1/*
2 * Copyright (c) 2021 Huawei Device Co., Ltd.
3 * Licensed under the Apache License, Version 2.0 (the "License");
4 * you may not use this file except in compliance with the License.
5 * You may obtain a copy of the License at
6 *
7 *     http://www.apache.org/licenses/LICENSE-2.0
8 *
9 * Unless required by applicable law or agreed to in writing, software
10 * distributed under the License is distributed on an "AS IS" BASIS,
11 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
12 * See the License for the specific language governing permissions and
13 * limitations under the License.
14 */
15
16#include "base/geometry/quaternion.h"
17
18namespace OHOS::Ace {
19namespace {
20
21constexpr double KEPSILON = 1e-5;
22
23} // namespace
24
25Quaternion Quaternion::Slerp(const Quaternion& to, double t) const
26{
27    if (t < 0.0 || t > 1.0) {
28        // https://www.euclideanspace.com/maths/algebra/realNormedAlgebra/quaternions/slerp/index.htm
29        // a scalar between 0.0 (at from) and 1.0 (at to)
30        return *this;
31    }
32
33    Quaternion from = *this;
34
35    double cosHalfAngle = from.x_ * to.x_ + from.y_ * to.y_ + from.z_ * to.z_ + from.w_ * to.w_;
36    if (cosHalfAngle < 0.0) {
37        // Since the half angle is > 90 degrees, the full rotation angle would
38        // exceed 180 degrees. The quaternions (x, y, z, w) and (-x, -y, -z, -w)
39        // represent the same rotation. Flipping the orientation of either
40        // quaternion ensures that the half angle is less than 90 and that we are
41        // taking the shortest path.
42        from = from.flip();
43        cosHalfAngle = -cosHalfAngle;
44    }
45
46    // Ensure that acos is well behaved at the boundary.
47    if (cosHalfAngle > 1.0) {
48        cosHalfAngle = 1.0;
49    }
50
51    double sinHalfAngle = std::sqrt(1.0 - cosHalfAngle * cosHalfAngle);
52    if (sinHalfAngle < KEPSILON) {
53        // Quaternions share common axis and angle.
54        return *this;
55    }
56
57    double half_angle = std::acos(cosHalfAngle);
58
59    double scaleA = std::sin((1.0 - t) * half_angle) / sinHalfAngle;
60    double scaleB = std::sin(t * half_angle) / sinHalfAngle;
61
62    return (scaleA * from) + (scaleB * to);
63}
64
65} // namespace OHOS::Ace
66