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hydra/src/quaternion.cpp

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//
// quaternion.cpp
// Kraken Engine / Hydra
//
// Copyright 2018 Kearwood Gilbert. All rights reserved.
//
// Redistribution and use in source and binary forms, with or without modification, are
// permitted provided that the following conditions are met:
//
// 1. Redistributions of source code must retain the above copyright notice, this list of
// conditions and the following disclaimer.
//
// 2. Redistributions in binary form must reproduce the above copyright notice, this list
// of conditions and the following disclaimer in the documentation and/or other materials
// provided with the distribution.
//
// THIS SOFTWARE IS PROVIDED BY KEARWOOD GILBERT ''AS IS'' AND ANY EXPRESS OR IMPLIED
// WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND
// FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL KEARWOOD GILBERT OR
// CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
// CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
// SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
// ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF
// ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
//
// The views and conclusions contained in the software and documentation are those of the
// authors and should not be interpreted as representing official policies, either expressed
// or implied, of Kearwood Gilbert.
//
#include "../include/hydra.h"
#include "krhelpers.h"
namespace kraken {
void Quaternion::init() {
c[0] = 1.0;
c[1] = 0.0;
c[2] = 0.0;
c[3] = 0.0;
}
Quaternion Quaternion::Create()
{
Quaternion r;
r.init();
return r;
}
void Quaternion::init(float w, float x, float y, float z) {
c[0] = w;
c[1] = x;
c[2] = y;
c[3] = z;
}
Quaternion Quaternion::Create(float w, float x, float y, float z)
{
Quaternion r;
r.init(w, x, y, z);
return r;
}
void Quaternion::init(const Quaternion& p) {
c[0] = p[0];
c[1] = p[1];
c[2] = p[2];
c[3] = p[3];
}
Quaternion Quaternion::Create(const Quaternion& p)
{
Quaternion r;
r.init(p);
return r;
}
void Quaternion::init(const Vector3 &euler) {
setEulerZYX(euler);
}
Quaternion Quaternion::Create(const Vector3 &euler)
{
Quaternion r;
r.init(euler);
return r;
}
void Quaternion::init(const Vector3 &from_vector, const Vector3 &to_vector) {
Vector3 a = Vector3::Cross(from_vector, to_vector);
c[0] = a[0];
c[1] = a[1];
c[2] = a[2];
c[3] = sqrt(from_vector.sqrMagnitude() * to_vector.sqrMagnitude()) + Vector3::Dot(from_vector, to_vector);
normalize();
}
Quaternion Quaternion::Create(const Vector3 &from_vector, const Vector3 &to_vector)
{
Quaternion r;
r.init(from_vector, to_vector);
return r;
}
void Quaternion::setEulerXYZ(const Vector3 &euler)
{
*this = Quaternion::FromAngleAxis(Vector3::Create(1.0f, 0.0f, 0.0f), euler.x)
* Quaternion::FromAngleAxis(Vector3::Create(0.0f, 1.0f, 0.0f), euler.y)
* Quaternion::FromAngleAxis(Vector3::Create(0.0f, 0.0f, 1.0f), euler.z);
}
void Quaternion::setEulerZYX(const Vector3 &euler) {
// ZYX Order!
float c1 = cos(euler[0] * 0.5f);
float c2 = cos(euler[1] * 0.5f);
float c3 = cos(euler[2] * 0.5f);
float s1 = sin(euler[0] * 0.5f);
float s2 = sin(euler[1] * 0.5f);
float s3 = sin(euler[2] * 0.5f);
c[0] = c1 * c2 * c3 + s1 * s2 * s3;
c[1] = s1 * c2 * c3 - c1 * s2 * s3;
c[2] = c1 * s2 * c3 + s1 * c2 * s3;
c[3] = c1 * c2 * s3 - s1 * s2 * c3;
}
float Quaternion::operator [](unsigned i) const {
