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//
// Redistribution and use in source and binary forms, with or without
// modification, are permitted provided that the following conditions
// are met:
// * Redistributions of source code must retain the above copyright
// notice, this list of conditions and the following disclaimer.
// * Redistributions in binary form must reproduce the above copyright
// notice, this list of conditions and the following disclaimer in the
// documentation and/or other materials provided with the distribution.
// * Neither the name of NVIDIA CORPORATION nor the names of its
// contributors may be used to endorse or promote products derived
// from this software without specific prior written permission.
//
// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS ``AS IS'' AND ANY
// EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
// PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR
// CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
// OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
//
// Copyright (c) 2008-2018 NVIDIA Corporation. All rights reserved.
// Copyright (c) 2004-2008 AGEIA Technologies, Inc. All rights reserved.
// Copyright (c) 2001-2004 NovodeX AG. All rights reserved.
#include "GuIntersectionRayCapsule.h"
#include "GuIntersectionRaySphere.h"
using namespace physx;
// PT: ray-capsule intersection code, originally from the old Magic Software library.
PxU32 Gu::intersectRayCapsuleInternal(const PxVec3& origin, const PxVec3& dir, const PxVec3& p0, const PxVec3& p1, float radius, PxReal s[2])
{
// set up quadratic Q(t) = a*t^2 + 2*b*t + c
PxVec3 kW = p1 - p0;
const float fWLength = kW.magnitude();
if(fWLength!=0.0f)
kW /= fWLength;
// PT: if the capsule is in fact a sphere, switch back to dedicated sphere code.
// This is not just an optimization, the rest of the code fails otherwise.
if(fWLength<=1e-6f)
{
const float d0 = (origin - p0).magnitudeSquared();
const float d1 = (origin - p1).magnitudeSquared();
const float approxLength = (PxMax(d0, d1) + radius)*2.0f;
return PxU32(Gu::intersectRaySphere(origin, dir, approxLength, p0, radius, s[0]));
}
// generate orthonormal basis
PxVec3 kU(0.0f);
if (fWLength > 0.0f)
{
PxReal fInvLength;
if ( PxAbs(kW.x) >= PxAbs(kW.y) )
{
// W.x or W.z is the largest magnitude component, swap them
fInvLength = PxRecipSqrt(kW.x*kW.x + kW.z*kW.z);
kU.x = -kW.z*fInvLength;
kU.y = 0.0f;
kU.z = kW.x*fInvLength;
}
else
{
// W.y or W.z is the largest magnitude component, swap them
fInvLength = PxRecipSqrt(kW.y*kW.y + kW.z*kW.z);
kU.x = 0.0f;
kU.y = kW.z*fInvLength;
kU.z = -kW.y*fInvLength;
}
}
PxVec3 kV = kW.cross(kU);
kV.normalize(); // PT: fixed november, 24, 2004. This is a bug in Magic.
// compute intersection
PxVec3 kD(kU.dot(dir), kV.dot(dir), kW.dot(dir));
const float fDLength = kD.magnitude();
const float fInvDLength = fDLength!=0.0f ? 1.0f/fDLength : 0.0f;
kD *= fInvDLength;
const PxVec3 kDiff = origin - p0;
const PxVec3 kP(kU.dot(kDiff), kV.dot(kDiff), kW.dot(kDiff));
const PxReal fRadiusSqr = radius*radius;
// Is the velocity parallel to the capsule direction? (or zero)
