]> de.git.xonotic.org Git - xonotic/netradiant.git/blobdiff - libs/math/quaternion.h
my own uncrustify run
[xonotic/netradiant.git] / libs / math / quaternion.h
index d91ad62a1da1fb2539696a707adc9675cd22f7eb..09520d8bb8b5a8407aaea066fbcd782be6a87cf6 100644 (file)
@@ -1,25 +1,25 @@
 /*
-Copyright (C) 2001-2006, William Joseph.
-All Rights Reserved.
+   Copyright (C) 2001-2006, William Joseph.
+   All Rights Reserved.
 
-This file is part of GtkRadiant.
+   This file is part of GtkRadiant.
 
-GtkRadiant is free software; you can redistribute it and/or modify
-it under the terms of the GNU General Public License as published by
-the Free Software Foundation; either version 2 of the License, or
-(at your option) any later version.
+   GtkRadiant is free software; you can redistribute it and/or modify
+   it under the terms of the GNU General Public License as published by
+   the Free Software Foundation; either version 2 of the License, or
+   (at your option) any later version.
 
-GtkRadiant is distributed in the hope that it will be useful,
-but WITHOUT ANY WARRANTY; without even the implied warranty of
-MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
-GNU General Public License for more details.
+   GtkRadiant is distributed in the hope that it will be useful,
+   but WITHOUT ANY WARRANTY; without even the implied warranty of
+   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+   GNU General Public License for more details.
 
-You should have received a copy of the GNU General Public License
-along with GtkRadiant; if not, write to the Free Software
-Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA  02110-1301  USA
-*/
+   You should have received a copy of the GNU General Public License
+   along with GtkRadiant; if not, write to the Free Software
+   Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA  02110-1301  USA
+ */
 
-#if !defined(INCLUDED_MATH_QUATERNION_H)
+#if !defined( INCLUDED_MATH_QUATERNION_H )
 #define INCLUDED_MATH_QUATERNION_H
 
 /// \file
@@ -30,297 +30,269 @@ Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA  02110-1301  USA
 /// \brief A quaternion stored in single-precision floating-point.
 typedef Vector4 Quaternion;
 
-const Quaternion c_quaternion_identity(0, 0, 0, 1);
+const Quaternion c_quaternion_identity( 0, 0, 0, 1 );
 
-inline Quaternion quaternion_multiplied_by_quaternion(const Quaternion& quaternion, const Quaternion& other)
-{
-  return Quaternion(
-    quaternion[3]*other[0] + quaternion[0]*other[3] + quaternion[1]*other[2] - quaternion[2]*other[1],
-    quaternion[3]*other[1] + quaternion[1]*other[3] + quaternion[2]*other[0] - quaternion[0]*other[2],
-    quaternion[3]*other[2] + quaternion[2]*other[3] + quaternion[0]*other[1] - quaternion[1]*other[0],
-    quaternion[3]*other[3] - quaternion[0]*other[0] - quaternion[1]*other[1] - quaternion[2]*other[2]
-  );
+inline Quaternion quaternion_multiplied_by_quaternion( const Quaternion& quaternion, const Quaternion& other ){
+       return Quaternion(
+                          quaternion[3] * other[0] + quaternion[0] * other[3] + quaternion[1] * other[2] - quaternion[2] * other[1],
+                          quaternion[3] * other[1] + quaternion[1] * other[3] + quaternion[2] * other[0] - quaternion[0] * other[2],
+                          quaternion[3] * other[2] + quaternion[2] * other[3] + quaternion[0] * other[1] - quaternion[1] * other[0],
+                          quaternion[3] * other[3] - quaternion[0] * other[0] - quaternion[1] * other[1] - quaternion[2] * other[2]
+                          );
 }
 
-inline void quaternion_multiply_by_quaternion(Quaternion& quaternion, const Quaternion& other)
-{
-  quaternion = quaternion_multiplied_by_quaternion(quaternion, other);
+inline void quaternion_multiply_by_quaternion( Quaternion& quaternion, const Quaternion& other ){
+       quaternion = quaternion_multiplied_by_quaternion( quaternion, other );
 }
 
