// 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/FIQuery.h> #include <Mathematics/TIQuery.h> #include <Mathematics/Vector3.h> #include <Mathematics/Hypersphere.h> #include <Mathematics/Line.h> namespace WwiseGTE { template <typename Real> class TIQuery<Real, Line3<Real>, Sphere3<Real>> { public: struct Result { bool intersect; }; Result operator()(Line3<Real> const& line, 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> diff = line.origin - sphere.center; Real a0 = Dot(diff, diff) - sphere.radius * sphere.radius; Real a1 = Dot(line.direction, diff); // Intersection occurs when Q(t) has real roots. Real discr = a1 * a1 - a0; result.intersect = (discr >= (Real)0); return result; } }; template <typename Real> class FIQuery<Real, Line3<Real>, Sphere3<Real>> { public: struct Result { bool intersect; int numIntersections; std::array<Real, 2> parameter; std::array<Vector3<Real>, 2> point; }; Result operator()(Line3<Real> const& line, Sphere3<Real> const& sphere) { Result result; DoQuery(line.origin, line.direction, sphere, result); for (int i = 0; i < result.numIntersections; ++i) { result.point[i] = line.origin + result.parameter[i] * line.direction; } return result; } protected: void DoQuery(Vector3<Real> const& lineOrigin, Vector3<Real> const& lineDirection, Sphere3<Real> const& sphere, Result& result) { // 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. Vector3<Real> diff = lineOrigin - sphere.center; Real a0 = Dot(diff, diff) - sphere.radius * sphere.radius; Real a1 = Dot(lineDirection, diff); // Intersection occurs when Q(t) has real roots. Real discr = a1 * a1 - a0; if (discr > (Real)0) { result.intersect = true; result.numIntersections = 2; Real root = std::sqrt(discr); result.parameter[0] = -a1 - root; result.parameter[1] = -a1 + root; } else if (discr < (Real)0) { result.intersect = false; result.numIntersections = 0; } else { result.intersect = true; result.numIntersections = 1; result.parameter[0] = -a1; } } }; }