128 lines
3.3 KiB
C++
128 lines
3.3 KiB
C++
/*
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* This Source Code Form is subject to the terms of the Mozilla Public
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* License, v. 2.0. If a copy of the MPL was not distributed with this
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* file, You can obtain one at http://mozilla.org/MPL/2.0/.
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*
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* Copyright 2015-2018 Danny Robson <danny@nerdcruft.net>
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*/
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#pragma once
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#include "../point.hpp"
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#include "../vector.hpp"
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namespace cruft::geom {
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/// represents an S dimensional plane in parametric form: ax + by + cz + d = 0
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template <size_t S, typename T>
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struct plane {
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plane () = default;
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plane (cruft::point<S,T> base, cruft::vector<S,T> normal);
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explicit plane (cruft::vector<S+1,T> _coefficients):
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coefficients (_coefficients)
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{ ; }
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cruft::vector<S+1,T> coefficients;
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};
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typedef plane<2,float> plane2f;
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typedef plane<3,float> plane3f;
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inline plane3f
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make_plane (cruft::point3f a, cruft::point3f b, cruft::point3f c)
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{
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return plane3f (a, normalised (cross (b - a, c - a)));
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}
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///////////////////////////////////////////////////////////////////////////
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/// returns the normal for a plane
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template <size_t S, typename T>
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cruft::vector<S,T>
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normal (plane<S,T> p)
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{
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return p.coefficients.template redim<S> ();
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}
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///////////////////////////////////////////////////////////////////////////
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/// normalises a plane's parametric form
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///
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/// useful only after manually modifying the coefficients (as in default
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/// construction and piecewise initialisation). a plane will otherwise be
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/// assumed to be in normal form.
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template <size_t S, typename T>
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plane<S,T>
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normalised (plane<S,T> p)
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{
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const auto mag = norm (normal (p));
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CHECK_NEZ (mag);
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return plane<S,T> (p.coefficients / mag);
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}
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///////////////////////////////////////////////////////////////////////////
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/// calculates the distance from a plane to a point.
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///
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/// positive distances are in front of the plane, negative is behind;
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///
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/// NOTE: `distance2` is _not_ the squared distance. It is the
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/// unnormalised distance. It needs to be divided by the norm of the
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/// plane normal.
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template <size_t S, typename T>
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T
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distance2 (plane<S,T> p, point<S,T> q)
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{
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return dot (p.coefficients, q.template redim<S+1> (1));
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}
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template <size_t S, typename T>
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T
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distance2 (point<S,T> p, plane<S,T> q)
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{
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return -distance2 (q, p);
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}
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template <size_t S, typename T>
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T
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distance (plane<S,T> p, point<S,T> q)
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{
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return distance2 (p, q) / norm (normal (p));
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}
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template <size_t S, typename T>
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T
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distance (point<S,T> p, plane<S,T> q)
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{
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return -distance (q, p);
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}
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///////////////////////////////////////////////////////////////////////////
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template <size_t S, typename T>
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auto
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furthest (plane<S,T> p, const std::vector<cruft::point<S,T>> &cloud)
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{
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T maxd = -INFINITY;
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auto best = cloud.begin ();
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for (auto q = cloud.begin (), last = cloud.end (); q != last; ++q) {
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if (auto d = distance (p, *q); d > maxd) {
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maxd = d;
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best = q;
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}
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}
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return std::make_tuple (best, maxd);
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}
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template <size_t S, typename T>
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auto
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furthest (plane<S,T>, std::vector<cruft::point<S,T>> &&) = delete;
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}
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