 /// \brief Constructs a quaternion which rotates between two points on the unit-sphere, \p from and \p to.
-inline Quaternion quaternion_for_unit_vectors(const Vector3& from, const Vector3& to)
-{
-  return Quaternion(vector3_cross(from, to), static_cast<float>(vector3_dot(from, to)));
+inline Quaternion quaternion_for_unit_vectors( const Vector3& from, const Vector3& to ){
+       return Quaternion( vector3_cross( from, to ), static_cast<float>( vector3_dot( from, to ) ) );
 }
 
-inline Quaternion quaternion_for_axisangle(const Vector3& axis, double angle)
-{
-  angle *= 0.5;
-  float sa = static_cast<float>(sin(angle));
-  return Quaternion(axis[0] * sa, axis[1] * sa, axis[2] * sa, static_cast<float>(cos(angle)));
+inline Quaternion quaternion_for_axisangle( const Vector3& axis, double angle ){
+       angle *= 0.5;
+       float sa = static_cast<float>( sin( angle ) );
+       return Quaternion( axis[0] * sa, axis[1] * sa, axis[2] * sa, static_cast<float>( cos( angle ) ) );
 }
 
-inline Quaternion quaternion_for_x(double angle)
-{
-  angle *= 0.5;
-  return Quaternion(static_cast<float>(sin(angle)), 0, 0, static_cast<float>(cos(angle)));
+inline Quaternion quaternion_for_x( double angle ){
+       angle *= 0.5;
+       return Quaternion( static_cast<float>( sin( angle ) ), 0, 0, static_cast<float>( cos( angle ) ) );
 }
 
-inline Quaternion quaternion_for_y(double angle)
-{
-  angle *= 0.5;
-  return Quaternion(0, static_cast<float>(sin(angle)), 0, static_cast<float>(cos(angle)));
+inline Quaternion quaternion_for_y( double angle ){
+       angle *= 0.5;
+       return Quaternion( 0, static_cast<float>( sin( angle ) ), 0, static_cast<float>( cos( angle ) ) );
 }
 
-inline Quaternion quaternion_for_z(double angle)
-{
-  angle *= 0.5;
-  return Quaternion(0, 0, static_cast<float>(sin(angle)), static_cast<float>(cos(angle)));
+inline Quaternion quaternion_for_z( double angle ){
+       angle *= 0.5;
+       return Quaternion( 0, 0, static_cast<float>( sin( angle ) ), static_cast<float>( cos( angle ) ) );
 }
 
-inline Quaternion quaternion_inverse(const Quaternion& quaternion)
-{
-  return Quaternion(vector3_negated(vector4_to_vector3(quaternion)), quaternion[3]);
+inline Quaternion quaternion_inverse( const Quaternion& quaternion ){
+       return Quaternion( vector3_negated( vector4_to_vector3( quaternion ) ), quaternion[3] );
 }
 
-inline void quaternion_conjugate(Quaternion& quaternion)
-{
-  quaternion = quaternion_inverse(quaternion);
+inline void quaternion_conjugate( Quaternion& quaternion ){
+       quaternion = quaternion_inverse( quaternion );
 }
 
-inline Quaternion quaternion_normalised(const Quaternion& quaternion)
-{
-  const double n = (1.0 / (quaternion[0] * quaternion[0] + quaternion[1] * quaternion[1] + quaternion[2] * quaternion[2] + quaternion[3] * quaternion[3]));
-  return Quaternion(
-    static_cast<float>(quaternion[0] * n),
-    static_cast<float>(quaternion[1] * n),
-    static_cast<float>(quaternion[2] * n),
-    static_cast<float>(quaternion[3] * n)
-  );
+inline Quaternion quaternion_normalised( const Quaternion& quaternion ){
+       const double n = ( 1.0 / ( quaternion[0] * quaternion[0] + quaternion[1] * quaternion[1] + quaternion[2] * quaternion[2] + quaternion[3] * quaternion[3] ) );
+       return Quaternion(
+                          static_cast<float>( quaternion[0] * n ),
+                          static_cast<float>( quaternion[1] * n ),
+                          static_cast<float>( quaternion[2] * n ),
+                          static_cast<float>( quaternion[3] * n )
+                          );
 }
 
