w * z2;

    return vec3(
        xy - wz,
        1.0f - (xx + zz),
        yz + wx
    );
}

vec3 renderstack::quaternion::right_axis

(

)

const

Definition at line 107 of file quaternion.cpp.

{
    float y2 = 2.0f * y;
    float z2 = 2.0f * z;
    float xy = x * y2;
    float xz = x * z2;
    float yy = y * y2;
    float zz = z * z2;
    float wy = w * y2;
    float wz = w * z2;

    return vec3(
        1.0f - (yy + zz),
        xy + wz,
        xz - wy
    );
}

quaternion renderstack::quaternion::operator*

(

quaternion const &

other

)

const

Definition at line 167 of file quaternion.cpp.

{
    float E   = (x + z) * (q2.x + q2.y);
    float F   = (z - x) * (q2.x - q2.y);
    float G   = (w + y) * (q2.w - q2.z);
    float H   = (w - y) * (q2.w + q2.z);
    float A   = F - E;
    float B   = F + E;
    float GmH = G - H;
    float GpH = G + H;

    return quaternion(
        (w + x) * (q2.w + q2.x) + 0.5f * (A - GpH),
        (w - x) * (q2.y + q2.z) + 0.5f * (B + GmH),
        (y + z) * (q2.w - q2.x) + 0.5f * (B - GmH),
        (z - y) * (q2.y - q2.z) + 0.5f * (A + GpH)
    );
}

quaternion& renderstack::quaternion::operator*=

(

quaternion const &

other

)

[inline]

Definition at line 77 of file quaternion.hpp.

{ return *this = *this * other; }

---

Field Documentation

float renderstack::quaternion::x

Definition at line 80 of file quaternion.hpp.

float renderstack::quaternion::y

Definition at line 81 of file quaternion.hpp.

float renderstack::quaternion::z

Definition at line 82 of file quaternion.hpp.

float renderstack::quaternion::w

Definition at line 83 of file quaternion.hpp.

---

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

• quaternion.hpp
• quaternion.cpp