1064 lines
17 KiB
C++
1064 lines
17 KiB
C++
/*
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----
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This file is part of SECONDO.
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Copyright (C) 2008, University in Hagen, Department of Computer Science,
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Database Systems for New Applications.
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SECONDO is free software; you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation; either version 2 of the License, or
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(at your option) any later version.
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SECONDO is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with SECONDO; if not, write to the Free Software
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Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
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----
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//paragraph [1] Title: [{\Large \bf \begin {center}] [\end {center}}]
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//[TOC] [\tableofcontents]
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//[ue] [\"u]
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//[ae] [\"a]
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//[oe] [\"o]
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//[x] [$\times $]
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//[->] [$\rightarrow $]
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//[pow] [\verb+^+]
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[1] Headerfile of the Point and Vector classes
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April - November 2008, M. H[oe]ger for bachelor thesis.
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[TOC]
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1 Introduction
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This file contains the definitions of the classes Point2D, Point3D, Vector2D
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and Vector3D.
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2 Defines and Includes
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*/
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#ifndef POINTVECTOR_H_
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#define POINTVECTOR_H_
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#include <math.h>
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#include <string>
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#include <iomanip>
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#include <sstream>
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#include <iostream>
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#include "NumericUtil.h"
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namespace temporalalgebra{
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namespace mregionops {
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/*
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2.1 VRML Constants
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Used for generating a VRML file for debugging.
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*/
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#define VRML_SCALE_FACTOR 0.3
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#define VRML_DOUBLE_PRECISION 2
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/*
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2.2 Forward declarations
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*/
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class Point2D;
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class Point3D;
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class Vector2D;
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class Vector3D;
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class Segment2D;
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/*
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3 Class Vector3D
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This class provides a spatial vector of dimension 3.
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It's components are represented by three double values.
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*/
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class Vector3D {
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public:
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/*
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3.1 Constructors
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*/
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inline Vector3D() :
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x(0.0), y(0.0), z(0.0) {
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}
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inline Vector3D(double _x, double _y, double _z) :
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x(_x), y(_y), z(_z) {
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}
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Vector3D(const Vector2D& v);
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/*
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3.2 Getter and setter methods
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*/
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inline double GetX() const {
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return x;
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}
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inline double GetY() const {
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return y;
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}
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inline double GetZ() const {
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return z;
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}
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inline double GetT() const {
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return z;
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}
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/*
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3.3 Operators and Predicates
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3.3.1 Length
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Returns the length of this vector.
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*/
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inline double Length() const {
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return sqrt(x*x + y*y + z*z);
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}
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/*
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3.3.2 Length2
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Returns the quadratic length of this vector.
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*/
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inline double Length2() const {
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return x*x + y*y + z*z;
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}
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/*
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3.3.3 IsZero
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Returns ~true~, if all components are nearly equal to zero.
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*/
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inline bool IsZero() const {
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return NumericUtil::NearlyEqual(x, 0.0) &&
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NumericUtil::NearlyEqual(y, 0.0) &&
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NumericUtil::NearlyEqual(z, 0.0);
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}
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/*
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3.3.4 operator -
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Returns the negative of this vector.
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*/
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inline Vector3D operator -() const {
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return Vector3D(-x, -y, -z);
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}
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/*
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3.3.5 operator [*]
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Returns the scalar multplication of w and c.
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*/
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inline friend Vector3D operator *(const double c, const Vector3D& w) {
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Vector3D v;
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v.x = c * w.x;
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v.y = c * w.y;
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v.z = c * w.z;
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return v;
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}
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inline friend Vector3D operator *(const Vector3D& w, const double c) {
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Vector3D v;
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v.x = c * w.x;
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v.y = c * w.y;
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v.z = c * w.z;
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return v;
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}
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/*
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3.3.6 operator /
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Returns the scalar multplication of w and 1/c.
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*/
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inline friend Vector3D operator /(const Vector3D& w, const double c) {
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Vector3D v;
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v.x = w.x / c;
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v.y = w.y / c;
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v.z = w.z / c;
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return v;
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}
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/*
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3.3.7 operator +
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Returns the vector sum of this and w.
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*/
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inline Vector3D operator +(const Vector3D& w) const {
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Vector3D v;
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v.x = x + w.x;
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v.y = y + w.y;
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v.z = z + w.z;
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return v;
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}
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/*
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3.3.8 operator -
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Returns the vector difference of this and w.
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*/
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inline Vector3D operator -(const Vector3D& w) const {
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Vector3D v;
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v.x = x - w.x;
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v.y = y - w.y;
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v.z = z - w.z;
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return v;
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}
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/*
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3.3.9 operator [*]
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Returns the dot product of this and w.