-inline void quaternion_normalise(Quaternion& quaternion)
-{
-  quaternion = quaternion_normalised(quaternion);
+inline void quaternion_normalise( Quaternion& quaternion ){
+       quaternion = quaternion_normalised( quaternion );
 }
 
 /// \brief Constructs a pure-rotation matrix from \p quaternion.
-inline Matrix4 matrix4_rotation_for_quaternion(const Quaternion& quaternion)
-{
+inline Matrix4 matrix4_rotation_for_quaternion( const Quaternion& quaternion ){
 #if 0
-  const double xx = quaternion[0] * quaternion[0];
-  const double xy = quaternion[0] * quaternion[1];
-  const double xz = quaternion[0] * quaternion[2];
-  const double xw = quaternion[0] * quaternion[3];
-
-  const double yy = quaternion[1] * quaternion[1];
-  const double yz = quaternion[1] * quaternion[2];
-  const double yw = quaternion[1] * quaternion[3];
-
-  const double zz = quaternion[2] * quaternion[2];
-  const double zw = quaternion[2] * quaternion[3];
-
-  return Matrix4(
-    static_cast<float>( 1 - 2 * ( yy + zz ) ),
-    static_cast<float>(     2 * ( xy + zw ) ),
-    static_cast<float>(     2 * ( xz - yw ) ),
-    0,
-    static_cast<float>(     2 * ( xy - zw ) ),
-    static_cast<float>( 1 - 2 * ( xx + zz ) ),
-    static_cast<float>(     2 * ( yz + xw ) ),
-    0,
-    static_cast<float>(     2 * ( xz + yw ) ),
-    static_cast<float>(     2 * ( yz - xw ) ),
-    static_cast<float>( 1 - 2 * ( xx + yy ) ),
-    0,
-    0,
-    0,
-    0,
-    1
-  );
+       const double xx = quaternion[0] * quaternion[0];
+       const double xy = quaternion[0] * quaternion[1];
+       const double xz = quaternion[0] * quaternion[2];
+       const double xw = quaternion[0] * quaternion[3];
+
+       const double yy = quaternion[1] * quaternion[1];
+       const double yz = quaternion[1] * quaternion[2];
+       const double yw = quaternion[1] * quaternion[3];
+
+       const double zz = quaternion[2] * quaternion[2];
+       const double zw = quaternion[2] * quaternion[3];
+
+       return Matrix4(
+                          static_cast<float>( 1 - 2 * ( yy + zz ) ),
+                          static_cast<float>(     2 * ( xy + zw ) ),
+                          static_cast<float>(     2 * ( xz - yw ) ),
+                          0,
+                          static_cast<float>(     2 * ( xy - zw ) ),
+                          static_cast<float>( 1 - 2 * ( xx + zz ) ),
+                          static_cast<float>(     2 * ( yz + xw ) ),
+                          0,
+                          static_cast<float>(     2 * ( xz + yw ) ),
+                          static_cast<float>(     2 * ( yz - xw ) ),
+                          static_cast<float>( 1 - 2 * ( xx + yy ) ),
+                          0,
+                          0,
+                          0,
+                          0,
+                          1
+                          );
 
