diff --git a/include/ui/TQuatHelpers.h b/include/ui/TQuatHelpers.h
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+/*
+ * Copyright 2013 The Android Open Source Project
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+
+#ifndef UI_TQUATHELPERS_H_
+#define UI_TQUATHELPERS_H_
+
+#include <math.h>
+#include <stdint.h>
+#include <sys/types.h>
+
+#include <iostream>
+
+#include <ui/vec3.h>
+
+#define PURE __attribute__((pure))
+
+namespace android {
+namespace details {
+// -------------------------------------------------------------------------------------
+
+/*
+ * No user serviceable parts here.
+ *
+ * Don't use this file directly, instead include ui/quat.h
+ */
+
+
+/*
+ * TQuatProductOperators implements basic arithmetic and basic compound assignment
+ * operators on a quaternion of type BASE<T>.
+ *
+ * BASE only needs to implement operator[] and size().
+ * By simply inheriting from TQuatProductOperators<BASE, T> BASE will automatically
+ * get all the functionality here.
+ */
+
+template <template<typename T> class QUATERNION, typename T>
+class TQuatProductOperators {
+public:
+    /* compound assignment from a another quaternion of the same size but different
+     * element type.
+     */
+    template <typename OTHER>
+    QUATERNION<T>& operator *= (const QUATERNION<OTHER>& r) {
+        QUATERNION<T>& q = static_cast<QUATERNION<T>&>(*this);
+        q = q * r;
+        return q;
+    }
+
+    /* compound assignment products by a scalar
+     */
+    QUATERNION<T>& operator *= (T v) {
+        QUATERNION<T>& lhs = static_cast<QUATERNION<T>&>(*this);
+        for (size_t i = 0; i < QUATERNION<T>::size(); i++) {
+            lhs[i] *= v;
+        }
+        return lhs;
+    }
+    QUATERNION<T>& operator /= (T v) {
+        QUATERNION<T>& lhs = static_cast<QUATERNION<T>&>(*this);
+        for (size_t i = 0; i < QUATERNION<T>::size(); i++) {
+            lhs[i] /= v;
+        }
+        return lhs;
+    }
+
+    /*
+     * NOTE: the functions below ARE NOT member methods. They are friend functions
+     * with they definition inlined with their declaration. This makes these
+     * template functions available to the compiler when (and only when) this class
+     * is instantiated, at which point they're only templated on the 2nd parameter
+     * (the first one, BASE<T> being known).
+     */
+
+    /* The operators below handle operation between quaternion of the same size
+     * but of a different element type.
+     */
+    template<typename RT>
+    friend inline
+    constexpr QUATERNION<T> PURE operator *(const QUATERNION<T>& q, const QUATERNION<RT>& r) {
+        // could be written as:
+        //  return QUATERNION<T>(
+        //            q.w*r.w - dot(q.xyz, r.xyz),
+        //            q.w*r.xyz + r.w*q.xyz + cross(q.xyz, r.xyz));
+
+        return QUATERNION<T>(
+                q.w*r.w - q.x*r.x - q.y*r.y - q.z*r.z,
+                q.w*r.x + q.x*r.w + q.y*r.z - q.z*r.y,
+                q.w*r.y - q.x*r.z + q.y*r.w + q.z*r.x,
+                q.w*r.z + q.x*r.y - q.y*r.x + q.z*r.w);
+    }
+
+    template<typename RT>
+    friend inline
+    constexpr TVec3<T> PURE operator *(const QUATERNION<T>& q, const TVec3<RT>& v) {
+        // note: if q is known to be a unit quaternion, then this simplifies to:
+        //  TVec3<T> t = 2 * cross(q.xyz, v)
+        //  return v + (q.w * t) + cross(q.xyz, t)
+        return imaginary(q * QUATERNION<T>(v, 0) * inverse(q));
+    }
+
+
+    /* For quaternions, we use explicit "by a scalar" products because it's much faster
+     * than going (implicitly) through the quaternion multiplication.
+     * For reference: we could use the code below instead, but it would be a lot slower.
+     *  friend inline
+     *  constexpr BASE<T> PURE operator *(const BASE<T>& q, const BASE<T>& r) {
+     *      return BASE<T>(
+     *              q.w*r.w - q.x*r.x - q.y*r.y - q.z*r.z,
+     *              q.w*r.x + q.x*r.w + q.y*r.z - q.z*r.y,
+     *              q.w*r.y - q.x*r.z + q.y*r.w + q.z*r.x,
+     *              q.w*r.z + q.x*r.y - q.y*r.x + q.z*r.w);
+     *
+     */
+    friend inline
+    constexpr QUATERNION<T> PURE operator *(QUATERNION<T> q, T scalar) {
+        // don't pass q by reference because we need a copy anyways
+        return q *= scalar;
+    }
+    friend inline
+    constexpr QUATERNION<T> PURE operator *(T scalar, QUATERNION<T> q) {
+        // don't pass q by reference because we need a copy anyways
+        return q *= scalar;
+    }
+
+    friend inline
+    constexpr QUATERNION<T> PURE operator /(QUATERNION<T> q, T scalar) {
+        // don't pass q by reference because we need a copy anyways
+        return q /= scalar;
+    }
+};
+
+
+/*
+ * TQuatFunctions implements functions on a quaternion of type BASE<T>.
+ *
+ * BASE only needs to implement operator[] and size().
+ * By simply inheriting from TQuatFunctions<BASE, T> BASE will automatically
+ * get all the functionality here.
