BLI_math_axis_angle.hh

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/* SPDX-FileCopyrightText: 2023 Blender Authors
 *
 * SPDX-License-Identifier: GPL-2.0-or-later */
 
#pragma once

 
#include "BLI_math_axis_angle_types.hh"
#include "BLI_math_euler_types.hh"
#include "BLI_math_quaternion_types.hh"
 
#include "BLI_math_matrix.hh"
#include "BLI_math_quaternion.hh"
 
namespace blender::math {
 
/* -------------------------------------------------------------------- */
 
template<typename T, typename AngleT>
AxisAngleBase<T, AngleT>::AxisAngleBase(const VecBase<T, 3> &axis, const AngleT &angle)
{
  BLI_assert(is_unit_scale(axis));
  axis_ = axis;
  angle_ = angle;
}
 
template<typename T, typename AngleT>
AxisAngleBase<T, AngleT>::AxisAngleBase(const AxisSigned axis, const AngleT &angle)
{
  axis_ = to_vector<VecBase<T, 3>>(axis);
  angle_ = angle;
}
 
template<typename T, typename AngleT>
AxisAngleBase<T, AngleT>::AxisAngleBase(const VecBase<T, 3> &from, const VecBase<T, 3> &to)
{
  BLI_assert(is_unit_scale(from));
  BLI_assert(is_unit_scale(to));
 
  T sin;
  T cos = dot(from, to);
  axis_ = normalize_and_get_length(cross(from, to), sin);
 
  if (sin <= std::numeric_limits<T>::epsilon()) {
    if (cos > T(0)) {
      /* Same vectors, zero rotation... */
      *this = identity();
      return;
    }
    /* Colinear but opposed vectors, 180 rotation... */
    axis_ = normalize(orthogonal(from));
    sin = T(0);
    cos = T(-1);
  }
  /* Avoid calculating the angle if possible. */
  angle_ = AngleT(cos, sin);
}

 
/* -------------------------------------------------------------------- */
 
template<typename T, typename AngleT>
QuaternionBase<T> to_quaternion(const AxisAngleBase<T, AngleT> &axis_angle)
{
  BLI_assert(math::is_unit_scale(axis_angle.axis()));
 
  AngleT half_angle = axis_angle.angle() / 2;
  T hs = math::sin(half_angle);
  T hc = math::cos(half_angle);
 
  VecBase<T, 3> xyz = axis_angle.axis() * hs;
  return QuaternionBase<T>(hc, xyz.x, xyz.y, xyz.z);
}

 
/* -------------------------------------------------------------------- */
 
template<typename T, typename AngleT>
Euler3Base<T> to_euler(const AxisAngleBase<T, AngleT> &axis_angle, EulerOrder order)
{
  /* Use quaternions as intermediate representation for now... */
  return to_euler(to_quaternion(axis_angle), order);
}
 
template<typename T, typename AngleT>
EulerXYZBase<T> to_euler(const AxisAngleBase<T, AngleT> &axis_angle)
{
  /* Check easy and exact conversions first. */
  const VecBase<T, 3> axis = axis_angle.axis();
  if (axis.x == T(1)) {
    return EulerXYZBase<T>(T(axis_angle.angle()), T(0), T(0));
  }
  if (axis.y == T(1)) {
    return EulerXYZBase<T>(T(0), T(axis_angle.angle()), T(0));
  }
  if (axis.z == T(1)) {
    return EulerXYZBase<T>(T(0), T(0), T(axis_angle.angle()));
  }
  /* Use quaternions as intermediate representation for now... */
  return to_euler(to_quaternion(axis_angle));
}

 
}  // namespace blender::math