 #else
-  const double x2 = quaternion[0] + quaternion[0];
-  const double y2 = quaternion[1] + quaternion[1]; 
-  const double z2 = quaternion[2] + quaternion[2];
-  const double xx = quaternion[0] * x2;
-  const double xy = quaternion[0] * y2;
-  const double xz = quaternion[0] * z2;
-  const double yy = quaternion[1] * y2;
-  const double yz = quaternion[1] * z2;
-  const double zz = quaternion[2] * z2;
-  const double wx = quaternion[3] * x2;
-  const double wy = quaternion[3] * y2;
-  const double wz = quaternion[3] * z2;
-
-  return Matrix4(
-    static_cast<float>( 1.0 - (yy + zz) ),
-    static_cast<float>(xy + wz),
-    static_cast<float>(xz - wy),
-    0,
-    static_cast<float>(xy - wz),
-    static_cast<float>( 1.0 - (xx + zz) ),
-    static_cast<float>(yz + wx),
-    0,
-    static_cast<float>(xz + wy),
-    static_cast<float>(yz - wx),
-    static_cast<float>( 1.0 - (xx + yy) ),
-    0,
-    0,
-    0,
-    0,
-    1
-  );
+       const double x2 = quaternion[0] + quaternion[0];
+       const double y2 = quaternion[1] + quaternion[1];
+       const double z2 = quaternion[2] + quaternion[2];
+       const double xx = quaternion[0] * x2;
+       const double xy = quaternion[0] * y2;
+       const double xz = quaternion[0] * z2;
+       const double yy = quaternion[1] * y2;
+       const double yz = quaternion[1] * z2;
+       const double zz = quaternion[2] * z2;
+       const double wx = quaternion[3] * x2;
+       const double wy = quaternion[3] * y2;
+       const double wz = quaternion[3] * z2;
+
+       return Matrix4(
+                          static_cast<float>( 1.0 - ( yy + zz ) ),
+                          static_cast<float>( xy + wz ),
+                          static_cast<float>( xz - wy ),
+                          0,
+                          static_cast<float>( xy - wz ),
+                          static_cast<float>( 1.0 - ( xx + zz ) ),
+                          static_cast<float>( yz + wx ),
+                          0,
+                          static_cast<float>( xz + wy ),
+                          static_cast<float>( yz - wx ),
+                          static_cast<float>( 1.0 - ( xx + yy ) ),
+                          0,
+                          0,
+                          0,
+                          0,
+                          1
+                          );
 
 #endif
 }
 
 const double c_half_sqrt2 = 0.70710678118654752440084436210485;
-const float c_half_sqrt2f = static_cast<float>(c_half_sqrt2);
+const float c_half_sqrt2f = static_cast<float>( c_half_sqrt2 );
 
-inline bool quaternion_component_is_90(float component)
-{
-  return (fabs(component) - c_half_sqrt2) < 0.001;
+inline bool quaternion_component_is_90( float component ){
+       return ( fabs( component ) - c_half_sqrt2 ) < 0.001;
 }
 
-inline Matrix4 matrix4_rotation_for_quaternion_quantised(const Quaternion& quaternion)
-{
-  if(quaternion.y() == 0
-    && quaternion.z() == 0
-    && quaternion_component_is_90(quaternion.x())
-    && quaternion_component_is_90(quaternion.w()))
-  {
-    return matrix4_rotation_for_sincos_x((quaternion.x() > 0) ? 1.f : -1.f, 0);
-  }
-
-  if(quaternion.x() == 0
-    && quaternion.z() == 0
-    && quaternion_component_is_90(quaternion.y())
-    && quaternion_component_is_90(quaternion.w()))
-  {
-    return matrix4_rotation_for_sincos_y((quaternion.y() > 0) ? 1.f : -1.f, 0);
-  }
-
-  if(quaternion.x() == 0
-    && quaternion.y() == 0
-    && quaternion_component_is_90(quaternion.z())
-    && quaternion_component_is_90(quaternion.w()))
-  {
-    return matrix4_rotation_for_sincos_z((quaternion.z() > 0) ? 1.f : -1.f, 0);
-  }
-
-  return matrix4_rotation_for_quaternion(quaternion);
+inline Matrix4 matrix4_rotation_for_quaternion_quantised( const Quaternion& quaternion ){
+       if ( quaternion.y() == 0
+                && quaternion.z() == 0
+                && quaternion_component_is_90( quaternion.x() )
+                && quaternion_component_is_90( quaternion.w() ) ) {
+               return matrix4_rotation_for_sincos_x( ( quaternion.x() > 0 ) ? 1.f : -1.f, 0 );
+       }
+
+       if ( quaternion.x() == 0
+                && quaternion.z() == 0
+                && quaternion_component_is_90( quaternion.y() )
+                && quaternion_component_is_90( quaternion.w() ) ) {
+               return matrix4_rotation_for_sincos_y( ( quaternion.y() > 0 ) ? 1.f : -1.f, 0 );
+       }
+
+       if ( quaternion.x() == 0
+                && quaternion.y() == 0
+                && quaternion_component_is_90( quaternion.z() )
+                && quaternion_component_is_90( quaternion.w() ) ) {
+               return matrix4_rotation_for_sincos_z( ( quaternion.z() > 0 ) ? 1.f : -1.f, 0 );
+       }
+
+       return matrix4_rotation_for_quaternion( quaternion );
 }
 