if ( PxAbs(kD.z) >= 1.0f - PX_EPS_REAL || fDLength < PX_EPS_REAL )
{
const float fAxisDir = dir.dot(kW);
const PxReal fDiscr = fRadiusSqr - kP.x*kP.x - kP.y*kP.y;
if ( fAxisDir < 0 && fDiscr >= 0.0f )
{
// Velocity anti-parallel to the capsule direction
const PxReal fRoot = PxSqrt(fDiscr);
s[0] = (kP.z + fRoot)*fInvDLength;
s[1] = -(fWLength - kP.z + fRoot)*fInvDLength;
return 2;
}
else if ( fAxisDir > 0 && fDiscr >= 0.0f )
{
// Velocity parallel to the capsule direction
const PxReal fRoot = PxSqrt(fDiscr);
s[0] = -(kP.z + fRoot)*fInvDLength;
s[1] = (fWLength - kP.z + fRoot)*fInvDLength;
return 2;
}
else
{
// sphere heading wrong direction, or no velocity at all
return 0;
}
}
// test intersection with infinite cylinder
PxReal fA = kD.x*kD.x + kD.y*kD.y;
PxReal fB = kP.x*kD.x + kP.y*kD.y;
PxReal fC = kP.x*kP.x + kP.y*kP.y - fRadiusSqr;
PxReal fDiscr = fB*fB - fA*fC;
if ( fDiscr < 0.0f )
{
// line does not intersect infinite cylinder
return 0;
}
PxU32 iQuantity = 0;
if ( fDiscr > 0.0f )
{
// line intersects infinite cylinder in two places
const PxReal fRoot = PxSqrt(fDiscr);
const PxReal fInv = 1.0f/fA;
PxReal fT = (-fB - fRoot)*fInv;
PxReal fTmp = kP.z + fT*kD.z;
const float epsilon = 1e-3f; // PT: see TA35174
if ( fTmp >= -epsilon && fTmp <= fWLength+epsilon )
s[iQuantity++] = fT*fInvDLength;
fT = (-fB + fRoot)*fInv;
fTmp = kP.z + fT*kD.z;
if ( fTmp >= -epsilon && fTmp <= fWLength+epsilon )
s[iQuantity++] = fT*fInvDLength;
if ( iQuantity == 2 )
{
// line intersects capsule wall in two places
return 2;
}
}
else
{
// line is tangent to infinite cylinder
const PxReal fT = -fB/fA;
const PxReal fTmp = kP.z + fT*kD.z;
if ( 0.0f <= fTmp && fTmp <= fWLength )
{
s[0] = fT*fInvDLength;
return 1;
}
}
// test intersection with bottom hemisphere
// fA = 1
fB += kP.z*kD.z;
fC += kP.z*kP.z;
fDiscr = fB*fB - fC;
if ( fDiscr > 0.0f )
{
const PxReal fRoot = PxSqrt(fDiscr);
PxReal fT = -fB - fRoot;
PxReal fTmp = kP.z + fT*kD.z;
if ( fTmp <= 0.0f )
{
s[iQuantity++] = fT*fInvDLength;
if ( iQuantity == 2 )
return 2;
}
fT = -fB + fRoot;
fTmp = kP.z + fT*kD.z;
if ( fTmp <= 0.0f )
{
s[iQuantity++] = fT*fInvDLength;
if ( iQuantity == 2 )
return 2;
}
}
else if ( fDiscr == 0.0f )
{
const PxReal fT = -fB;
const PxReal fTmp = kP.z + fT*kD.z;
if ( fTmp <= 0.0f )
{
s[iQuantity++] = fT*fInvDLength;
if ( iQuantity == 2 )
return 2;
}
}
// test intersection with top hemisphere
// fA = 1
fB -= kD.z*fWLength;
fC += fWLength*(fWLength - 2.0f*kP.z);
fDiscr = fB*fB - fC;
if ( fDiscr > 0.0f )
{
const PxReal fRoot = PxSqrt(fDiscr);
PxReal fT = -fB - fRoot;
PxReal fTmp = kP.z + fT*kD.z;
if ( fTmp >= fWLength )
{
s[iQuantity++] = fT*fInvDLength;
if ( iQuantity == 2 )
return 2;
}
fT = -fB + fRoot;
fTmp = kP.z + fT*kD.z;
if ( fTmp >= fWLength )
{
s[iQuantity++] = fT*fInvDLength;
if ( iQuantity == 2 )
return 2;
}
}
else if ( fDiscr == 0.0f )
{
const PxReal fT = -fB;
const PxReal fTmp = kP.z + fT*kD.z;
if ( fTmp >= fWLength )
{
s[iQuantity++] = fT*fInvDLength;
if ( iQuantity == 2 )
return 2;
}
}
return iQuantity;
}
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