vpPlane.cpp

/*
 * ViSP, open source Visual Servoing Platform software.
 * Copyright (C) 2005 - 2025 by Inria. All rights reserved.
 *
 * This software is free software; you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation; either version 2 of the License, or
 * (at your option) any later version.
 * See the file LICENSE.txt at the root directory of this source
 * distribution for additional information about the GNU GPL.
 *
 * For using ViSP with software that can not be combined with the GNU
 * GPL, please contact Inria about acquiring a ViSP Professional
 * Edition License.
 *
 * See https://visp.inria.fr for more information.
 *
 * This software was developed at:
 * Inria Rennes - Bretagne Atlantique
 * Campus Universitaire de Beaulieu
 * 35042 Rennes Cedex
 * France
 *
 * If you have questions regarding the use of this file, please contact
 * Inria at visp@inria.fr
 *
 * This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
 * WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
 *
 * Description:
 * Plane geometrical structure.
 */

 
#include <visp3/core/vpPlane.h>
 
#include <cmath>  // std::fabs
#include <limits> // numeric_limits
 
BEGIN_VISP_NAMESPACE
vpPlane &vpPlane::operator=(const vpPlane &p)
{
  A = p.A;
  B = p.B;
  C = p.C;
  D = p.D;
 
  return *this;
}

vpPlane::vpPlane() : A(0), B(0), C(0), D(0) { }

vpPlane::vpPlane(double a, double b, double c, double d) : A(a), B(b), C(c), D(d) { }

vpPlane::vpPlane(const vpPlane &P) : A(0), B(0), C(0), D(0)
{
  setA(P.getA());
  setB(P.getB());
  setC(P.getC());
  setD(P.getD());
}

vpPlane::vpPlane(const vpPoint &P, const vpColVector &normal, const vpPlaneFrame &frame) : A(0), B(0), C(0), D(0)
{
  const unsigned int index_0 = 0;
  const unsigned int index_1 = 1;
  const unsigned int index_2 = 2;
  // Equation of the plane is given by:
  A = normal[index_0];
  B = normal[index_1];
  C = normal[index_2];
 
  if (frame == vpPlane::camera_frame) {
    D = -((A * P.get_X()) + (B * P.get_Y()) + (C * P.get_Z()));
  }
  else {
    D = -((A * P.get_oX()) + (B * P.get_oY()) + (C * P.get_oZ()));
  }
}

vpPlane &vpPlane::init(const vpPlane &P)
{
  setA(P.getA());
  setB(P.getB());
  setC(P.getC());
  setD(P.getD());
 
  return *this;
}

vpPlane &vpPlane::init(const vpPoint &P, const vpColVector &normal, const vpPlaneFrame &frame)
{
  const unsigned int index_0 = 0;
  const unsigned int index_1 = 1;
  const unsigned int index_2 = 2;
  // Equation of the plane is given by:
  A = normal[index_0];
  B = normal[index_1];
  C = normal[index_2];
 
  if (frame == vpPlane::camera_frame) {
    D = -((A * P.get_X()) + (B * P.get_Y()) + (C * P.get_Z()));
  }
  else {
    D = -((A * P.get_oX()) + (B * P.get_oY()) + (C * P.get_oZ()));
  }
 
  return *this;
}

vpPlane &vpPlane::init(const vpColVector &P, const vpColVector &normal)
{
  const unsigned int index_0 = 0;
  const unsigned int index_1 = 1;
  const unsigned int index_2 = 2;
  // Equation of the plane is given by:
  A = normal[index_0];
  B = normal[index_1];
  C = normal[index_2];
 
  D = -((A * P[0]) + (B * P[1]) + (C * P[index_2]));
 
  return *this;
}

vpPlane &vpPlane::init(const vpPoint &P, const vpPoint &Q, const vpPoint &R, const vpPlaneFrame &frame)
{
  vpColVector a(3);
  vpColVector b(3);
  vpColVector n(3);
  const unsigned int index_0 = 0;
  const unsigned int index_1 = 1;
  const unsigned int index_2 = 2;
  if (frame == vpPlane::camera_frame) {
    // Calculate vector corresponding to PQ
    a[index_0] = P.get_X() - Q.get_X();
    a[index_1] = P.get_Y() - Q.get_Y();
    a[index_2] = P.get_Z() - Q.get_Z();
 
