/* -*- Mode: C++; tab-width: 2; indent-tabs-mode: nil; c-basic-offset: 2 -*- * This Source Code Form is subject to the terms of the Mozilla Public * License, v. 2.0. If a copy of the MPL was not distributed with this * file, You can obtain one at http://mozilla.org/MPL/2.0/. */ #ifndef GFX_QUATERNION_H #define GFX_QUATERNION_H #include "mozilla/gfx/BasePoint4D.h" #include "mozilla/gfx/Matrix.h" #include "nsAlgorithm.h" #include <algorithm> struct gfxQuaternion : public mozilla::gfx::BasePoint4D<gfxFloat, gfxQuaternion> { typedef mozilla::gfx::BasePoint4D<gfxFloat, gfxQuaternion> Super; gfxQuaternion() : Super() {} gfxQuaternion(gfxFloat aX, gfxFloat aY, gfxFloat aZ, gfxFloat aW) : Super(aX, aY, aZ, aW) {} explicit gfxQuaternion(const mozilla::gfx::Matrix4x4& aMatrix) { w = 0.5 * sqrt(std::max(1 + aMatrix[0][0] + aMatrix[1][1] + aMatrix[2][2], 0.0f)); x = 0.5 * sqrt(std::max(1 + aMatrix[0][0] - aMatrix[1][1] - aMatrix[2][2], 0.0f)); y = 0.5 * sqrt(std::max(1 - aMatrix[0][0] + aMatrix[1][1] - aMatrix[2][2], 0.0f)); z = 0.5 * sqrt(std::max(1 - aMatrix[0][0] - aMatrix[1][1] + aMatrix[2][2], 0.0f)); if(aMatrix[2][1] > aMatrix[1][2]) x = -x; if(aMatrix[0][2] > aMatrix[2][0]) y = -y; if(aMatrix[1][0] > aMatrix[0][1]) z = -z; } // Convert from |direction axis, angle| pair to gfxQuaternion. // // Reference: // https://en.wikipedia.org/wiki/Quaternions_and_spatial_rotation // // if the direction axis is (x, y, z) = xi + yj + zk, // and the angle is |theta|, this formula can be done using // an extension of Euler's formula: // q = cos(theta/2) + (xi + yj + zk)(sin(theta/2)) // = cos(theta/2) + // x*sin(theta/2)i + y*sin(theta/2)j + z*sin(theta/2)k // Note: aDirection should be an unit vector and // the unit of aAngle should be Radian. gfxQuaternion(const mozilla::gfx::Point3D &aDirection, gfxFloat aAngle) { MOZ_ASSERT(mozilla::gfx::FuzzyEqual(aDirection.Length(), 1.0f), "aDirection should be an unit vector"); x = aDirection.x * sin(aAngle/2.0); y = aDirection.y * sin(aAngle/2.0); z = aDirection.z * sin(aAngle/2.0); w = cos(aAngle/2.0); } gfxQuaternion Slerp(const gfxQuaternion &aOther, gfxFloat aCoeff) { gfxFloat dot = mozilla::clamped(DotProduct(aOther), -1.0, 1.0); if (dot == 1.0) { return *this; } gfxFloat theta = acos(dot); gfxFloat rsintheta = 1/sqrt(1 - dot*dot); gfxFloat rightWeight = sin(aCoeff*theta)*rsintheta; gfxQuaternion left = *this; gfxQuaternion right = aOther; left *= cos(aCoeff*theta) - dot*rightWeight; right *= rightWeight; return left + right; } mozilla::gfx::Matrix4x4 ToMatrix() { mozilla::gfx::Matrix4x4 temp; temp[0][0] = 1 - 2 * (y * y + z * z); temp[0][1] = 2 * (x * y + w * z); temp[0][2] = 2 * (x * z - w * y); temp[1][0] = 2 * (x * y - w * z); temp[1][1] = 1 - 2 * (x * x + z * z); temp[1][2] = 2 * (y * z + w * x); temp[2][0] = 2 * (x * z + w * y); temp[2][1] = 2 * (y * z - w * x); temp[2][2] = 1 - 2 * (x * x + y * y); return temp; } }; #endif /* GFX_QUATERNION_H */