return c[i];
}
float &Quaternion::operator [](unsigned i) {
return c[i];
}
Vector3 Quaternion::eulerXYZ() const {
float a2 = 2 * (c[0] * c[2] - c[1] * c[3]);
if(a2 <= -0.99999) {
return Vector3::Create(
2.0f * atan2(c[1], c[0]),
-PI * 0.5f,
0
);
} else if(a2 >= 0.99999) {
return Vector3::Create(
2.0f * atan2(c[1], c[0]),
PI * 0.5f,
0
);
} else {
return Vector3::Create(
atan2f(2 * (c[0] * c[1] + c[2] * c[3]), (1 - 2 * (c[1] * c[1] + c[2] * c[2]))),
asinf(a2),
atan2f(2 * (c[0] * c[3] + c[1] * c[2]), (1 - 2 * (c[2] * c[2] + c[3] * c[3])))
);
}
}
bool operator ==(Quaternion &v1, Quaternion &v2) {
return
v1[0] == v2[0]
&& v1[1] == v2[1]
&& v1[2] == v2[2]
&& v1[3] == v2[3];
}
bool operator !=(Quaternion &v1, Quaternion &v2) {
return
v1[0] != v2[0]
|| v1[1] != v2[1]
|| v1[2] != v2[2]
|| v1[3] != v2[3];
}
Quaternion Quaternion::operator *(const Quaternion &v) {
float t0 = (c[3]-c[2])*(v[2]-v[3]);
float t1 = (c[0]+c[1])*(v[0]+v[1]);
float t2 = (c[0]-c[1])*(v[2]+v[3]);
float t3 = (c[3]+c[2])*(v[0]-v[1]);
float t4 = (c[3]-c[1])*(v[1]-v[2]);
float t5 = (c[3]+c[1])*(v[1]+v[2]);
float t6 = (c[0]+c[2])*(v[0]-v[3]);
float t7 = (c[0]-c[2])*(v[0]+v[3]);
float t8 = t5+t6+t7;
float t9 = (t4+t8)/2;
return Quaternion::Create(
t0+t9-t5,
t1+t9-t8,
t2+t9-t7,
t3+t9-t6
);
}
Quaternion Quaternion::operator *(float v) const {
return Quaternion::Create(c[0] * v, c[1] * v, c[2] * v, c[3] * v);
}
Quaternion Quaternion::operator /(float num) const {
float inv_num = 1.0f / num;
return Quaternion::Create(c[0] * inv_num, c[1] * inv_num, c[2] * inv_num, c[3] * inv_num);
}
Quaternion Quaternion::operator +(const Quaternion &v) const {
return Quaternion::Create(c[0] + v[0], c[1] + v[1], c[2] + v[2], c[3] + v[3]);
}
Quaternion Quaternion::operator -(const Quaternion &v) const {
return Quaternion::Create(c[0] - v[0], c[1] - v[1], c[2] - v[2], c[3] - v[3]);
}
Quaternion& Quaternion::operator +=(const Quaternion& v) {
c[0] += v[0];
c[1] += v[1];
c[2] += v[2];
c[3] += v[3];
return *this;
}
Quaternion& Quaternion::operator -=(const Quaternion& v) {
c[0] -= v[0];
c[1] -= v[1];
c[2] -= v[2];
c[3] -= v[3];
return *this;
}
Quaternion& Quaternion::operator *=(const Quaternion& v) {
float t0 = (c[3]-c[2])*(v[2]-v[3]);
float t1 = (c[0]+c[1])*(v[0]+v[1]);
float t2 = (c[0]-c[1])*(v[2]+v[3]);
float t3 = (c[3]+c[2])*(v[0]-v[1]);
float t4 = (c[3]-c[1])*(v[1]-v[2]);
float t5 = (c[3]+c[1])*(v[1]+v[2]);
float t6 = (c[0]+c[2])*(v[0]-v[3]);
float t7 = (c[0]-c[2])*(v[0]+v[3]);
float t8 = t5+t6+t7;
float t9 = (t4+t8)/2;
c[0] = t0+t9-t5;
c[1] = t1+t9-t8;
c[2] = t2+t9-t7;
c[3] = t3+t9-t6;
return *this;
}
Quaternion& Quaternion::operator *=(const float& v) {
c[0] *= v;
c[1] *= v;
c[2] *= v;
c[3] *= v;
return *this;
}
Quaternion& Quaternion::operator /=(const float& v) {
float inv_v = 1.0f / v;
c[0] *= inv_v;
c[1] *= inv_v;
c[2] *= inv_v;
c[3] *= inv_v;
return *this;
}
Quaternion Quaternion::operator +() const {
return *this;
}
Quaternion Quaternion::operator -() const {
return Quaternion::Create(-c[0], -c[1], -c[2], -c[3]);
}
Quaternion Quaternion::Normalize(const Quaternion &v1) {
float inv_magnitude = 1.0f / sqrtf(v1[0] * v1[0] + v1[1] * v1[1] + v1[2] * v1[2] + v1[3] * v1[3]);
return Quaternion::Create(
v1[0] * inv_magnitude,
v1[1] * inv_magnitude,
v1[2] * inv_magnitude,
v1[3] * inv_magnitude
);
}
void Quaternion::normalize() {
float inv_magnitude = 1.0f / sqrtf(c[0] * c[0] + c[1] * c[1] + c[2] * c[2] + c[3] * c[3]);
