// David Eberly, Geometric Tools, Redmond WA 98052 // Copyright (c) 1998-2020 // Distributed under the Boost Software License, Version 1.0. // https://www.boost.org/LICENSE_1_0.txt // https://www.geometrictools.com/License/Boost/LICENSE_1_0.txt // Version: 4.0.2019.08.13 #pragma once #include <Mathematics/IntrIntervals.h> #include <Mathematics/IntrLine3Sphere3.h> #include <Mathematics/Segment.h> namespace WwiseGTE { template <typename Real> class TIQuery<Real, Segment3<Real>, Sphere3<Real>> { public: struct Result { bool intersect; }; Result operator()(Segment3<Real> const& segment, Sphere3<Real> const& sphere) { // The sphere is (X-C)^T*(X-C)-1 = 0 and the line is X = P+t*D. // Substitute the line equation into the sphere equation to // obtain a quadratic equation Q(t) = t^2 + 2*a1*t + a0 = 0, where // a1 = D^T*(P-C) and a0 = (P-C)^T*(P-C)-1. Result result; Vector3<Real> segOrigin, segDirection; Real segExtent; segment.GetCenteredForm(segOrigin, segDirection, segExtent); Vector3<Real> diff = segOrigin - sphere.center; Real a0 = Dot(diff, diff) - sphere.radius * sphere.radius; Real a1 = Dot(segDirection, diff); Real discr = a1 * a1 - a0; if (discr < (Real)0) { result.intersect = false; return result; } Real tmp0 = segExtent * segExtent + a0; Real tmp1 = ((Real)2) * a1 * segExtent; Real qm = tmp0 - tmp1; Real qp = tmp0 + tmp1; if (qm * qp <= (Real)0) { result.intersect = true; return result; } result.intersect = (qm > (Real)0 && std::fabs(a1) < segExtent); return result; } }; template <typename Real> class FIQuery<Real, Segment3<Real>, Sphere3<Real>> : public FIQuery<Real, Line3<Real>, Sphere3<Real>> { public: struct Result : public FIQuery<Real, Line3<Real>, Sphere3<Real>>::Result { // No additional information to compute. }; Result operator()(Segment3<Real> const& segment, Sphere3<Real> const& sphere) { Vector3<Real> segOrigin, segDirection; Real segExtent; segment.GetCenteredForm(segOrigin, segDirection, segExtent); Result result; DoQuery(segOrigin, segDirection, segExtent, sphere, result); for (int i = 0; i < result.numIntersections; ++i) { result.point[i] = segOrigin + result.parameter[i] * segDirection; } return result; } protected: void DoQuery(Vector3<Real> const& segOrigin, Vector3<Real> const& segDirection, Real segExtent, Sphere3<Real> const& sphere, Result& result) { FIQuery<Real, Line3<Real>, Sphere3<Real>>::DoQuery(segOrigin, segDirection, sphere, result); if (result.intersect) { // The line containing the segment intersects the sphere; the // t-interval is [t0,t1]. The segment intersects the sphere // as long as [t0,t1] overlaps the segment t-interval // [-segExtent,+segExtent]. std::array<Real, 2> segInterval = { -segExtent, segExtent }; FIQuery<Real, std::array<Real, 2>, std::array<Real, 2>> iiQuery; auto iiResult = iiQuery(result.parameter, segInterval); if (iiResult.intersect) { result.numIntersections = iiResult.numIntersections; result.parameter = iiResult.overlap; } else { result.intersect = false; result.numIntersections = 0; } } } }; }