math: move the matrix-to-quaternion code to a global header.

This lets us use the code for non-float variable types. I also got
rid of the mat4-to-quat code so that users are forced to use the
mat3-to-quat code and possibly discover places where their code is
suboptimal.

doc/samples/btphystest.cpp

@@ -1,8 +1,14 @@
 //
-// BtPhysTest
+//  BtPhysTest
 //
-// Copyright: (c) 2009-2013 Benjamin "Touky" Huet <huet.benjamin@gmail.com>
-//            (c) 2012-2013 Sam Hocevar <sam@hocevar.net>
+//  Copyright © 2009—2015 Benjamin “Touky” Huet <huet.benjamin@gmail.com>
+//            © 2012—2015 Sam Hocevar <sam@hocevar.net>
+//
+//  This program is free software. It comes without any warranty, to
+//  the extent permitted by applicable law. You can redistribute it
+//  and/or modify it under the terms of the Do What the Fuck You Want
+//  to Public License, Version 2, as published by the WTFPL Task Force.
+//  See http://www.wtfpl.net/ for more details.
 //
 
 #if HAVE_CONFIG_H
@@ -558,7 +564,7 @@ void BtPhysTest::TickGame(float seconds)
             GroundMat = CenterMx *
                         mat4(quat::fromeuler_xyz(vec3(.0f, 20.f, 20.0f) * seconds))
                         * GroundMat;
-            PhysObj->SetTransform(GroundMat[3].xyz, quat(GroundMat));
+            PhysObj->SetTransform(GroundMat[3].xyz, quat(mat3(GroundMat)));
         }
     }
 #endif //USE_ROTATION
@@ -573,14 +579,14 @@ void BtPhysTest::TickGame(float seconds)
             if (i == 0)
             {
                 GroundMat = GroundMat * mat4(quat::fromeuler_xyz(vec3(20.f, .0f, .0f) * seconds));
-                PhysObj->SetTransform(GroundMat[3].xyz, quat(GroundMat));
+                PhysObj->SetTransform(GroundMat[3].xyz, quat(mat3(GroundMat)));
             }
             else if (i == 1)
             {
                 GroundMat =
                     mat4::translate(vec3(-15.0f, 5.0f, lol::cos(m_loop_value) * 8.f)) *
                     mat4(quat::fromeuler_xyz(vec3(.0f, lol::cos(m_loop_value) * 20.f, .0f)));
-                PhysObj->SetTransform(GroundMat[3].xyz, quat(GroundMat));
+                PhysObj->SetTransform(GroundMat[3].xyz, quat(mat3(GroundMat)));
             }
         }
     }

doc/samples/physicobject.h

@@ -1,9 +1,11 @@
 //
-// Orbital
+//  Orbital
 //
-// Copyright: (c) 2009-2013 Cédric Lecacheur <jordx@free.fr>
-//            (c) 2009-2013 Benjamin "Touky" Huet <huet.benjamin@gmail.com>
-//            (c) 2012 Sam Hocevar <sam@hocevar.net>
+//  Copyright © 2009—2013 Cédric Lecacheur <jordx@free.fr>
+//            © 2009—2013 Benjamin “Touky� Huet <huet.benjamin@gmail.com>
+//            © 2012—2015 Sam Hocevar <sam@hocevar.net>
+//
+//  No licensing terms yet. All rights reserved.
 //
 
 #pragma once
@@ -355,7 +357,7 @@ public:
         m_physics->AddToSimulation(new_sim);
     }
 
-    void SetTransform(const lol::vec3& base_location, const lol::quat& base_rotation=lol::quat(lol::mat4(1.0f)))
+    void SetTransform(const lol::vec3& base_location, const lol::quat& base_rotation = lol::quat(lol::mat3(1.0f)))
     {
         if (m_is_character)
             m_character->SetTransform(base_location, base_rotation);

doc/samples/physics/easyconstraint.h

@@ -1,12 +1,14 @@
 //
-// Lol Engine
+//  Lol Engine
 //
-// Copyright: (c) 2010-2013 Sam Hocevar <sam@hocevar.net>
-//            (c) 2009-2013 Benjamin "Touky" Huet <huet.benjamin@gmail.com>
-//   This program is free software; you can redistribute it and/or
-//   modify it under the terms of the Do What The Fuck You Want To
-//   Public License, Version 2, as published by Sam Hocevar. See
-//   http://www.wtfpl.net/ for more details.
+//  Copyright © 2010—2015 Sam Hocevar <sam@hocevar.net>
+//            © 2009—2013 Benjamin “Touky” Huet <huet.benjamin@gmail.com>
+//
+//  This library is free software. It comes without any warranty, to
+//  the extent permitted by applicable law. You can redistribute it
+//  and/or modify it under the terms of the Do What the Fuck You Want
+//  to Public License, Version 2, as published by the WTFPL Task Force.
+//  See http://www.wtfpl.net/ for more details.
 //
 
