Revision control
++ // Copyright (c) 2001-2004 NovodeX AG. All rights reserved.
++ // Copyright (c) 2004-2008 AGEIA Technologies, Inc. All rights reserved.
++ // SPDX-FileCopyrightText: Copyright (c) 2008-2026 NVIDIA CORPORATION & AFFILIATES. All rights reserved.
++ // SPDX-License-Identifier: Apache-2.0
++
++ #ifndef PX_VEC_QUAT_H
++ #define PX_VEC_QUAT_H
++
++ #if !PX_DOXYGEN
++ namespace physx
++ {
++ #endif
++ namespace aos
++ {
++
++ #ifndef PX_PIDIV2
++ #define PX_PIDIV2 1.570796327f
++ #endif
++
++ //////////////////////////////////
++ // QuatV
++ //////////////////////////////////
++ PX_FORCE_INLINE QuatV QuatVLoadXYZW(const PxF32 x, const PxF32 y, const PxF32 z, const PxF32 w)
++ {
++ return V4LoadXYZW(x, y, z, w);
++ }
++
++ PX_FORCE_INLINE QuatV QuatVLoadU(const PxF32* v)
++ {
++ return V4LoadU(v);
++ }
++
++ PX_FORCE_INLINE QuatV QuatVLoadA(const PxF32* v)
++ {
++ return V4LoadA(v);
++ }
++
++ PX_FORCE_INLINE QuatV QuatV_From_RotationAxisAngle(const Vec3V u, const FloatV a)
++ {
++ // q = cos(a/2) + u*sin(a/2)
++ const FloatV half = FLoad(0.5f);
++ const FloatV hangle = FMul(a, half);
++ const FloatV piByTwo(FLoad(PX_PIDIV2));
++ const FloatV PiByTwoMinHangle(FSub(piByTwo, hangle));
++ const Vec4V hangle2(Vec4V_From_Vec3V(V3Merge(hangle, PiByTwoMinHangle, hangle)));
++
++ /*const FloatV sina = FSin(hangle);
++ const FloatV cosa = FCos(hangle);*/
++
++ const Vec4V _sina = V4Sin(hangle2);
++ const FloatV sina = V4GetX(_sina);
++ const FloatV cosa = V4GetY(_sina);
++
++ const Vec3V v = V3Scale(u, sina);
++ // return V4Sel(BTTTF(), Vec4V_From_Vec3V(v), V4Splat(cosa));
++ return V4SetW(Vec4V_From_Vec3V(v), cosa);
++ }
++
++ // Normalize
++ PX_FORCE_INLINE QuatV QuatNormalize(const QuatV q)
++ {
++ return V4Normalize(q);
++ }
++
++ PX_FORCE_INLINE FloatV QuatLength(const QuatV q)
++ {
++ return V4Length(q);
++ }
++
++ PX_FORCE_INLINE FloatV QuatLengthSq(const QuatV q)
++ {
++ return V4LengthSq(q);
++ }
++
++ PX_FORCE_INLINE FloatV QuatDot(const QuatV a, const QuatV b) // convert this PxQuat to a unit quaternion
++ {
++ return V4Dot(a, b);
++ }
++
++ PX_FORCE_INLINE QuatV QuatConjugate(const QuatV q)
++ {
++ return V4SetW(V4Neg(q), V4GetW(q));
++ }
++
++ PX_FORCE_INLINE Vec3V QuatGetImaginaryPart(const QuatV q)
++ {
++ return Vec3V_From_Vec4V(q);
++ }
++
++ /** brief computes rotation of x-axis */
++ PX_FORCE_INLINE Vec3V QuatGetBasisVector0(const QuatV q)
++ {
++ /*const PxF32 x2 = x*2.0f;
++ const PxF32 w2 = w*2.0f;
++ return PxVec3( (w * w2) - 1.0f + x*x2,
++ (z * w2) + y*x2,
++ (-y * w2) + z*x2);*/
++
++ const FloatV two = FLoad(2.0f);
++ const FloatV w = V4GetW(q);
++ const Vec3V u = Vec3V_From_Vec4V(q);
++
++ const FloatV x2 = FMul(V3GetX(u), two);
++ const FloatV w2 = FMul(w, two);
++
++ const Vec3V a = V3Scale(u, x2);
++ const Vec3V tmp = V3Merge(w, V3GetZ(u), FNeg(V3GetY(u)));
++ // const Vec3V b = V3Scale(tmp, w2);
++ // const Vec3V ab = V3Add(a, b);
