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86 lines
3.5 KiB
86 lines
3.5 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/Cone.h>
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#include <Mathematics/OrientedBox.h>
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#include <Mathematics/IntrAlignedBox3Cone3.h>
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// Test for intersection of a box and a cone. The cone can be infinite
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// 0 <= minHeight < maxHeight = std::numeric_limits<Real>::max()
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// or finite (cone frustum)
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// 0 <= minHeight < maxHeight < std::numeric_limits<Real>::max().
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// The algorithm is described in
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// https://www.geometrictools.com/Documentation/IntersectionBoxCone.pdf
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// and reports an intersection only when th intersection set has positive
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// volume. For example, let the box be outside the cone. If the box is
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// below the minHeight plane at the cone vertex and just touches the cone
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// vertex, no intersection is reported. If the box is above the maxHeight
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// plane and just touches the disk capping the cone, either at a single
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// point, a line segment of points or a polygon of points, no intersection
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// is reported.
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// TODO: These queries were designed when an infinite cone was defined
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// by choosing maxHeight of std::numeric_limits<Real>::max(). The Cone<N,Real>
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// class has been redesigned not to use std::numeric_limits to allow for
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// arithmetic systems that do not have representations for infinities
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// (such as BSNumber and BSRational). The intersection queries need to be
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// rewritten for the new class design. FOR NOW, the queries will work with
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// float/double when you create a cone using the cone-frustum constructor
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// Cone(ray, angle, minHeight, std::numeric_limits<Real>::max()).
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namespace gte
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{
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template <typename Real>
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class TIQuery<Real, OrientedBox<3, Real>, Cone<3, Real>>
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:
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public TIQuery<Real, AlignedBox<3, Real>, Cone<3, Real>>
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{
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public:
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struct Result
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:
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public TIQuery<Real, AlignedBox<3, Real>, Cone<3, Real>>::Result
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{
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// No additional information to compute.
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};
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Result operator()(OrientedBox<3, Real> const& box, Cone<3, Real> const& cone)
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{
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// Transform the cone and box so that the cone vertex is at the
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// origin and the box is axis aligned. This allows us to call the
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// base class operator()(...).
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Vector<3, Real> diff = box.center - cone.ray.origin;
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Vector<3, Real> xfrmBoxCenter
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{
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Dot(box.axis[0], diff),
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Dot(box.axis[1], diff),
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Dot(box.axis[2], diff)
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};
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AlignedBox<3, Real> xfrmBox;
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xfrmBox.min = xfrmBoxCenter - box.extent;
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xfrmBox.max = xfrmBoxCenter + box.extent;
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Cone<3, Real> xfrmCone = cone;
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for (int i = 0; i < 3; ++i)
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{
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xfrmCone.ray.origin[i] = (Real)0;
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xfrmCone.ray.direction[i] = Dot(box.axis[i], cone.ray.direction);
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}
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// Test for intersection between the aligned box and the cone.
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auto bcResult = TIQuery<Real, AlignedBox<3, Real>, Cone<3, Real>>::operator()(xfrmBox, xfrmCone);
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Result result;
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result.intersect = bcResult.intersect;
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return result;
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}
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};
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// Template alias for convenience.
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template <typename Real>
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using TIOrientedBox3Cone3 = TIQuery<Real, OrientedBox<3, Real>, Cone<3, Real>>;
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}
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