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- // Copyright 2017 The Chromium Authors. All rights reserved.
- // Use of this source code is governed by a BSD-style license that can be
- // found in the LICENSE file.
- #include "ui/gfx/geometry/quaternion.h"
- #include <algorithm>
- #include <cmath>
- #include "base/numerics/math_constants.h"
- #include "base/strings/stringprintf.h"
- #include "ui/gfx/geometry/vector3d_f.h"
- namespace gfx {
- namespace {
- const double kEpsilon = 1e-5;
- } // namespace
- Quaternion::Quaternion(const Vector3dF& axis, double theta) {
- // Rotation angle is the product of |angle| and the magnitude of |axis|.
- double length = axis.Length();
- if (std::abs(length) < kEpsilon)
- return;
- Vector3dF normalized = axis;
- normalized.Scale(1.0 / length);
- theta *= 0.5;
- double s = sin(theta);
- x_ = normalized.x() * s;
- y_ = normalized.y() * s;
- z_ = normalized.z() * s;
- w_ = cos(theta);
- }
- Quaternion::Quaternion(const Vector3dF& from, const Vector3dF& to) {
- double dot = gfx::DotProduct(from, to);
- double norm = sqrt(from.LengthSquared() * to.LengthSquared());
- double real = norm + dot;
- gfx::Vector3dF axis;
- if (real < kEpsilon * norm) {
- real = 0.0f;
- axis = std::abs(from.x()) > std::abs(from.z())
- ? gfx::Vector3dF{-from.y(), from.x(), 0.0}
- : gfx::Vector3dF{0.0, -from.z(), from.y()};
- } else {
- axis = gfx::CrossProduct(from, to);
- }
- x_ = axis.x();
- y_ = axis.y();
- z_ = axis.z();
- w_ = real;
- *this = this->Normalized();
- }
- Quaternion Quaternion::FromAxisAngle(double x,
- double y,
- double z,
- double angle) {
- double length = std::sqrt(x * x + y * y + z * z);
- if (std::abs(length) < kEpsilon)
- return Quaternion(0, 0, 0, 1);
- double scale = std::sin(0.5 * angle) / length;
- return Quaternion(scale * x, scale * y, scale * z, std::cos(0.5 * angle));
- }
- // Adapted from https://www.euclideanspace.com/maths/algebra/realNormedAlgebra/
- // quaternions/slerp/index.htm
- Quaternion Quaternion::Slerp(const Quaternion& to, double t) const {
- Quaternion from = *this;
- double cos_half_angle =
- from.x_ * to.x_ + from.y_ * to.y_ + from.z_ * to.z_ + from.w_ * to.w_;
- if (cos_half_angle < 0) {
- // Since the half angle is > 90 degrees, the full rotation angle would
- // exceed 180 degrees. The quaternions (x, y, z, w) and (-x, -y, -z, -w)
- // represent the same rotation. Flipping the orientation of either
- // quaternion ensures that the half angle is less than 90 and that we are
- // taking the shortest path.
- from = from.flip();
- cos_half_angle = -cos_half_angle;
- }
- // Ensure that acos is well behaved at the boundary.
- if (cos_half_angle > 1)
- cos_half_angle = 1;
- double sin_half_angle = std::sqrt(1.0 - cos_half_angle * cos_half_angle);
- if (sin_half_angle < kEpsilon) {
- // Quaternions share common axis and angle.
- return *this;
- }
- double half_angle = std::acos(cos_half_angle);
- double scaleA = std::sin((1 - t) * half_angle) / sin_half_angle;
- double scaleB = std::sin(t * half_angle) / sin_half_angle;
- return (scaleA * from) + (scaleB * to);
- }
- Quaternion Quaternion::Lerp(const Quaternion& q, double t) const {
- return (((1.0 - t) * *this) + (t * q)).Normalized();
- }
- double Quaternion::Length() const {
- return x_ * x_ + y_ * y_ + z_ * z_ + w_ * w_;
- }
- Quaternion Quaternion::Normalized() const {
- double length = Length();
- if (length < kEpsilon)
- return *this;
- return *this / sqrt(length);
- }
- std::string Quaternion::ToString() const {
- // q = (con(abs(v_theta)/2), v_theta/abs(v_theta) * sin(abs(v_theta)/2))
- float abs_theta = acos(w_) * 2;
- float scale = 1. / sin(abs_theta * .5);
- gfx::Vector3dF v(x_, y_, z_);
- v.Scale(scale);
- return base::StringPrintf("[%f %f %f %f], v:", x_, y_, z_, w_) +
- v.ToString() +
- base::StringPrintf(", θ:%fπ", abs_theta / base::kPiFloat);
- }
- } // namespace gfx
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