++ const Vec3V ab = V3ScaleAdd(tmp, w2, a);
++ return V3SetX(ab, FSub(V3GetX(ab), FOne()));
++ }
++
++ /** brief computes rotation of y-axis */
++ PX_FORCE_INLINE Vec3V QuatGetBasisVector1(const QuatV q)
++ {
++ /*const PxF32 y2 = y*2.0f;
++ const PxF32 w2 = w*2.0f;
++ return PxVec3( (-z * w2) + x*y2,
++ (w * w2) - 1.0f + y*y2,
++ (x * w2) + z*y2);*/
++
++ const FloatV two = FLoad(2.0f);
++ const FloatV w = V4GetW(q);
++ const Vec3V u = Vec3V_From_Vec4V(q);
++
++ const FloatV y2 = FMul(V3GetY(u), two);
++ const FloatV w2 = FMul(w, two);
++
++ const Vec3V a = V3Scale(u, y2);
++ const Vec3V tmp = V3Merge(FNeg(V3GetZ(u)), w, V3GetX(u));
++ // const Vec3V b = V3Scale(tmp, w2);
++ // const Vec3V ab = V3Add(a, b);
++ const Vec3V ab = V3ScaleAdd(tmp, w2, a);
++ return V3SetY(ab, FSub(V3GetY(ab), FOne()));
++ }
++
++ /** brief computes rotation of z-axis */
++ PX_FORCE_INLINE Vec3V QuatGetBasisVector2(const QuatV q)
++ {
++ /*const PxF32 z2 = z*2.0f;
++ const PxF32 w2 = w*2.0f;
++ return PxVec3( (y * w2) + x*z2,
++ (-x * w2) + y*z2,
++ (w * w2) - 1.0f + z*z2);*/
++
++ const FloatV two = FLoad(2.0f);
++ const FloatV w = V4GetW(q);
++ const Vec3V u = Vec3V_From_Vec4V(q);
++
++ const FloatV z2 = FMul(V3GetZ(u), two);
++ const FloatV w2 = FMul(w, two);
++
++ const Vec3V a = V3Scale(u, z2);
++ const Vec3V tmp = V3Merge(V3GetY(u), FNeg(V3GetX(u)), w);
++ /*const Vec3V b = V3Scale(tmp, w2);
++ const Vec3V ab = V3Add(a, b);*/
++ const Vec3V ab = V3ScaleAdd(tmp, w2, a);
++ return V3SetZ(ab, FSub(V3GetZ(ab), FOne()));
++ }
++
++ PX_FORCE_INLINE Vec3V QuatRotate(const QuatV q, const Vec3V v)
++ {
++ /*
++ const PxVec3 qv(x,y,z);
++ return (v*(w*w-0.5f) + (qv.cross(v))*w + qv*(qv.dot(v)))*2;
++ */
++
++ const FloatV two = FLoad(2.0f);
++ // const FloatV half = FloatV_From_F32(0.5f);
++ const FloatV nhalf = FLoad(-0.5f);
++ const Vec3V u = Vec3V_From_Vec4V(q);
++ const FloatV w = V4GetW(q);
++ // const FloatV w2 = FSub(FMul(w, w), half);
++ const FloatV w2 = FScaleAdd(w, w, nhalf);
++ const Vec3V a = V3Scale(v, w2);
++ // const Vec3V b = V3Scale(V3Cross(u, v), w);
++ // const Vec3V c = V3Scale(u, V3Dot(u, v));
++ // return V3Scale(V3Add(V3Add(a, b), c), two);
++ const Vec3V temp = V3ScaleAdd(V3Cross(u, v), w, a);
++ return V3Scale(V3ScaleAdd(u, V3Dot(u, v), temp), two);
++ }
++
++ // PT: same as QuatRotate but operates on a Vec4V
++ PX_FORCE_INLINE Vec4V QuatRotate4V(const QuatV q, const Vec4V v)
++ {
++ const FloatV two = FLoad(2.0f);
++ const FloatV nhalf = FLoad(-0.5f);
++ const Vec4V u = q; // PT: W not cleared here
++ const FloatV w = V4GetW(q);
++ const FloatV w2 = FScaleAdd(w, w, nhalf);
++ const Vec4V a = V4Scale(v, w2); // PT: W has non-zero data here
++ const Vec4V temp = V4ScaleAdd(V4Cross(u, v), w, a);
++ return V4Scale(V4ScaleAdd(u, V4Dot3(u, v), temp), two); // PT: beware, V4Dot3 has one more instruction here
++ }
++
++ // PT: avoid some multiplies when immediately normalizing a rotated vector