-inline Quaternion quaternion_for_matrix4_rotation(const Matrix4& matrix4)
-{
-  Matrix4 transposed = matrix4_transposed(matrix4);
-
-  double trace = transposed[0] + transposed[5] + transposed[10] + 1.0;
-
-  if(trace > 0.0001)
-  {
-    double S = 0.5 / sqrt(trace);
-    return Quaternion(
-      static_cast<float>((transposed[9] - transposed[6]) * S),
-      static_cast<float>((transposed[2] - transposed[8]) * S),
-      static_cast<float>((transposed[4] - transposed[1]) * S),
-      static_cast<float>(0.25 / S)
-    );
-  }
-
-  if(transposed[0] >= transposed[5] && transposed[0] >= transposed[10])
-  {
-    double S = 2.0 * sqrt(1.0 + transposed[0] - transposed[5] - transposed[10]);
-    return Quaternion(
-      static_cast<float>(0.25 / S),
-      static_cast<float>((transposed[1] + transposed[4]) / S),
-      static_cast<float>((transposed[2] + transposed[8]) / S),
-      static_cast<float>((transposed[6] + transposed[9]) / S)
-    );
-  }
-  
-  if(transposed[5] >= transposed[0] && transposed[5] >= transposed[10])
-  {
-    double S = 2.0 * sqrt(1.0 + transposed[5] - transposed[0] - transposed[10]);
-    return Quaternion(
-      static_cast<float>((transposed[1] + transposed[4]) / S),
-      static_cast<float>(0.25 / S),
-      static_cast<float>((transposed[6] + transposed[9]) / S),
-      static_cast<float>((transposed[2] + transposed[8]) / S)
-    );
-  }
-
-  double S = 2.0 * sqrt(1.0 + transposed[10] - transposed[0] - transposed[5]);
-  return Quaternion(
-    static_cast<float>((transposed[2] + transposed[8]) / S),
-    static_cast<float>((transposed[6] + transposed[9]) / S),
-    static_cast<float>(0.25 / S),
-    static_cast<float>((transposed[1] + transposed[4]) / S)
-  );
+inline Quaternion quaternion_for_matrix4_rotation( const Matrix4& matrix4 ){
+       Matrix4 transposed = matrix4_transposed( matrix4 );
+
+       double trace = transposed[0] + transposed[5] + transposed[10] + 1.0;
+
+       if ( trace > 0.0001 ) {
+               double S = 0.5 / sqrt( trace );
+               return Quaternion(
+                                  static_cast<float>( ( transposed[9] - transposed[6] ) * S ),
+                                  static_cast<float>( ( transposed[2] - transposed[8] ) * S ),
+                                  static_cast<float>( ( transposed[4] - transposed[1] ) * S ),
+                                  static_cast<float>( 0.25 / S )
+                                  );
+       }
+
+       if ( transposed[0] >= transposed[5] && transposed[0] >= transposed[10] ) {
+               double S = 2.0 * sqrt( 1.0 + transposed[0] - transposed[5] - transposed[10] );
+               return Quaternion(
+                                  static_cast<float>( 0.25 / S ),
+                                  static_cast<float>( ( transposed[1] + transposed[4] ) / S ),
+                                  static_cast<float>( ( transposed[2] + transposed[8] ) / S ),
+                                  static_cast<float>( ( transposed[6] + transposed[9] ) / S )
+                                  );
+       }
+
+       if ( transposed[5] >= transposed[0] && transposed[5] >= transposed[10] ) {
+               double S = 2.0 * sqrt( 1.0 + transposed[5] - transposed[0] - transposed[10] );
+               return Quaternion(
+                                  static_cast<float>( ( transposed[1] + transposed[4] ) / S ),
+                                  static_cast<float>( 0.25 / S ),
+                                  static_cast<float>( ( transposed[6] + transposed[9] ) / S ),
+                                  static_cast<float>( ( transposed[2] + transposed[8] ) / S )
+                                  );
+       }
+
+       double S = 2.0 * sqrt( 1.0 + transposed[10] - transposed[0] - transposed[5] );
+       return Quaternion(
+                          static_cast<float>( ( transposed[2] + transposed[8] ) / S ),
+                          static_cast<float>( ( transposed[6] + transposed[9] ) / S ),
+                          static_cast<float>( 0.25 / S ),
+                          static_cast<float>( ( transposed[1] + transposed[4] ) / S )
+                          );
 }
 
