libcruft-util/geom/plane.hpp

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/*
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* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* 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
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
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*
* Copyright 2015-2018 Danny Robson <danny@nerdcruft.net>
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*/
#pragma once
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#include "../point.hpp"
#include "../vector.hpp"
#include "../matrix.hpp"
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namespace util::geom {
/// represents an S dimensional plane in parametric form: ax + by + cz + d = 0
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template <size_t S, typename T>
struct plane {
plane () = default;
plane (util::point<S,T> base, util::vector<S,T> normal);
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explicit plane (util::vector<S+1,T> _coefficients):
coefficients (_coefficients)
{ ; }
util::vector<S+1,T> coefficients;
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};
typedef plane<2,float> plane2f;
typedef plane<3,float> plane3f;
inline plane3f
make_plane (util::point3f a, util::point3f b, util::point3f c)
{
return plane3f (a, normalised (cross (b - a, c - a)));
}
///////////////////////////////////////////////////////////////////////////
/// returns the normal for a plane
template <size_t S, typename T>
util::vector<S,T>
normal (plane<S,T> p)
{
return p.coefficients.template redim<S> ();
}
///////////////////////////////////////////////////////////////////////////
/// normalises a plane's parametric form
///
/// useful only after manually modifying the coefficients (as in default
/// construction and piecewise initialisation). a plane will otherwise be
/// assumed to be in normal form.
template <size_t S, typename T>
plane<S,T>
normalised (plane<S,T> p)
{
const auto mag = norm (normal (p));
CHECK_NEZ (mag);
return plane<S,T> (p.coefficients / mag);
}
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///////////////////////////////////////////////////////////////////////////
/// calculates the distance from a plane to a point.
///
/// positive distances are in front of the plane, negative is behind;
///
/// NOTE: `distance2` is _not_ the squared distance. It is the
/// unnormalised distance. It needs to be divided by the norm of the
/// plane normal.
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template <size_t S, typename T>
T
distance2 (plane<S,T> p, point<S,T> q)
{
return dot (p.coefficients, q.template redim<S+1> (1));
}
template <size_t S, typename T>
T
distance2 (point<S,T> p, plane<S,T> q)
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{
return -distance2 (q, p);
}
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template <size_t S, typename T>
T
distance (plane<S,T> p, point<S,T> q)
{
return distance2 (p, q) / norm (normal (p));
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}
template <size_t S, typename T>
T
distance (point<S,T> p, plane<S,T> q)
{
return -distance (q, p);
}
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///////////////////////////////////////////////////////////////////////////
template <size_t S, typename T>
auto
furthest (plane<S,T> p, const std::vector<util::point<S,T>> &cloud)
{
T maxd = -INFINITY;
auto best = cloud.begin ();
for (auto q = cloud.begin (), last = cloud.end (); q != last; ++q) {
if (auto d = distance (p, *q); d > maxd) {
maxd = d;
best = q;
}
}
return std::make_tuple (best, maxd);
}
template <size_t S, typename T>
auto
furthest (plane<S,T>, std::vector<util::point<S,T>> &&) = delete;
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}