++ PX_FORCE_INLINE Vec3V QuatRotateAndNormalize(const QuatV q, const Vec3V v)
++ {
++ const FloatV nhalf = FLoad(-0.5f);
++ const Vec3V u = Vec3V_From_Vec4V(q);
++ const FloatV w = V4GetW(q);
++ const FloatV w2 = FScaleAdd(w, w, nhalf);
++ const Vec3V a = V3Scale(v, w2);
++ const Vec3V temp = V3ScaleAdd(V3Cross(u, v), w, a);
++ return V3Normalize(V3ScaleAdd(u, V3Dot(u, v), temp));
++ }
++
++ PX_FORCE_INLINE Vec3V QuatTransform(const QuatV q, const Vec3V p, const Vec3V v)
++ {
++ // p + q.rotate(v)
++ const FloatV two = FLoad(2.0f);
++ // const FloatV half = FloatV_From_F32(0.5f);
++ const FloatV nhalf = FLoad(-0.5f);
++ const Vec3V u = Vec3V_From_Vec4V(q);
++ const FloatV w = V4GetW(q);
++ // const FloatV w2 = FSub(FMul(w, w), half);
++ const FloatV w2 = FScaleAdd(w, w, nhalf);
++ const Vec3V a = V3Scale(v, w2);
++ /*const Vec3V b = V3Scale(V3Cross(u, v), w);
++ const Vec3V c = V3Scale(u, V3Dot(u, v));
++ return V3ScaleAdd(V3Add(V3Add(a, b), c), two, p);*/
++ const Vec3V temp = V3ScaleAdd(V3Cross(u, v), w, a);
++ const Vec3V z = V3ScaleAdd(u, V3Dot(u, v), temp);
++ return V3ScaleAdd(z, two, p);
++ }
++
++ PX_FORCE_INLINE Vec3V QuatRotateInv(const QuatV q, const Vec3V v)
++ {
++ // const PxVec3 qv(x,y,z);
++ // return (v*(w*w-0.5f) - (qv.cross(v))*w + qv*(qv.dot(v)))*2;
++
++ const FloatV two = FLoad(2.0f);
++ const FloatV nhalf = FLoad(-0.5f);
++ const Vec3V u = Vec3V_From_Vec4V(q);
++ const FloatV w = V4GetW(q);
++ const FloatV w2 = FScaleAdd(w, w, nhalf);
++ const Vec3V a = V3Scale(v, w2);
++ /*const Vec3V b = V3Scale(V3Cross(u, v), w);
++ const Vec3V c = V3Scale(u, V3Dot(u, v));
++ return V3Scale(V3Add(V3Sub(a, b), c), two);*/
++ const Vec3V temp = V3NegScaleSub(V3Cross(u, v), w, a);
++ return V3Scale(V3ScaleAdd(u, V3Dot(u, v), temp), two);
++ }
++
++ PX_FORCE_INLINE QuatV QuatMul(const QuatV a, const QuatV b)
++ {
++ const Vec4V imagA = a;
++ const Vec4V imagB = b;
++ const FloatV rA = V4GetW(a);
++ const FloatV rB = V4GetW(b);
++
++ const FloatV real = FSub(FMul(rA, rB), V4Dot3(imagA, imagB));
++ const Vec4V v0 = V4Scale(imagA, rB);
++ const Vec4V v1 = V4Scale(imagB, rA);
++ const Vec4V v2 = V4Cross(imagA, imagB);
++ const Vec4V imag = V4Add(V4Add(v0, v1), v2);
++
++ return V4SetW(imag, real);
++ }
++
++ PX_FORCE_INLINE QuatV QuatAdd(const QuatV a, const QuatV b)
++ {
++ return V4Add(a, b);
++ }
++
++ PX_FORCE_INLINE QuatV QuatNeg(const QuatV q)
++ {
++ return V4Neg(q);
++ }
++
++ PX_FORCE_INLINE QuatV QuatSub(const QuatV a, const QuatV b)
++ {
++ return V4Sub(a, b);
++ }
++
++ PX_FORCE_INLINE QuatV QuatScale(const QuatV a, const FloatV b)
++ {
++ return V4Scale(a, b);
++ }
++
++ PX_FORCE_INLINE QuatV QuatMerge(const FloatV* const floatVArray)
++ {
++ return V4Merge(floatVArray);
++ }
++
++ PX_FORCE_INLINE QuatV QuatMerge(const FloatVArg x, const FloatVArg y, const FloatVArg z, const FloatVArg w)
++ {