 /// \brief Returns \p self concatenated with the rotation transform produced by \p rotation.
 /// The concatenated rotation occurs before \p self.
-inline Matrix4 matrix4_rotated_by_quaternion(const Matrix4& self, const Quaternion& rotation)
-{
-  return matrix4_multiplied_by_matrix4(self, matrix4_rotation_for_quaternion(rotation));
+inline Matrix4 matrix4_rotated_by_quaternion( const Matrix4& self, const Quaternion& rotation ){
+       return matrix4_multiplied_by_matrix4( self, matrix4_rotation_for_quaternion( rotation ) );
 }
 
 /// \brief Concatenates \p self with the rotation transform produced by \p rotation.
 /// The concatenated rotation occurs before \p self.
-inline void matrix4_rotate_by_quaternion(Matrix4& self, const Quaternion& rotation)
-{
-  self = matrix4_rotated_by_quaternion(self, rotation);
+inline void matrix4_rotate_by_quaternion( Matrix4& self, const Quaternion& rotation ){
+       self = matrix4_rotated_by_quaternion( self, rotation );
 }
 
 /// \brief Rotates \p self by \p rotation, using \p pivotpoint.
-inline void matrix4_pivoted_rotate_by_quaternion(Matrix4& self, const Quaternion& rotation, const Vector3& pivotpoint)
-{
-  matrix4_translate_by_vec3(self, pivotpoint);
-  matrix4_rotate_by_quaternion(self, rotation);
-  matrix4_translate_by_vec3(self, vector3_negated(pivotpoint));
+inline void matrix4_pivoted_rotate_by_quaternion( Matrix4& self, const Quaternion& rotation, const Vector3& pivotpoint ){
+       matrix4_translate_by_vec3( self, pivotpoint );
+       matrix4_rotate_by_quaternion( self, rotation );
+       matrix4_translate_by_vec3( self, vector3_negated( pivotpoint ) );
 }
 
-inline Vector3 quaternion_transformed_point(const Quaternion& quaternion, const Vector3& point)
-{
-  double xx = quaternion.x() * quaternion.x();
-  double yy = quaternion.y() * quaternion.y();
-  double zz = quaternion.z() * quaternion.z();
-  double ww = quaternion.w() * quaternion.w();
+inline Vector3 quaternion_transformed_point( const Quaternion& quaternion, const Vector3& point ){
+       double xx = quaternion.x() * quaternion.x();
+       double yy = quaternion.y() * quaternion.y();
+       double zz = quaternion.z() * quaternion.z();
+       double ww = quaternion.w() * quaternion.w();
 