 #pragma once
@@ -90,8 +92,8 @@ private:
     void CustomInitConstraintToHinge()
     {
         m_hinge_constraint = new btHingeConstraint(*m_a_physobj->m_rigid_body, *m_b_physobj->m_rigid_body,
-                                                        btTransform(LOL2BT_QUAT(quat(m_a_transform)), LOL2BT_VEC3(m_a_transform[3].xyz * LOL2BT_UNIT)),
-                                                        btTransform(LOL2BT_QUAT(quat(m_b_transform)), LOL2BT_VEC3(m_b_transform[3].xyz * LOL2BT_UNIT)),
+                                                        btTransform(LOL2BT_QUAT(quat(mat3(m_a_transform))), LOL2BT_VEC3(m_a_transform[3].xyz * LOL2BT_UNIT)),
+                                                        btTransform(LOL2BT_QUAT(quat(mat3(m_b_transform))), LOL2BT_VEC3(m_b_transform[3].xyz * LOL2BT_UNIT)),
                                                         m_using_ref_a);
         m_typed_constraint = m_hinge_constraint;
     }
@@ -99,8 +101,8 @@ private:
     void CustomInitConstraintToSlider()
     {
         m_slider_constraint = new btSliderConstraint(*m_a_physobj->m_rigid_body, *m_b_physobj->m_rigid_body,
-                                                        btTransform(LOL2BT_QUAT(quat(m_a_transform)), LOL2BT_VEC3(m_a_transform[3].xyz * LOL2BT_UNIT)),
-                                                        btTransform(LOL2BT_QUAT(quat(m_b_transform)), LOL2BT_VEC3(m_b_transform[3].xyz * LOL2BT_UNIT)),
+                                                        btTransform(LOL2BT_QUAT(quat(mat3(m_a_transform))), LOL2BT_VEC3(m_a_transform[3].xyz * LOL2BT_UNIT)),
+                                                        btTransform(LOL2BT_QUAT(quat(mat3(m_b_transform))), LOL2BT_VEC3(m_b_transform[3].xyz * LOL2BT_UNIT)),
                                                         m_using_ref_a);
         m_typed_constraint = m_slider_constraint;
     }
@@ -108,16 +110,16 @@ private:
     void CustomInitConstraintToConeTwist()
     {
         m_cone_twist_constraint = new btConeTwistConstraint(*m_a_physobj->m_rigid_body, *m_b_physobj->m_rigid_body,
-                                                        btTransform(LOL2BT_QUAT(quat(m_a_transform)), LOL2BT_VEC3(m_a_transform[3].xyz * LOL2BT_UNIT)),
-                                                        btTransform(LOL2BT_QUAT(quat(m_b_transform)), LOL2BT_VEC3(m_b_transform[3].xyz * LOL2BT_UNIT)));
+                                                        btTransform(LOL2BT_QUAT(quat(mat3(m_a_transform))), LOL2BT_VEC3(m_a_transform[3].xyz * LOL2BT_UNIT)),
+                                                        btTransform(LOL2BT_QUAT(quat(mat3(m_b_transform))), LOL2BT_VEC3(m_b_transform[3].xyz * LOL2BT_UNIT)));
         m_typed_constraint = m_cone_twist_constraint;
     }
 
     void CustomInitConstraintTo6Dof()
     {
         m_6dof_constraint = new btGeneric6DofConstraint(*m_a_physobj->m_rigid_body, *m_b_physobj->m_rigid_body,
-                                                        btTransform(LOL2BT_QUAT(quat(m_a_transform)), LOL2BT_VEC3(m_a_transform[3].xyz * LOL2BT_UNIT)),
-                                                        btTransform(LOL2BT_QUAT(quat(m_b_transform)), LOL2BT_VEC3(m_b_transform[3].xyz * LOL2BT_UNIT)),
+                                                        btTransform(LOL2BT_QUAT(quat(mat3(m_a_transform))), LOL2BT_VEC3(m_a_transform[3].xyz * LOL2BT_UNIT)),
+                                                        btTransform(LOL2BT_QUAT(quat(mat3(m_b_transform))), LOL2BT_VEC3(m_b_transform[3].xyz * LOL2BT_UNIT)),
                                                         m_using_ref_a);
         m_typed_constraint = m_6dof_constraint;
     }

