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Added slerp, lerp and mix functions for quaternions. Added, fixed and clarified documentation.
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@ -88,7 +88,7 @@ namespace glm
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/// @param m Input matrix multiplied by this rotation matrix.
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/// @param angle Rotation angle expressed in radians if GLM_FORCE_RADIANS is define or degrees otherwise.
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/// @param axis Rotation axis, recommanded to be normalized.
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/// @tparam T Value type used to build the matrix. Currently supported: half (not recommanded), float or double.
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/// @tparam T Value type used to build the matrix. Supported: half, float or double.
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/// @see gtc_matrix_transform
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/// @see gtx_transform
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/// @see - rotate(T angle, T x, T y, T z)
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@ -171,15 +171,48 @@ namespace detail
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detail::tquat<T> const & q1,
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detail::tquat<T> const & q2);
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/// Returns a SLERP interpolated quaternion of x and y according a.
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/// Spherical linear interpolation of two quaternions.
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/// The interpolation is oriented and the rotation is performed at constant speed.
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///
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/// @param x A quaternion
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/// @param y A quaternion
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/// @param a Interpolation factor. The interpolation is defined beyond the range [0, 1].
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/// @tparam T Value type used to build the quaternion. Supported: half, float or double.
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/// @see gtc_quaternion
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template <typename T>
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detail::tquat<T> mix(
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detail::tquat<T> const & x,
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detail::tquat<T> const & y,
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T const & a);
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/// Linear interpolation of two quaternions.
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/// The interpolation is oriented.
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///
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/// @param x A quaternion
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/// @param y A quaternion
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/// @param a Interpolation factor. The interpolation is defined beyond the range [0, 1].
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/// @tparam T Value type used to build the quaternion. Supported: half, float or double.
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/// @see gtc_quaternion
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template <typename T>
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detail::tquat<T> lerp(
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detail::tquat<T> const & x,
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detail::tquat<T> const & y,
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T const & a);
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/// Spherical linear interpolation of two quaternions.
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/// The interpolation always take the short path and the rotation is performed at constant speed.
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///
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/// @param x A quaternion
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/// @param y A quaternion
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/// @param a Interpolation factor. The interpolation is defined beyond the range [0, 1].
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/// @tparam T Value type used to build the quaternion. Supported: half, float or double.
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/// @see gtc_quaternion
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template <typename T>
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detail::tquat<T> slerp(
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detail::tquat<T> const & x,
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detail::tquat<T> const & y,
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T const & a);
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/// Returns the q conjugate.
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///
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/// @see gtc_quaternion
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@ -443,6 +443,7 @@ namespace detail
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return normalize(beta * x + alpha * y);
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}
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*/
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template <typename T>
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GLM_FUNC_QUALIFIER detail::tquat<T> mix
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(
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@ -450,6 +451,45 @@ namespace detail
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detail::tquat<T> const & y,
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T const & a
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)
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{
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T cosTheta = dot(x, y);
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// Perform a linear interpolation when cosTheta is close to 1 to avoid side effect of sin(angle) becoming a zero denominator
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if(cosTheta > T(1) - epsilon<T>())
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{
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// Linear interpolation
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return detail::tquat<T>(
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mix(x.w, y.w, a),
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mix(x.x, y.x, a),
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mix(x.y, y.y, a),
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mix(x.z, y.z, a));
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}
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else
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{
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// Essential Mathematics, page 467
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T angle = acos(cosTheta);
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return (sin((T(1) - a) * angle) * x + sin(a * angle) * z) / sin(angle);
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}
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}
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template <typename T>
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GLM_FUNC_QUALIFIER detail::tquat<T> lerp
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(
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detail::tquat<T> const & x,
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detail::tquat<T> const & y,
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T const & a
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)
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{
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return x * (T(1) - a) + (y * a);
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}
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template <typename T>
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GLM_FUNC_QUALIFIER detail::tquat<T> slerp
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(
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detail::tquat<T> const & x,
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detail::tquat<T> const & y,
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T const & a
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)
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{
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detail::tquat<T> z = y;
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