++ return V4Merge(x, y, z, w);
++ }
++
++ PX_FORCE_INLINE QuatV QuatIdentity()
++ {
++ return V4SetW(V4Zero(), FOne());
++ }
++
++ PX_FORCE_INLINE bool isFiniteQuatV(const QuatV q)
++ {
++ return isFiniteVec4V(q);
++ }
++
++ #if (PX_LINUX || PX_SWITCH) && PX_CLANG
++ #pragma clang diagnostic push
++ #pragma clang diagnostic ignored "-Wbitwise-instead-of-logical" // bitwise intentionally chosen for performance
++ #endif
++
++ PX_FORCE_INLINE bool isValidQuatV(const QuatV q)
++ {
++ const FloatV unitTolerance = FLoad(1e-4f);
++ const FloatV tmp = FAbs(FSub(QuatLength(q), FOne()));
++ const BoolV con = FIsGrtr(unitTolerance, tmp);
++ return isFiniteVec4V(q) & (BAllEqTTTT(con) == 1);
++ }
++
++ PX_FORCE_INLINE bool isSaneQuatV(const QuatV q)
++ {
++ const FloatV unitTolerance = FLoad(1e-2f);
++ const FloatV tmp = FAbs(FSub(QuatLength(q), FOne()));
++ const BoolV con = FIsGrtr(unitTolerance, tmp);
++ return isFiniteVec4V(q) & (BAllEqTTTT(con) == 1);
++ }
++
++ #if PX_LINUX && PX_CLANG
++ #pragma clang diagnostic pop
++ #endif
++
++ PX_FORCE_INLINE Mat33V QuatGetMat33V(const QuatVArg q)
++ {
++ // const FloatV two = FloatV_From_F32(2.0f);
++ // const FloatV one = FOne();
++
++ // const FloatV x = V4GetX(q);
++ // const FloatV y = V4GetY(q);
++ // const FloatV z = V4GetZ(q);
++ // const Vec4V _q = V4Mul(q, two);
++ //
++ ////const FloatV w = V4GetW(q);
++
++ // const Vec4V t0 = V4Mul(_q, x); // 2xx, 2xy, 2xz, 2xw
++ // const Vec4V t1 = V4Mul(_q, y); // 2xy, 2yy, 2yz, 2yw
++ // const Vec4V t2 = V4Mul(_q, z); // 2xz, 2yz, 2zz, 2zw
++ ////const Vec4V t3 = V4Mul(_q, w); // 2xw, 2yw, 2zw, 2ww
++
++ // const FloatV xx2 = V4GetX(t0);
++ // const FloatV xy2 = V4GetY(t0);
++ // const FloatV xz2 = V4GetZ(t0);
++ // const FloatV xw2 = V4GetW(t0);
++
++ // const FloatV yy2 = V4GetY(t1);
++ // const FloatV yz2 = V4GetZ(t1);
++ // const FloatV yw2 = V4GetW(t1);
++
++ // const FloatV zz2 = V4GetZ(t2);
++ // const FloatV zw2 = V4GetW(t2);
++
++ ////const FloatV ww2 = V4GetW(t3);
++
++ // const FloatV c00 = FSub(one, FAdd(yy2, zz2));
++ // const FloatV c01 = FSub(xy2, zw2);
++ // const FloatV c02 = FAdd(xz2, yw2);
++
++ // const FloatV c10 = FAdd(xy2, zw2);
++ // const FloatV c11 = FSub(one, FAdd(xx2, zz2));
++ // const FloatV c12 = FSub(yz2, xw2);
++
++ // const FloatV c20 = FSub(xz2, yw2);
++ // const FloatV c21 = FAdd(yz2, xw2);
++ // const FloatV c22 = FSub(one, FAdd(xx2, yy2));
++
++ // const Vec3V c0 = V3Merge(c00, c10, c20);
++ // const Vec3V c1 = V3Merge(c01, c11, c21);
++ // const Vec3V c2 = V3Merge(c02, c12, c22);
++
++ // return Mat33V(c0, c1, c2);
++
++ const FloatV one = FOne();
++ const FloatV x = V4GetX(q);
++ const FloatV y = V4GetY(q);
++ const FloatV z = V4GetZ(q);
++ const FloatV w = V4GetW(q);
++
++ const FloatV x2 = FAdd(x, x);
++ const FloatV y2 = FAdd(y, y);
++ const FloatV z2 = FAdd(z, z);
++
++ const FloatV xx = FMul(x2, x);
++ const FloatV yy = FMul(y2, y);