doc/samples/physics/easyphysics.cpp

@@ -1,13 +1,15 @@
 //
-// Lol Engine
+//  Lol Engine
 //
-// Copyright: (c) 2010-2013 Sam Hocevar <sam@hocevar.net>
-//            (c) 2009-2013 Cédric Lecacheur <jordx@free.fr>
-//            (c) 2009-2013 Benjamin "Touky" Huet <huet.benjamin@gmail.com>
-//   This program is free software; you can redistribute it and/or
-//   modify it under the terms of the Do What The Fuck You Want To
-//   Public License, Version 2, as published by Sam Hocevar. See
-//   http://www.wtfpl.net/ for more details.
+//  Copyright © 2010—2015 Sam Hocevar <sam@hocevar.net>
+//            © 2009—2013 Cédric Lecacheur <jordx@free.fr>
+//            © 2009—2013 Benjamin “Touky� Huet <huet.benjamin@gmail.com>
+//
+//  This library is free software. It comes without any warranty, to
+//  the extent permitted by applicable law. You can redistribute it
+//  and/or modify it under the terms of the Do What the Fuck You Want
+//  to Public License, Version 2, as published by the WTFPL Task Force.
+//  See http://www.wtfpl.net/ for more details.
 //
 
 #if HAVE_CONFIG_H
@@ -158,15 +160,15 @@ void EasyPhysic::SetTransform(const lol::vec3& base_location, const lol::quat& b
 void EasyPhysic::BaseTransformChanged(const lol::mat4& PreviousMatrix, const lol::mat4& NewMatrix)
 {
     mat4 PreviousMatrixLoc = ((m_base_lock_location)?(PreviousMatrix):(lol::mat4::translate(PreviousMatrix[3].xyz)));
-    mat4 PreviousMatrixRot = ((m_base_lock_rotation)?(lol::mat4(lol::quat(PreviousMatrix))):(lol::mat4(1.f)));
+    mat4 PreviousMatrixRot = ((m_base_lock_rotation)?(lol::mat4(lol::quat(lol::mat3(PreviousMatrix)))):(lol::mat4(1.f)));
     mat4 NewMatrixLoc = ((m_base_lock_location)?(NewMatrix):(lol::mat4::translate(NewMatrix[3].xyz)));
-    mat4 NewMatrixRot = ((m_base_lock_rotation)?(lol::mat4(lol::quat(NewMatrix))):(lol::mat4(1.f)));
+    mat4 NewMatrixRot = ((m_base_lock_rotation)?(lol::mat4(lol::quat(lol::mat3(NewMatrix)))):(lol::mat4(1.f)));
 
     if (m_ghost_object || (m_rigid_body->getCollisionFlags() & btCollisionObject::CF_KINEMATIC_OBJECT))
     {
         mat4 ThisMatrixLoc = NewMatrixLoc * inverse(PreviousMatrixLoc) * lol::mat4::translate(m_local_to_world[3].xyz);
-        mat4 ThisMatrixRot = NewMatrixRot * inverse(PreviousMatrixRot) * lol::mat4(lol::quat(m_local_to_world));
-        SetTransform(ThisMatrixLoc[3].xyz, lol::quat(ThisMatrixRot));
+        mat4 ThisMatrixRot = NewMatrixRot * inverse(PreviousMatrixRot) * lol::mat4(lol::quat(lol::mat3(m_local_to_world)));
+        SetTransform(ThisMatrixLoc[3].xyz, lol::quat(lol::mat3(ThisMatrixRot)));
     }
 }
 
@@ -247,7 +249,7 @@ void EasyPhysic::InitBodyToGhost()
     m_collision_object = m_ghost_object;
     m_collision_object->setUserPointer(this);
 