-  double xy2 = quaternion.x() * quaternion.y() * 2;
-  double xz2 = quaternion.x() * quaternion.z() * 2;
-  double xw2 = quaternion.x() * quaternion.w() * 2;
-  double yz2 = quaternion.y() * quaternion.z() * 2;
-  double yw2 = quaternion.y() * quaternion.w() * 2;
-  double zw2 = quaternion.z() * quaternion.w() * 2;
+       double xy2 = quaternion.x() * quaternion.y() * 2;
+       double xz2 = quaternion.x() * quaternion.z() * 2;
+       double xw2 = quaternion.x() * quaternion.w() * 2;
+       double yz2 = quaternion.y() * quaternion.z() * 2;
+       double yw2 = quaternion.y() * quaternion.w() * 2;
+       double zw2 = quaternion.z() * quaternion.w() * 2;
 
        return Vector3(
-    static_cast<float>(ww * point.x() + yw2 * point.z() - zw2 * point.y() + xx * point.x() + xy2 * point.y() + xz2 * point.z() - zz * point.x() - yy * point.x()),
-    static_cast<float>(xy2 * point.x() + yy * point.y() + yz2 * point.z() + zw2 * point.x() - zz * point.y() + ww * point.y() - xw2 * point.z() - xx * point.y()),
-    static_cast<float>(xz2 * point.x() + yz2 * point.y() + zz * point.z() - yw2 * point.x() - yy * point.z() + xw2 * point.y() - xx * point.z() + ww * point.z())
-  );
+                          static_cast<float>( ww * point.x() + yw2 * point.z() - zw2 * point.y() + xx * point.x() + xy2 * point.y() + xz2 * point.z() - zz * point.x() - yy * point.x() ),
+                          static_cast<float>( xy2 * point.x() + yy * point.y() + yz2 * point.z() + zw2 * point.x() - zz * point.y() + ww * point.y() - xw2 * point.z() - xx * point.y() ),
+                          static_cast<float>( xz2 * point.x() + yz2 * point.y() + zz * point.z() - yw2 * point.x() - yy * point.z() + xw2 * point.y() - xx * point.z() + ww * point.z() )
+                          );
 }
 
 /// \brief Constructs a pure-rotation transform from \p axis and \p angle (radians).
-inline Matrix4 matrix4_rotation_for_axisangle(const Vector3& axis, double angle)
-{
-  return matrix4_rotation_for_quaternion(quaternion_for_axisangle(axis, angle));
+inline Matrix4 matrix4_rotation_for_axisangle( const Vector3& axis, double angle ){
+       return matrix4_rotation_for_quaternion( quaternion_for_axisangle( axis, angle ) );
 }
 
 /// \brief Rotates \p self about \p axis by \p angle.
-inline void matrix4_rotate_by_axisangle(Matrix4& self, const Vector3& axis, double angle)
-{
-  matrix4_multiply_by_matrix4(self, matrix4_rotation_for_axisangle(axis, angle));
+inline void matrix4_rotate_by_axisangle( Matrix4& self, const Vector3& axis, double angle ){
+       matrix4_multiply_by_matrix4( self, matrix4_rotation_for_axisangle( axis, angle ) );
 }
 
 /// \brief Rotates \p self about \p axis by \p angle using \p pivotpoint.
-inline void matrix4_pivoted_rotate_by_axisangle(Matrix4& self, const Vector3& axis, double angle, const Vector3& pivotpoint)
-{
-  matrix4_translate_by_vec3(self, pivotpoint);
-  matrix4_rotate_by_axisangle(self, axis, angle);
-  matrix4_translate_by_vec3(self, vector3_negated(pivotpoint));
+inline void matrix4_pivoted_rotate_by_axisangle( Matrix4& self, const Vector3& axis, double angle, const Vector3& pivotpoint ){
+       matrix4_translate_by_vec3( self, pivotpoint );
+       matrix4_rotate_by_axisangle( self, axis, angle );
+       matrix4_translate_by_vec3( self, vector3_negated( pivotpoint ) );
 }