+ */
+template <template<typename T> class QUATERNION, typename T>
+class TQuatFunctions {
+public:
+    /*
+     * NOTE: the functions below ARE NOT member methods. They are friend functions
+     * with they definition inlined with their declaration. This makes these
+     * template functions available to the compiler when (and only when) this class
+     * is instantiated, at which point they're only templated on the 2nd parameter
+     * (the first one, BASE<T> being known).
+     */
+
+    template<typename RT>
+    friend inline
+    constexpr T PURE dot(const QUATERNION<T>& p, const QUATERNION<RT>& q) {
+        return p.x * q.x +
+               p.y * q.y +
+               p.z * q.z +
+               p.w * q.w;
+    }
+
+    friend inline
+    constexpr T PURE norm(const QUATERNION<T>& q) {
+        return std::sqrt( dot(q, q) );
+    }
+
+    friend inline
+    constexpr T PURE length(const QUATERNION<T>& q) {
+        return norm(q);
+    }
+
+    friend inline
+    constexpr T PURE length2(const QUATERNION<T>& q) {
+        return dot(q, q);
+    }
+
+    friend inline
+    constexpr QUATERNION<T> PURE normalize(const QUATERNION<T>& q) {
+        return length(q) ? q / length(q) : QUATERNION<T>(1);
+    }
+
+    friend inline
+    constexpr QUATERNION<T> PURE conj(const QUATERNION<T>& q) {
+        return QUATERNION<T>(q.w, -q.x, -q.y, -q.z);
+    }
+
+    friend inline
+    constexpr QUATERNION<T> PURE inverse(const QUATERNION<T>& q) {
+        return conj(q) * (1 / dot(q, q));
+    }
+
+    friend inline
+    constexpr T PURE real(const QUATERNION<T>& q) {
+        return q.w;
+    }
+
+    friend inline
+    constexpr TVec3<T> PURE imaginary(const QUATERNION<T>& q) {
+        return q.xyz;
+    }
+
+    friend inline
+    constexpr QUATERNION<T> PURE unreal(const QUATERNION<T>& q) {
+        return QUATERNION<T>(q.xyz, 0);
+    }
+
+    friend inline
+    constexpr QUATERNION<T> PURE cross(const QUATERNION<T>& p, const QUATERNION<T>& q) {
+        return unreal(p*q);
+    }
+
+    friend inline
+    QUATERNION<T> PURE exp(const QUATERNION<T>& q) {
+        const T nq(norm(q.xyz));
+        return std::exp(q.w)*QUATERNION<T>((sin(nq)/nq)*q.xyz, cos(nq));
+    }
+
+    friend inline
+    QUATERNION<T> PURE log(const QUATERNION<T>& q) {
+        const T nq(norm(q));
+        return QUATERNION<T>((std::acos(q.w/nq)/norm(q.xyz))*q.xyz, log(nq));
+    }
+
+    friend inline
+    QUATERNION<T> PURE pow(const QUATERNION<T>& q, T a) {
+        // could also be computed as: exp(a*log(q));
+        const T nq(norm(q));
+        const T theta(a*std::acos(q.w / nq));
+        return std::pow(nq, a) * QUATERNION<T>(normalize(q.xyz) * std::sin(theta), std::cos(theta));
+    }
+
+    friend inline
+    QUATERNION<T> PURE slerp(const QUATERNION<T>& p, const QUATERNION<T>& q, T t) {
+        // could also be computed as: pow(q * inverse(p), t) * p;
+        const T d = dot(p, q);
+        const T npq = sqrt(dot(p, p) * dot(q, q));  // ||p|| * ||q||
+        const T a = std::acos(std::abs(d) / npq);
+        const T a0 = a * (1 - t);
+        const T a1 = a * t;
+        const T isina = 1 / sin(a);
+        const T s0 = std::sin(a0) * isina;
+        const T s1 = std::sin(a1) * isina;
+        // ensure we're taking the "short" side
+        return normalize(s0 * p + ((d < 0) ? (-s1) : (s1)) * q);
+    }
+
+    friend inline
+    constexpr QUATERNION<T> PURE lerp(const QUATERNION<T>& p, const QUATERNION<T>& q, T t) {
+        return ((1 - t) * p) + (t * q);
+    }
+
+    friend inline
+    constexpr QUATERNION<T> PURE nlerp(const QUATERNION<T>& p, const QUATERNION<T>& q, T t) {
+        return normalize(lerp(p, q, t));
+    }
+
+    friend inline
+    constexpr QUATERNION<T> PURE positive(const QUATERNION<T>& q) {
+        return q.w < 0 ? -q : q;
+    }
+};
+
+/*
+ * TQuatDebug implements functions on a vector of type BASE<T>.
+ *
+ * BASE only needs to implement operator[] and size().
+ * By simply inheriting from TQuatDebug<BASE, T> BASE will automatically
+ * get all the functionality here.
+ */
+template <template<typename T> class QUATERNION, typename T>
+class TQuatDebug {
+public:
+    /*
+     * NOTE: the functions below ARE NOT member methods. They are friend functions
+     * with they definition inlined with their declaration. This makes these
+     * template functions available to the compiler when (and only when) this class
+     * is instantiated, at which point they're only templated on the 2nd parameter
+     * (the first one, BASE<T> being known).
+     */
+    friend std::ostream& operator<< (std::ostream& stream, const QUATERNION<T>& q) {
+        return stream << "< " << q.w << " + " << q.x << "i + " << q.y << "j + " << q.z << "k >";
+    }
+};
+#undef PURE
+
+// -------------------------------------------------------------------------------------
+}  // namespace details
+}  // namespace android
+
+
+#endif  // UI_TQUATHELPERS_H_