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*/
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inline double operator *(const Vector3D& w) const {
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return (x * w.x + y * w.y + z * w.z);
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}
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/*
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3.3.10 operator power
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Returns the cross product of this and w.
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*/
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inline Vector3D operator ^(const Vector3D& w) const {
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Vector3D v;
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v.x = y * w.z - z * w.y;
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v.y = z * w.x - x * w.z;
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v.z = x * w.y - y * w.x;
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return v;
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}
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/*
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3.3.11 Normalize
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Normalize this vector to length one.
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*/
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inline void Normalize() {
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const double len = sqrt(x*x + y*y + z*z);
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if (len != 0.0) {
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x /= len;
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y /= len;
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z /= len;
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}
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}
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/*
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3.3.12 operator ==
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Returns ~true~, if all components of this are nearly equal to all
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components of p.
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*/
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inline bool operator ==(const Vector3D& p) const {
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return NumericUtil::NearlyEqual(x, p.x) && NumericUtil::NearlyEqual(y,
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p.y) && NumericUtil::NearlyEqual(z, p.z);
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}
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private:
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double x;
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double y;
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double z;
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};
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/*
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4 Class Vector2D
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This class provides a spatial vector of dimension 2.
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It's components are represented by two double values.
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*/
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class Vector2D {
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public:
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/*
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4.1 Constructors
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*/
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inline Vector2D() :
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x(0.0), y(0.0) {
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}
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inline Vector2D(double _x, double _y) :
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x(_x), y(_y) {
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}
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Vector2D(const Vector3D& v);
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/*
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4.2 Getter and setter methods
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*/
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inline double GetX() const {
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return x;
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}
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inline double GetW() const {
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return x;
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}
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inline double GetY() const {
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return y;
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}
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inline double GetT() const {
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return y;
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}
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/*
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4.3 Operators and Predicates
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4.3.1 Length
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Returns the length of this vector.
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*/
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inline double Length() const {
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return sqrt(x*x + y*y);
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}
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/*
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4.3.2 Length2
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Returns the quadratic length of this vector.
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*/
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inline double Length2() const {
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return x*x + y*y;
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}
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/*
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4.3.3 IsZero
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Returns ~true~, if all components are nearly equal to zero.
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*/
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inline bool IsZero() const {
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return NumericUtil::NearlyEqual(x, 0.0) &&
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NumericUtil::NearlyEqual(y, 0.0);
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}
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/*
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4.3.4 operator -
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Returns the negative of this vector.
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*/
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inline Vector2D operator -() const {
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return Vector2D(-x, -y);
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}
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/*
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4.3.5 operator [*]
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Returns the scalar multplication of w and c.
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*/
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inline friend Vector2D operator *(const double c, const Vector2D& w) {
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Vector2D v;
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v.x = c * w.x;
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v.y = c * w.y;
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return v;
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}
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inline friend Vector2D operator *(const Vector2D& w, const double c) {
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Vector2D v;
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v.x = c * w.x;
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v.y = c * w.y;
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return v;
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}
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/*
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4.3.6 operator /
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Returns the scalar multplication of w and 1/c.
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*/
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inline friend Vector2D operator /(const Vector2D& w, const double c) {
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Vector2D v;
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v.x = w.x / c;
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v.y = w.y / c;
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return v;
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}
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/*
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3.3.7 operator +
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Returns the vector sum of this and w.
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*/
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inline Vector2D operator +(const Vector2D& w) const {
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Vector2D v;
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v.x = x + w.x;
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v.y = y + w.y;
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return v;
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}
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/*
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3.3.8 operator -
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Returns the vector difference of this and w.
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*/
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inline Vector2D operator -(const Vector2D& w) const {
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Vector2D v;
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v.x = x - w.x;
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v.y = y - w.y;
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return v;
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}
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/*
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3.3.9 operator [*]
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Returns the dot product of this and w.
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*/
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inline double operator *(const Vector2D& w) const {
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return (x * w.x + y * w.y);
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}
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/*
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3.3.10 operator $|$
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Returns the perp product of this and w: a scalar.
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*/
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inline double operator |(const Vector2D& w) const {
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return (x * w.y - y * w.x);
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}
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/*
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3.3.11 operator power
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Returns the cross product of this and w: a Vector3D
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*/
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inline Vector3D operator ^(const Vector2D& w) const {
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return Vector3D(0.0, 0.0, x * w.y - y * w.x);
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}
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/*
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3.3.12 Normalize
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Normalize this vector to length one.
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*/
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inline void Normalize() {
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const double len = sqrt(x*x + y*y);
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if (len != 0.0) {
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x /= len;
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y /= len;
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}
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}
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/*
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3.3.13 operator ==
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Returns ~true~, if all components of this are nearly equal to all
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components of p.
