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138 lines
3.9 KiB
138 lines
3.9 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/Vector.h>
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// A box has center C, axis directions U[i], and extents e[i]. The set
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// {U[0],...,U[N-1]} is orthonormal, which means the vectors are
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// unit-length and mutually perpendicular. The extents are nonnegative;
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// zero is allowed, meaning the box is degenerate in the corresponding
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// direction. A point X is represented in box coordinates by
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// X = C + y[0]*U[0] + y[1]*U[1]. This point is inside or on the
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// box whenever |y[i]| <= e[i] for all i.
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namespace gte
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{
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template <int N, typename Real>
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class OrientedBox
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{
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public:
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// Construction and destruction. The default constructor sets the
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// center to (0,...,0), axis d to Vector<N,Real>::Unit(d) and
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// extent d to +1.
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OrientedBox()
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{
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center.MakeZero();
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for (int i = 0; i < N; ++i)
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{
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axis[i].MakeUnit(i);
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extent[i] = (Real)1;
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}
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}
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OrientedBox(Vector<N, Real> const& inCenter,
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std::array<Vector<N, Real>, N> const& inAxis,
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Vector<N, Real> const& inExtent)
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:
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center(inCenter),
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axis(inAxis),
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extent(inExtent)
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{
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}
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// Compute the vertices of the box. If index i has the bit pattern
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// i = b[N-1]...b[0], then
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// vertex[i] = center + sum_{d=0}^{N-1} sign[d] * extent[d] * axis[d]
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// where sign[d] = 2*b[d] - 1.
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void GetVertices(std::array<Vector<N, Real>, (1 << N)>& vertex) const
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{
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unsigned int const dsup = static_cast<unsigned int>(N);
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std::array<Vector<N, Real>, N> product;
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for (unsigned int d = 0; d < dsup; ++d)
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{
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product[d] = extent[d] * axis[d];
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}
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int const imax = (1 << N);
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for (int i = 0; i < imax; ++i)
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{
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vertex[i] = center;
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for (unsigned int d = 0, mask = 1; d < dsup; ++d, mask <<= 1)
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{
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Real sign = (i & mask ? (Real)1 : (Real)-1);
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vertex[i] += sign * product[d];
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}
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}
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}
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// Public member access. It is required that extent[i] >= 0.
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Vector<N, Real> center;
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std::array<Vector<N, Real>, N> axis;
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Vector<N, Real> extent;
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public:
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// Comparisons to support sorted containers.
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bool operator==(OrientedBox const& box) const
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{
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return center == box.center && axis == box.axis && extent == box.extent;
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}
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bool operator!=(OrientedBox const& box) const
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{
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return !operator==(box);
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}
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bool operator< (OrientedBox const& box) const
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{
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if (center < box.center)
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{
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return true;
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}
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if (center > box.center)
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{
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return false;
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}
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if (axis < box.axis)
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{
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return true;
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}
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if (axis > box.axis)
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{
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return false;
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}
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return extent < box.extent;
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}
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bool operator<=(OrientedBox const& box) const
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{
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return !box.operator<(*this);
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}
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bool operator> (OrientedBox const& box) const
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{
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return box.operator<(*this);
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}
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bool operator>=(OrientedBox const& box) const
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{
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return !operator<(box);
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}
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};
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// Template aliases for convenience.
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template <typename Real>
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using OrientedBox2 = OrientedBox<2, Real>;
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template <typename Real>
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using OrientedBox3 = OrientedBox<3, Real>;
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}
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