Hyperplane.h

// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
// SPDX-License-Identifier: MPL-2.0
 
#ifndef EIGEN_HYPERPLANE_H
#define EIGEN_HYPERPLANE_H
 
// IWYU pragma: private
#include "./InternalHeaderCheck.h"
 
namespace Eigen {

template <typename Scalar_, int AmbientDim_, int Options_>
class Hyperplane {
 public:
  EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(Scalar_,
                                                             AmbientDim_ == Dynamic ? Dynamic : AmbientDim_ + 1)
  enum { AmbientDimAtCompileTime = AmbientDim_, Options = Options_ };
  using Scalar = Scalar_;
  using RealScalar = typename NumTraits<Scalar>::Real;
  using Index = Eigen::Index;  
  using VectorType = Matrix<Scalar, AmbientDimAtCompileTime, 1>;
  using Coefficients =
      Matrix<Scalar, Index(AmbientDimAtCompileTime) == Dynamic ? Dynamic : Index(AmbientDimAtCompileTime) + 1, 1,
             Options>;
  using NormalReturnType = Block<Coefficients, AmbientDimAtCompileTime, 1>;
  using ConstNormalReturnType = const Block<const Coefficients, AmbientDimAtCompileTime, 1>;

  EIGEN_DEVICE_FUNC inline Hyperplane() {}
 
  template <int OtherOptions>
  EIGEN_DEVICE_FUNC Hyperplane(const Hyperplane<Scalar, AmbientDimAtCompileTime, OtherOptions>& other)
      : m_coeffs(other.coeffs()) {}

  EIGEN_DEVICE_FUNC inline explicit Hyperplane(Index _dim) : m_coeffs(_dim + 1) {}

  EIGEN_DEVICE_FUNC inline Hyperplane(const VectorType& n, const VectorType& e) : m_coeffs(n.size() + 1) {
    normal() = n;
    offset() = -n.dot(e);
  }

  EIGEN_DEVICE_FUNC inline Hyperplane(const VectorType& n, const Scalar& d) : m_coeffs(n.size() + 1) {
    normal() = n;
    offset() = d;
  }

  EIGEN_DEVICE_FUNC static inline Hyperplane Through(const VectorType& p0, const VectorType& p1) {
    Hyperplane result(p0.size());
    result.normal() = (p1 - p0).unitOrthogonal();
    result.offset() = -p0.dot(result.normal());
    return result;
  }

  EIGEN_DEVICE_FUNC static inline Hyperplane Through(const VectorType& p0, const VectorType& p1, const VectorType& p2) {
    EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(VectorType, 3)
    Hyperplane result(p0.size());
    VectorType v0(p2 - p0), v1(p1 - p0);
    result.normal() = v0.cross(v1);
    RealScalar norm = result.normal().norm();
    if (norm <= v0.norm() * v1.norm() * NumTraits<RealScalar>::epsilon()) {
      Matrix<Scalar, 2, 3> m;
      m << v0.transpose(), v1.transpose();
      JacobiSVD<Matrix<Scalar, 2, 3>, ComputeFullV> svd(m);
      result.normal() = svd.matrixV().col(2);
    } else
      result.normal() /= norm;
    result.offset() = -p0.dot(result.normal());
    return result;
  }

  // FIXME: for consistency, consider implementing as a static Through function.
  EIGEN_DEVICE_FUNC explicit Hyperplane(const ParametrizedLine<Scalar, AmbientDimAtCompileTime>& parametrized) {
    normal() = parametrized.direction().unitOrthogonal();
    offset() = -parametrized.origin().dot(normal());
  }

  EIGEN_DEVICE_FUNC inline Index dim() const {
    return AmbientDimAtCompileTime == Dynamic ? m_coeffs.size() - 1 : Index(AmbientDimAtCompileTime);
  }

  EIGEN_DEVICE_FUNC void normalize(void) { m_coeffs /= normal().norm(); }

  EIGEN_DEVICE_FUNC inline Scalar signedDistance(const VectorType& p) const { return normal().dot(p) + offset(); }

  EIGEN_DEVICE_FUNC inline Scalar absDistance(const VectorType& p) const { return numext::abs(signedDistance(p)); }

  EIGEN_DEVICE_FUNC inline VectorType projection(const VectorType& p) const { return p - signedDistance(p) * normal(); }

  EIGEN_DEVICE_FUNC inline ConstNormalReturnType normal() const {
    return ConstNormalReturnType(m_coeffs, 0, 0, dim(), 1);
  }

  EIGEN_DEVICE_FUNC inline NormalReturnType normal() { return NormalReturnType(m_coeffs, 0, 0, dim(), 1); }

  EIGEN_DEVICE_FUNC inline const Scalar& offset() const { return m_coeffs.coeff(dim()); }