c[0] *= inv_magnitude;
c[1] *= inv_magnitude;
c[2] *= inv_magnitude;
c[3] *= inv_magnitude;
}
Quaternion Quaternion::Conjugate(const Quaternion &v1) {
return Quaternion::Create(v1[0], -v1[1], -v1[2], -v1[3]);
}
void Quaternion::conjugate() {
c[1] = -c[1];
c[2] = -c[2];
c[3] = -c[3];
}
void Quaternion::invert() {
conjugate();
normalize();
}
Quaternion Quaternion::Invert(const Quaternion &v1) {
return Normalize(Conjugate(v1));
}
Matrix4 Quaternion::rotationMatrix() const {
Matrix4 matRotate;
matRotate.init();
/*
Vector3 euler = eulerXYZ();
matRotate.rotate(euler.x, X_AXIS);
matRotate.rotate(euler.y, Y_AXIS);
matRotate.rotate(euler.z, Z_AXIS);
*/
// FINDME - Determine why the more optimal routine commented below wasn't working
matRotate.c[0] = 1.0f - 2.0f * (c[2] * c[2] + c[3] * c[3]);
matRotate.c[1] = 2.0f * (c[1] * c[2] - c[0] * c[3]);
matRotate.c[2] = 2.0f * (c[0] * c[2] + c[1] * c[3]);
matRotate.c[4] = 2.0f * (c[1] * c[2] + c[0] * c[3]);
matRotate.c[5] = 1.0f - 2.0f * (c[1] * c[1] + c[3] * c[3]);
matRotate.c[6] = 2.0f * (c[2] * c[3] - c[0] * c[1]);
matRotate.c[8] = 2.0f * (c[1] * c[3] - c[0] * c[2]);
matRotate.c[9] = 2.0f * (c[0] * c[1] + c[2] * c[3]);
matRotate.c[10] = 1.0f - 2.0f * (c[1] * c[1] + c[2] * c[2]);
return matRotate;
}
Quaternion Quaternion::FromAngleAxis(const Vector3 &axis, float angle)
{
float ha = angle * 0.5f;
float sha = sin(ha);
return Quaternion::Create(cos(ha), axis.x * sha, axis.y * sha, axis.z * sha);
}
Quaternion Quaternion::FromRotationMatrix(const Matrix4 &m)
{
// see http://www.euclideanspace.com/maths/geometry/rotations/conversions/matrixToQuaternion/index.htm
const float trace = m[0] + m[5] + m[10];
float w, x, y, z;
if (trace > 0.0) {
const float s = 0.5f / sqrt(trace + 1.0f);
w = 0.25f / s;
x = (m[9] - m[6]) * s;
y = (m[2] - m[8]) * s;
z = (m[4] - m[1]) * s;
} else if (m[0] > m[5] && m[0] > m[10]) {
const float s = 2.0f * sqrt(1.0f + m[0] - m[5] - m[10]);
w = (m[9] - m[6]) / s;
x = 0.25f * s;
y = (m[1] + m[4]) / s;
z = (m[2] + m[8]) / s;
} else if (m[5] > m[10]) {
const float s = 2.0f * sqrt(1.0f + m[5] - m[0] - m[10]);
w = (m[2] - m[8]) / s;
x = (m[1] + m[4]) / s;
y = 0.25f * s;
z = (m[6] + m[9]) / s;
} else {
const float s = 2.0f * sqrt(1.0f + m[10] - m[0] - m[5]);
w = (m[4] - m[1]) / s;
x = (m[2] + m[8]) / s;
y = (m[6] + m[9]) / s;
z = 0.25f * s;
}
return Quaternion::Create(w, x, y, z);
}
float Quaternion::Dot(const Quaternion &v1, const Quaternion &v2)
{
return v1.c[0] * v2.c[0] + v1.c[1] * v2.c[1] + v1.c[2] * v2.c[2] + v1.c[3] * v2.c[3];
}
Quaternion Quaternion::Lerp(const Quaternion &a, const Quaternion &b, float t)
{
if (t <= 0.0f) {
return a;
} else if (t >= 1.0f) {
return b;
}
return a * (1.0f - t) + b * t;
}
Quaternion Quaternion::Slerp(const Quaternion &a, const Quaternion &b, float t)
{
if (t <= 0.0f) {
return a;
}
if (t >= 1.0f) {
return b;
}
float coshalftheta = Dot(a, b);
Quaternion c = a;
// Angle is greater than 180. We can negate the angle/quat to get the
// shorter rotation to reach the same destination.
if ( coshalftheta < 0.0f ) {
coshalftheta = -coshalftheta;
c = -c;
}
if ( coshalftheta > (1.0f - std::numeric_limits<float>::epsilon())) {
// Angle is tiny - save some computation by lerping instead.
return Lerp(c, b, t);
}
float halftheta = acos(coshalftheta);
return (c * sin((1.0f - t) * halftheta) + b * sin(t * halftheta)) / sin(halftheta);
}
} // namespace kraken
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