++ const FloatV zz = FMul(z2, z);
++
++ const FloatV xy = FMul(x2, y);
++ const FloatV xz = FMul(x2, z);
++ const FloatV xw = FMul(x2, w);
++
++ const FloatV yz = FMul(y2, z);
++ const FloatV yw = FMul(y2, w);
++ const FloatV zw = FMul(z2, w);
++
++ const FloatV v = FSub(one, xx);
++
++ const Vec3V column0 = V3Merge(FSub(FSub(one, yy), zz), FAdd(xy, zw), FSub(xz, yw));
++ const Vec3V column1 = V3Merge(FSub(xy, zw), FSub(v, zz), FAdd(yz, xw));
++ const Vec3V column2 = V3Merge(FAdd(xz, yw), FSub(yz, xw), FSub(v, yy));
++ return Mat33V(column0, column1, column2);
++ }
++
++ PX_FORCE_INLINE QuatV Mat33GetQuatV(const Mat33V& a)
++ {
++ const FloatV one = FOne();
++ const FloatV zero = FZero();
++ const FloatV half = FLoad(0.5f);
++ const FloatV two = FLoad(2.0f);
++ const FloatV scale = FLoad(0.25f);
++ const FloatV a00 = V3GetX(a.col0);
++ const FloatV a11 = V3GetY(a.col1);
++ const FloatV a22 = V3GetZ(a.col2);
++
++ const FloatV a21 = V3GetZ(a.col1); // row=2, col=1;
++ const FloatV a12 = V3GetY(a.col2); // row=1, col=2;
++ const FloatV a02 = V3GetX(a.col2); // row=0, col=2;
++ const FloatV a20 = V3GetZ(a.col0); // row=2, col=0;
++ const FloatV a10 = V3GetY(a.col0); // row=1, col=0;
++ const FloatV a01 = V3GetX(a.col1); // row=0, col=1;
++
++ const Vec3V vec0 = V3Merge(a21, a02, a10);
++ const Vec3V vec1 = V3Merge(a12, a20, a01);
++ const Vec3V v = V3Sub(vec0, vec1);
++ const Vec3V g = V3Add(vec0, vec1);
++
++ const FloatV trace = FAdd(a00, FAdd(a11, a22));
++
++ if(FAllGrtrOrEq(trace, zero))
++ {
++ const FloatV h = FSqrt(FAdd(trace, one));
++ const FloatV w = FMul(half, h);
++ const FloatV s = FMul(half, FRecip(h));
++ const Vec3V u = V3Scale(v, s);
++ return V4SetW(Vec4V_From_Vec3V(u), w);
++ }
++ else
++ {
++ const FloatV ntrace = FNeg(trace);
++ const Vec3V d = V3Merge(a00, a11, a22);
++ const BoolV con0 = BAllTrue3(V3IsGrtrOrEq(V3Splat(a00), d));
++ const BoolV con1 = BAllTrue3(V3IsGrtrOrEq(V3Splat(a11), d));
++
++ const FloatV t0 = FAdd(one, FScaleAdd(a00, two, ntrace));
++ const FloatV t1 = FAdd(one, FScaleAdd(a11, two, ntrace));
++ const FloatV t2 = FAdd(one, FScaleAdd(a22, two, ntrace));
++
++ const FloatV t = FSel(con0, t0, FSel(con1, t1, t2));
++
++ const FloatV h = FMul(two, FSqrt(t));
++ const FloatV s = FRecip(h);
++ const FloatV g0 = FMul(scale, h);
++ const Vec3V vs = V3Scale(v, s);
++ const Vec3V gs = V3Scale(g, s);
++ const FloatV gsx = V3GetX(gs);
++ const FloatV gsy = V3GetY(gs);
++ const FloatV gsz = V3GetZ(gs);
++ // vs.x= (a21 - a12)*s; vs.y=(a02 - a20)*s; vs.z=(a10 - a01)*s;
++ // gs.x= (a21 + a12)*s; gs.y=(a02 + a20)*s; gs.z=(a10 + a01)*s;
++ const Vec4V v0 = V4Merge(g0, gsz, gsy, V3GetX(vs));
++ const Vec4V v1 = V4Merge(gsz, g0, gsx, V3GetY(vs));
++ const Vec4V v2 = V4Merge(gsy, gsx, g0, V3GetZ(vs));
++ return V4Sel(con0, v0, V4Sel(con1, v1, v2));
++ }
++ }
++
++ } // namespace aos
++ #if !PX_DOXYGEN
++ } // namespace physx
++ #endif
++
++ #endif