-    SetTransform(m_local_to_world[3].xyz, lol::quat(m_local_to_world));
+    SetTransform(m_local_to_world[3].xyz, lol::quat(lol::mat3(m_local_to_world)));
 
     m_ghost_object->setCollisionFlags(m_ghost_object->getCollisionFlags());
 }

doc/samples/physics/easyphysics.h

@@ -1,12 +1,14 @@
 //
-// Lol Engine
+//  Lol Engine
 //
-// Copyright: (c) 2010-2013 Sam Hocevar <sam@hocevar.net>
-//            (c) 2009-2013 Benjamin "Touky" Huet <huet.benjamin@gmail.com>
-//   This program is free software; you can redistribute it and/or
-//   modify it under the terms of the Do What The Fuck You Want To
-//   Public License, Version 2, as published by Sam Hocevar. See
-//   http://www.wtfpl.net/ for more details.
+//  Copyright © 2010—2015 Sam Hocevar <sam@hocevar.net>
+//            © 2009—2013 Benjamin “Touky” Huet <huet.benjamin@gmail.com>
+//
+//  This library is free software. It comes without any warranty, to
+//  the extent permitted by applicable law. You can redistribute it
+//  and/or modify it under the terms of the Do What the Fuck You Want
+//  to Public License, Version 2, as published by the WTFPL Task Force.
+//  See http://www.wtfpl.net/ for more details.
 //
 
 #pragma once
@@ -46,9 +48,9 @@ public:
 
     virtual bool CanChangeCollisionChannel() { return (m_rigid_body == NULL); }
     virtual mat4 GetTransform();
-    virtual void SetTransform(const lol::vec3& base_location, const lol::quat& base_rotation=lol::quat(lol::mat4(1.0f)));
+    virtual void SetTransform(const vec3& base_location, const quat& base_rotation = quat(mat3(1.0f)));
 protected:
-    virtual void BaseTransformChanged(const lol::mat4& PreviousMatrix, const lol::mat4& NewMatrix);
+    virtual void BaseTransformChanged(const mat4& PreviousMatrix, const mat4& NewMatrix);
 public:
     virtual void SetMass(float mass);
     virtual float GetMass() { return m_mass; }

src/camera.cpp

@@ -1,12 +1,14 @@
 //
-// Lol Engine
+//  Lol Engine
 //
-// Copyright: (c) 2010-2013 Sam Hocevar <sam@hocevar.net>
-//                2012-2013 Benjamin "Touky" Huet <huet.benjamin@gmail.com>
-//   This program is free software; you can redistribute it and/or
-//   modify it under the terms of the Do What The Fuck You Want To
-//   Public License, Version 2, as published by Sam Hocevar. See
-//   http://www.wtfpl.net/ for more details.
+//  Copyright © 2010—2015 Sam Hocevar <sam@hocevar.net>
+//            © 2009—2013 Benjamin “Touky” Huet <huet.benjamin@gmail.com>
+//
+//  This library is free software. It comes without any warranty, to
+//  the extent permitted by applicable law. You can redistribute it
+//  and/or modify it under the terms of the Do What the Fuck You Want
+//  to Public License, Version 2, as published by the WTFPL Task Force.
+//  See http://www.wtfpl.net/ for more details.
 //
 
 #include <lol/engine-internal.h>
@@ -215,7 +217,7 @@ vec3 Camera::GetRotationEuler() const
 
 quat Camera::GetRotation() const
 {
-    return quat(inverse(m_view_matrix));
+    return quat(inverse(mat3(m_view_matrix)));
 }
 
 // Calculate the frustum height at a given distance from the camera.

src/lol/math/transform.h

@@ -1,11 +1,13 @@
 //
-// Lol Engine
+//  Lol Engine
 //
-// Copyright: (c) 2010-2014 Sam Hocevar <sam@hocevar.net>
-//   This program is free software; you can redistribute it and/or
-//   modify it under the terms of the Do What The Fuck You Want To
-//   Public License, Version 2, as published by Sam Hocevar. See
-//   http://www.wtfpl.net/ for more details.
+//  Copyright © 2010—2015 Sam Hocevar <sam@hocevar.net>
+//
+//  This library is free software. It comes without any warranty, to
+//  the extent permitted by applicable law. You can redistribute it
+//  and/or modify it under the terms of the Do What the Fuck You Want
+//  to Public License, Version 2, as published by the WTFPL Task Force.
+//  See http://www.wtfpl.net/ for more details.
 //
 
 #pragma once
@@ -97,8 +99,37 @@ struct quat_t : public linear_ops::base<T>
     explicit inline constexpr quat_t(T W)
       : w(W), x(0), y(0), z(0) {}
 
