47 lines
1.6 KiB
47 lines
1.6 KiB
// David Eberly, Geometric Tools, Redmond WA 98052
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// Copyright (c) 1998-2021
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// Distributed under the Boost Software License, Version 1.0.
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// https://www.boost.org/LICENSE_1_0.txt
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// https://www.geometrictools.com/License/Boost/LICENSE_1_0.txt
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// Version: 4.0.2019.08.13
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#pragma once
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#include <Mathematics/TIQuery.h>
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#include <Mathematics/Halfspace.h>
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#include <Mathematics/Hyperellipsoid.h>
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#include <Mathematics/Matrix3x3.h>
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// Queries for intersection of objects with halfspaces. These are useful for
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// containment testing, object culling, and clipping.
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namespace gte
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{
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template <typename Real>
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class TIQuery<Real, Halfspace3<Real>, Ellipsoid3<Real>>
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{
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public:
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struct Result
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{
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bool intersect;
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};
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Result operator()(Halfspace3<Real> const& halfspace, Ellipsoid3<Real> const& ellipsoid)
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{
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// Project the ellipsoid onto the normal line. The plane of the
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// halfspace occurs at the origin (zero) of the normal line.
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Result result;
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Matrix3x3<Real> MInverse;
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ellipsoid.GetMInverse(MInverse);
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Real discr = Dot(halfspace.normal, MInverse * halfspace.normal);
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Real extent = std::sqrt(std::max(discr, (Real)0));
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Real center = Dot(halfspace.normal, ellipsoid.center) - halfspace.constant;
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Real tmax = center + extent;
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// The ellipsoid and halfspace intersect when the projection
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// interval maximum is nonnegative.
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result.intersect = (tmax >= (Real)0);
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return result;
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}
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};
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}
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