    // Calculate vector corresponding to PR
    b[index_0] = P.get_X() - R.get_X();
    b[index_1] = P.get_Y() - R.get_Y();
    b[index_2] = P.get_Z() - R.get_Z();
  }
  else {
    // Calculate vector corresponding to PQ
    a[index_0] = P.get_oX() - Q.get_oX();
    a[index_1] = P.get_oY() - Q.get_oY();
    a[index_2] = P.get_oZ() - Q.get_oZ();
 
    // Calculate vector corresponding to PR
    b[index_0] = P.get_oX() - R.get_oX();
    b[index_1] = P.get_oY() - R.get_oY();
    b[index_2] = P.get_oZ() - R.get_oZ();
  }
  // Calculate normal vector to plane PQ x PR
  n = vpColVector::cross(a, b);
 
  // Equation of the plane is given by:
  A = n[index_0];
  B = n[index_1];
  C = n[index_2];
  if (frame == vpPlane::camera_frame) {
    D = -((A * P.get_X()) + (B * P.get_Y()) + (C * P.get_Z()));
  }
  else {
    D = -((A * P.get_oX()) + (B * P.get_oY()) + (C * P.get_oZ()));
  }
 
  double norm = sqrt((A * A) + (B * B) + (C * C));
  A /= norm;
  B /= norm;
  C /= norm;
  D /= norm;
 
  return *this;
}

vpPlane::vpPlane(const vpPoint &P, const vpPoint &Q, const vpPoint &R, const vpPlaneFrame &frame) : A(0), B(0), C(0), D(0)
{
  init(P, Q, R, frame);
}

double vpPlane::computeZ(double x, double y) const
{
  return -getD() / ((getA() * x) + (getB() * y) + getC());
}

vpColVector vpPlane::getNormal() const
{
  const unsigned int val_3 = 3;
  vpColVector n(val_3);
  const unsigned int index_0 = 0;
  const unsigned int index_1 = 1;
  const unsigned int index_2 = 2;
  n[index_0] = A;
  n[index_1] = B;
  n[index_2] = C;
 
  return n;
}

void vpPlane::getNormal(vpColVector &n) const
{
  const unsigned int val_3 = 3;
  n.resize(val_3);
  const unsigned int index_0 = 0;
  const unsigned int index_1 = 1;
  const unsigned int index_2 = 2;
  n[index_0] = A;
  n[index_1] = B;
  n[index_2] = C;
}

void vpPlane::projectionPointOnPlan(const vpPoint &P, vpPoint &Pproj, const vpPlaneFrame &frame) const
{
  double x0, y0, z0;
  double rho;
 
  if (frame == vpPlane::camera_frame) {
    x0 = P.get_X() / P.get_W();
    y0 = P.get_Y() / P.get_W();
    z0 = P.get_Z() / P.get_W();
 
    rho = -((A * x0) + (B * y0) + (C * z0) + D) / ((A * A) + (B * B) + (C * C));
 
    Pproj.set_X(x0 + (A * rho));
    Pproj.set_Y(y0 + (B * rho));
    Pproj.set_Z(z0 + (C * rho));
    Pproj.set_W(1);
  }
  else {
    x0 = P.get_oX() / P.get_oW();
    y0 = P.get_oY() / P.get_oW();
    z0 = P.get_oZ() / P.get_oW();
 
    rho = -((A * x0) + (B * y0) + (C * z0) + D) / ((A * A) + (B * B) + (C * C));
 