-    explicit quat_t(mat_t<T,3,3> const &m);
-    explicit quat_t(mat_t<T,4,4> const &m);
+    /* Construct a unit quaternion from a pure rotation matrix */
+    explicit quat_t(mat_t<T,3,3> const &m)
+    {
+        T tr = m[0][0] + m[1][1] + m[2][2];
+
+        if (tr > T(0))
+        {
+            T const p = T(0.5) * std::sqrt(T(1) + tr);
+            T const q = T(0.25) / p;
+
+            w = p;
+            x = q * (m[1][2] - m[2][1]);
+            y = q * (m[2][0] - m[0][2]);
+            z = q * (m[0][1] - m[1][0]);
+        }
+        else
+        {
+            int i = (m[0][0] > m[1][1] && m[0][0] > m[2][2]) ? 0
+                  : (m[1][1] > m[2][2]) ? 1
+                  : 2;
+            int j = (i + 1) % 3, k = (i + 2) % 3;
+
+            T const p = T(0.5) * lol::sqrt(T(1) - tr + m[i][i] + m[i][i]);
+            T const q = T(0.25) / p;
+
+            w              = q * (m[j][k] - m[k][j]);
+            (*this)[1 + i] = p;
+            (*this)[1 + j] = q * (m[i][j] + m[j][i]);
+            (*this)[1 + k] = q * (m[k][i] + m[i][k]);
+        }
+    }
 
     LOL_COMMON_MEMBER_OPS(w)
 

src/math/transform.cpp

@@ -1,11 +1,13 @@
 //
-// Lol Engine
+//  Lol Engine
 //
-// Copyright: (c) 2010-2014 Sam Hocevar <sam@hocevar.net>
-//   This program is free software; you can redistribute it and/or
-//   modify it under the terms of the Do What The Fuck You Want To
-//   Public License, Version 2, as published by Sam Hocevar. See
-//   http://www.wtfpl.net/ for more details.
+//  Copyright © 2010—2015 Sam Hocevar <sam@hocevar.net>
+//
+//  This library is free software. It comes without any warranty, to
+//  the extent permitted by applicable law. You can redistribute it
+//  and/or modify it under the terms of the Do What the Fuck You Want
+//  to Public License, Version 2, as published by the WTFPL Task Force.
+//  See http://www.wtfpl.net/ for more details.
 //
 
 #include <lol/engine-internal.h>
@@ -13,47 +15,6 @@
 namespace lol
 {
 
-static inline void mat_to_quat(quat &that, mat3 const &m)
-{
-    float tr = m[0][0] + m[1][1] + m[2][2];
-
-    if (tr > 0)
-    {
-        float const p = 0.5f * std::sqrt(1.0f + tr);
-        float const q = 0.25f / p;
-
-        that.w = p;
-        that.x = q * (m[1][2] - m[2][1]);
-        that.y = q * (m[2][0] - m[0][2]);
-        that.z = q * (m[0][1] - m[1][0]);
-    }
-    else
-    {
-        int i = (m[0][0] > m[1][1] && m[0][0] > m[2][2]) ? 0
-              : (m[1][1] > m[2][2]) ? 1
-              : 2;
-        int j = (i + 1) % 3, k = (i + 2) % 3;
-
-        float const p = 0.5f * std::sqrt(1.0f - tr + 2.f * m[i][i]);
-        float const q = 0.25f / p;
-
-        that.w      = q * (m[j][k] - m[k][j]);
-        that[1 + i] = p;
-        that[1 + j] = q * (m[i][j] + m[j][i]);
-        that[1 + k] = q * (m[k][i] + m[i][k]);
-    }
-}
-
-template<> quat::quat_t(mat3 const &m)
-{
-    mat_to_quat(*this, m);
-}
-
-template<> quat::quat_t(mat4 const &m)
-{
-    mat_to_quat(*this, mat3(m));
-}
-
 template<> quat quat::rotate(float degrees, vec3 const &v)
 {
     float half_angle = radians(degrees) * 0.5f;

src/t/entity/camera.cpp

@@ -2,7 +2,7 @@
 //  Lol Engine — Unit tests
 //
 //  Copyright © 2010—2014 Sam Hocevar <sam@hocevar.net>
-//            © 2013 Benjamin "Touky" Huet <huet.benjamin@gmail.com>
+//            © 2013 Benjamin “Touky” Huet <huet.benjamin@gmail.com>
 //
 //  This program is free software. It comes without any warranty, to
 //  the extent permitted by applicable law. You can redistribute it
@@ -40,7 +40,7 @@ lolunit_declare_fixture(CameraTest)
         target = vec3::zero;
         up = vec3::axis_y;
         m_lookat = mat4::lookat(eye, target, up);
-        q_lookat = quat(m_lookat);
+        q_lookat = quat(mat3(m_lookat));
         v_lookat = vec3::toeuler_zyx(q_lookat);
         fov = 90.f;
         screen_size = 800.f;