136 lines
3.7 KiB
C++
136 lines
3.7 KiB
C++
/*
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* Licensed under the Apache License, Version 2.0 (the "License");
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* you may not use this file except in compliance with the License.
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* You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS,
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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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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#include "../matrix.hpp"
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namespace util::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 (util::point<S,T> base, util::vector<S,T> normal);
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explicit plane (util::vector<S+1,T> _coefficients):
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coefficients (_coefficients)
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{ ; }
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util::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 (util::point3f a, util::point3f b, util::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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util::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<util::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<util::point<S,T>> &&) = delete;
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}
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