  EIGEN_DEVICE_FUNC inline Scalar& offset() { return m_coeffs(dim()); }

  EIGEN_DEVICE_FUNC inline const Coefficients& coeffs() const { return m_coeffs; }

  EIGEN_DEVICE_FUNC inline Coefficients& coeffs() { return m_coeffs; }

  EIGEN_DEVICE_FUNC VectorType intersection(const Hyperplane& other) const {
    EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(VectorType, 2)
    Scalar det = coeffs().coeff(0) * other.coeffs().coeff(1) - coeffs().coeff(1) * other.coeffs().coeff(0);
    // since the line equations ax+by=c are normalized with a^2+b^2=1, the following tests
    // whether the two lines are approximately parallel.
    if (internal::isMuchSmallerThan(det, Scalar(1))) {  // special case where the two lines are approximately parallel.
                                                        // Pick any point on the first line.
      if (numext::abs(coeffs().coeff(1)) > numext::abs(coeffs().coeff(0)))
        return VectorType(coeffs().coeff(1), -coeffs().coeff(2) / coeffs().coeff(1) - coeffs().coeff(0));
      else
        return VectorType(-coeffs().coeff(2) / coeffs().coeff(0) - coeffs().coeff(1), coeffs().coeff(0));
    } else {  // general case
      Scalar invdet = Scalar(1) / det;
      return VectorType(
          invdet * (coeffs().coeff(1) * other.coeffs().coeff(2) - other.coeffs().coeff(1) * coeffs().coeff(2)),
          invdet * (other.coeffs().coeff(0) * coeffs().coeff(2) - coeffs().coeff(0) * other.coeffs().coeff(2)));
    }
  }

  template <typename XprType>
  EIGEN_DEVICE_FUNC inline Hyperplane& transform(const MatrixBase<XprType>& mat, TransformTraits traits = Affine) {
    if (traits == Affine) {
      normal() = mat.inverse().transpose() * normal();
      m_coeffs /= normal().norm();
    } else if (traits == Isometry)
      normal() = mat * normal();
    else {
      eigen_assert(0 && "invalid traits value in Hyperplane::transform()");
    }
    return *this;
  }

  template <int TrOptions>
  EIGEN_DEVICE_FUNC inline Hyperplane& transform(const Transform<Scalar, AmbientDimAtCompileTime, Affine, TrOptions>& t,
                                                 TransformTraits traits = Affine) {
    transform(t.linear(), traits);
    offset() -= normal().dot(t.translation());
    return *this;
  }

  template <typename NewScalarType>
  EIGEN_DEVICE_FUNC inline
      typename internal::cast_return_type<Hyperplane,
                                          Hyperplane<NewScalarType, AmbientDimAtCompileTime, Options> >::type
      cast() const {
    return
        typename internal::cast_return_type<Hyperplane,
                                            Hyperplane<NewScalarType, AmbientDimAtCompileTime, Options> >::type(*this);
  }

  template <typename OtherScalarType, int OtherOptions>
  EIGEN_DEVICE_FUNC inline explicit Hyperplane(
      const Hyperplane<OtherScalarType, AmbientDimAtCompileTime, OtherOptions>& other) {
    m_coeffs = other.coeffs().template cast<Scalar>();
  }

  template <int OtherOptions>
  EIGEN_DEVICE_FUNC bool isApprox(
      const Hyperplane<Scalar, AmbientDimAtCompileTime, OtherOptions>& other,
      const typename NumTraits<Scalar>::Real& prec = NumTraits<Scalar>::dummy_precision()) const {
    return m_coeffs.isApprox(other.m_coeffs, prec);
  }

  template <int OtherOptions>
  EIGEN_DEVICE_FUNC bool isCoincident(
      const Hyperplane<Scalar, AmbientDimAtCompileTime, OtherOptions>& other,
      const typename NumTraits<Scalar>::Real& prec = NumTraits<Scalar>::dummy_precision()) const {
    const RealScalar this_norm = normal().norm();
    const RealScalar other_norm = other.normal().norm();
    eigen_assert(this_norm > RealScalar(0) && other_norm > RealScalar(0));
    // Normalizing accounts for |gamma|; what is left of it is a unit-modulus factor, and the
    // normals themselves determine it, since the inner product of two coincident unit normals is
    // exactly that factor. Orthogonal normals leave it undetermined, but no factor makes those
    // agree either, so the choice made for them does not matter.
    const Scalar inner = normal().dot(other.normal());
    const RealScalar inner_norm = numext::abs(inner);
    const Scalar phase = inner_norm > RealScalar(0) ? inner / Scalar(inner_norm) : Scalar(1);
    if (!((other.normal() / Scalar(other_norm) - phase * (normal() / Scalar(this_norm))).norm() <= prec)) return false;
    return internal::isApprox(other.offset() / Scalar(other_norm), numext::conj(phase) * (offset() / Scalar(this_norm)),
                              prec);
  }
 
 protected:
  Coefficients m_coeffs;
};
 
}  // end namespace Eigen
 
#endif  // EIGEN_HYPERPLANE_H