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61 lines
2.0 KiB
61 lines
2.0 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/Hyperellipsoid.h>
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#include <Mathematics/Line.h>
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namespace gte
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{
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// Project an ellipse onto a line. The projection interval is
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// [smin,smax] and corresponds to the line segment P+s*D, where
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// smin <= s <= smax.
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template <typename Real>
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void Project(Ellipse2<Real> const& ellipse, Line2<Real> const& line,
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Real& smin, Real& smax)
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{
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// Center of projection interval.
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Real center = Dot(line.direction, ellipse.center - line.origin);
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// Radius of projection interval.
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Real tmp[2] =
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{
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ellipse.extent[0] * Dot(line.direction, ellipse.axis[0]),
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ellipse.extent[1] * Dot(line.direction, ellipse.axis[1])
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};
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Real rSqr = tmp[0] * tmp[0] + tmp[1] * tmp[1];
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Real radius = std::sqrt(rSqr);
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smin = center - radius;
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smax = center + radius;
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}
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// Project an ellipsoid onto a line. The projection interval is
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// [smin,smax] and corresponds to the line segment P+s*D, where
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// smin <= s <= smax.
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template <typename Real>
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void Project(Ellipsoid3<Real> const& ellipsoid,
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Line3<Real> const& line, Real& smin, Real& smax)
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{
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// Center of projection interval.
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Real center = Dot(line.direction, ellipsoid.center - line.origin);
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// Radius of projection interval.
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Real tmp[3] =
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{
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ellipsoid.extent[0] * Dot(line.direction, ellipsoid.axis[0]),
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ellipsoid.extent[1] * Dot(line.direction, ellipsoid.axis[1]),
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ellipsoid.extent[2] * Dot(line.direction, ellipsoid.axis[2])
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};
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Real rSqr = tmp[0] * tmp[0] + tmp[1] * tmp[1] + tmp[2] * tmp[2];
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Real radius = std::sqrt(rSqr);
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smin = center - radius;
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smax = center + radius;
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}
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}
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