    Pproj.set_oX(x0 + (A * rho));
    Pproj.set_oY(y0 + (B * rho));
    Pproj.set_oZ(z0 + (C * rho));
    Pproj.set_oW(1);
  }
}
 
double vpPlane::rayIntersection(const vpPoint &M0, const vpPoint &M1, vpColVector &H) const
{
  double k, scal;
  const unsigned int index_0 = 0;
  const unsigned int index_1 = 1;
  const unsigned int index_2 = 2;
 
  // --comment: if M0.get_X() diff 0 or M0.get_Y() diff 0 or M0.get_Z() diff 0
  if ((std::fabs(M0.get_X()) > std::numeric_limits<double>::epsilon()) ||
      (std::fabs(M0.get_Y()) > std::numeric_limits<double>::epsilon()) ||
      (std::fabs(M0.get_Z()) > std::numeric_limits<double>::epsilon())) {
    double R[3];
    R[index_0] = M1.get_X() - M0.get_X();
    R[index_1] = M1.get_Y() - M0.get_Y();
    R[index_2] = M1.get_Z() - M0.get_Z();
 
    scal = (getA() * R[index_0]) + (getB() * R[index_1]) + (getC() * R[index_2]);
    // --comment: if scal != 0
    if (std::fabs(scal) > std::numeric_limits<double>::epsilon()) {
      k = -((getA() * M0.get_X()) + (getB() * M0.get_Y()) + (getC() * M0.get_Z()) + getD()) / scal;
    }
    else {
      k = 0;
    }
 
    H[index_0] = M0.get_X() + (k * R[index_0]);
    H[index_1] = M0.get_Y() + (k * R[index_1]);
    H[index_2] = M0.get_Z() + (k * R[index_2]);
  }
  else {
    scal = (getA() * M1.get_X()) + (getB() * M1.get_Y()) + (getC() * M1.get_Z());
    // --comment: if scal != 0
    if (std::fabs(scal) > std::numeric_limits<double>::epsilon()) {
      k = -getD() / scal;
    }
    else {
      k = 0;
    }
    H[index_0] = k * M1.get_X();
    H[index_1] = k * M1.get_Y();
    H[index_2] = k * M1.get_Z();
  }
 
  return k;
}
 
double vpPlane::getIntersection(const vpColVector &M1, vpColVector &H) const
{
  double k, scal;
  const unsigned int index_0 = 0;
  const unsigned int index_1 = 1;
  const unsigned int index_2 = 2;
 
  scal = (A * M1[index_0]) + (B * M1[index_1]) + (C * M1[index_2]);
  // --comment: if scal != 0
  if (std::fabs(scal) > std::numeric_limits<double>::epsilon()) {
    k = -getD() / scal;
  }
  else {
    k = 0;
  }
  H[index_0] = k * M1[index_0];
  H[index_1] = k * M1[index_1];
  H[index_2] = k * M1[index_2];
 
  return k;
}

void vpPlane::changeFrame(const vpHomogeneousMatrix &cMo)
{
  // Save current plane parameters
  double Ao = A;
  double Bo = B;
  double Co = C;
  double Do = D;
  const unsigned int index_0 = 0;
  const unsigned int index_1 = 1;
  const unsigned int index_2 = 2;
  const unsigned int index_3 = 3;
  A = (cMo[index_0][0] * Ao) + (cMo[index_0][1] * Bo) + (cMo[index_0][index_2] * Co);
  B = (cMo[index_1][0] * Ao) + (cMo[index_1][1] * Bo) + (cMo[index_1][index_2] * Co);
  C = (cMo[index_2][0] * Ao) + (cMo[index_2][1] * Bo) + (cMo[index_2][index_2] * Co);
  D = Do - ((cMo[index_0][index_3] * A) + (cMo[index_1][index_3] * B) + (cMo[index_2][index_3] * C));
}

VISP_EXPORT std::ostream &operator<<(std::ostream &os, const vpPlane &p)
{
  return (os << "(" << p.getA() << "," << p.getB() << "," << p.getC() << "," << p.getD() << ") ");
}
END_VISP_NAMESPACE