use quaternions for centering

@KyokushinPL says was the only version that worked. Let's give it a try.

Goddamn issue: #63

1 files changed, 71 insertions, 0 deletions

diff --git a/opentrack/quat.hpp b/opentrack/quat.hpp
new file mode 100644
index 00000000..e5e74df4
--- /dev/null
+++ b/opentrack/quat.hpp
@@ -0,0 +1,71 @@
+/* Copyright (c) 2012 Patrick Ruoff
+ *
+ * Permission to use, copy, modify, and/or distribute this software for any
+ * purpose with or without fee is hereby granted, provided that the above
+ * copyright notice and this permission notice appear in all copies.
+ */
+
+#pragma once
+#include <cmath>
+
+class Quat {
+private:
+    static constexpr double pi = 3.141592653;
+    static constexpr double r2d = 180./pi;
+    double a,b,c,d; // quaternion coefficients
+public:
+    Quat() : a(1.),b(0.),c(0.),d(0.) {}
+    Quat(double yaw, double pitch, double roll) { *this = from_euler_rads(yaw, pitch, roll); }
+    Quat(double a, double b, double c, double d) : a(a),b(b),c(c),d(d) {}
+
+    Quat inv() const
+    {
+        return Quat(a,-b,-c, -d);
+    }
+
+    // conversions
+    // see http://en.wikipedia.org/wiki/Conversion_between_quaternions_and_Euler_angles
+    static Quat from_euler_rads(double yaw, double pitch, double roll)
+    {
+
+        const double sin_phi = sin(roll/2.);
+        const double cos_phi = cos(roll/2.);
+        const double sin_the = sin(pitch/2.);
+        const double cos_the = cos(pitch/2.);
+        const double sin_psi = sin(yaw/2.);
+        const double cos_psi = cos(yaw/2.);
+
+        Quat q;
+
+        q.a = cos_phi*cos_the*cos_psi + sin_phi*sin_the*sin_psi;
+        q.b = sin_phi*cos_the*cos_psi - cos_phi*sin_the*sin_psi;
+        q.c = cos_phi*sin_the*cos_psi + sin_phi*cos_the*sin_psi;
+        q.d = cos_phi*cos_the*sin_psi - sin_phi*sin_the*cos_psi;
+
+        return q;
+    }
+
+    void to_euler_rads(double& yaw, double& pitch, double& roll) const
+    {
+        roll = atan2(2.*(a*b + c*d), 1. - 2.*(b*b + c*c));
+        pitch = asin(2.*(a*c - b*d));
+        yaw =  atan2(2.*(a*d + b*c), 1. - 2.*(c*c + d*d));
+    }
+
+    void to_euler_degrees(double& yaw, double& pitch, double& roll) const
+    {
+        to_euler_rads(yaw, pitch, roll);
+        yaw *= r2d;
+        pitch *= r2d;
+        roll *= r2d;
+    }
+
+    const Quat operator*(const Quat& B) const
+    {
+        const Quat& A = *this;
+        return Quat(A.a*B.a - A.b*B.b - A.c*B.c - A.d*B.d,	// quaternion multiplication
+                    A.a*B.b + A.b*B.a + A.c*B.d - A.d*B.c,
+                    A.a*B.c - A.b*B.d + A.c*B.a + A.d*B.b,
+                    A.a*B.d + A.b*B.c - A.c*B.b + A.d*B.a);
+    }
+};