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*/
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inline bool operator ==(const Vector2D& p) const {
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return NumericUtil::NearlyEqual(x, p.x) && NumericUtil::NearlyEqual(y,
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p.y);
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}
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private:
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double x;
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double y;
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};
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/*
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5 Class Point2D
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This class provides a point in the euclidian plane.
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It's components are represented by two double values.
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*/
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class Point2D {
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public:
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/*
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5.1 Constructors
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*/
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inline Point2D() :
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x(0.0), y(0.0) {
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}
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inline Point2D(double _x, double _y) :
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x(_x), y(_y) {
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}
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Point2D(const Point3D& p);
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/*
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5.2 Getter and setter methods.
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*/
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inline double GetX() const {
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return x;
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}
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inline double GetW() const {
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return x;
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}
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inline double GetY() const {
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return y;
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}
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inline double GetT() const {
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return y;
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}
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/*
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5.3 Operators and Predicates
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5.3.1 Operators for comparison.
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*/
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inline bool operator ==(const Point2D& p) const {
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return NumericUtil::NearlyEqual(x, p.x) &&
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NumericUtil::NearlyEqual(y, p.y);
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}
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inline bool operator !=(const Point2D& p) const {
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return !(*this == p);
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}
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inline bool operator <(const Point2D& p) const {
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if (NumericUtil::Lower(x, p.x))
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return true;
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if (NumericUtil::Greater(x, p.x))
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return false;
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return NumericUtil::Lower(y, p.y);
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}
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/*
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5.3.2 operator -
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Returns the Vector2D pointing from p to this.
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*/
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inline Vector2D operator -(const Point2D& p) const {
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return Vector2D(x - p.x, y - p.y);
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}
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/*
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5.3.3 operator +
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Returns the translation of this along v.
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*/
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inline Point2D operator +(const Vector2D& v) const
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{
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Point2D p;
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p.x = x + v.GetX();
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p.y = y + v.GetY();
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return p;
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}
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/*
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5.3.4 operator -
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Returns the translation of this along -v.
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*/
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inline Point2D operator -(const Vector2D& v) const
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{
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Point2D p;
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p.x = x - v.GetX();
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p.y = y - v.GetY();
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return p;
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}
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/*
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5.3.5 operator +
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Returns the affine sum of this and p.
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*/
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inline Point2D operator +(const Point2D& p)const
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{
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Point2D sum;
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sum.x = x + p.x;
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sum.y = y + p.y;
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return sum;
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}
|
|
|
|
/*
|
|
5.3.6 operator [*]
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|
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|
Returns this point, scaled by the factor f.
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|
|
|
*/
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|
|
|
inline Point2D operator *(const double& f) const {
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|
|
|
Point2D res;
|
|
res.x = x * f;
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|
res.y = y * f;
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|
return res;
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|
}
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|
|
|
/*
|
|
5.3.7 Distance
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|
Returns the distance between this and p.
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|
|
|
*/
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|
|
|
inline double Distance(const Point2D& p) const {
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|
|
|
return (p - *this).Length();
|
|
}
|
|
|
|
/*
|
|
5.3.8 Distance2
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|
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|
Returns the quadratic distance between this and p.
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|
|
|
*/
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|
|
|
inline double Distance2(const Point2D& p) const {
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|
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|
return (p - *this).Length2();
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|
}
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|
|
|
/*
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|
5.3.9 WhichSide
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|
|
Let l be the line defined by the points start and end.
|
|
Then WhichSide returns:
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|
* A value greater than zero, if this is left of l.
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|
* A value lower than zero, if this is right of l.
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|
* Zero, if this is on l.
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|
|
|
*/
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|
|
|
inline double WhichSide(const Point2D& start, const Point2D& end) const {
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|
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|
// This is the fast version:
|
|
//return (start.x - x) * (end.y - y) - (end.x - x) * (start.y - y);
|
|
|
|
// This is slower, but numerical more stable:
|
|
Vector2D v1 = end - start;
|
|
Vector2D v2 = *this - start;
|
|
|
|
v1.Normalize();
|
|
v2.Normalize();
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|
|
|
return v1 | v2;
|
|
}
|
|
|
|
double WhichSide(const Segment2D& s) const;
|
|
|
|
/*
|
|
5.3.10 IsLeft/IsRight/IsColinear
|
|
|
|
This predicates evaluates the WhichSide method using
|
|
an epsilon to avoid rounding errors.
|
|
|
|
*/
|
|
|
|
inline bool IsLeft(const Point2D& start, const Point2D& end) const {
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|
|
|
return NumericUtil::Greater(WhichSide(start, end), 0.0);
|
|
}
|
|
|
|
inline bool IsRight(const Point2D& start, const Point2D& end) const {
|
|
|
|
return NumericUtil::Lower(WhichSide(start, end), 0.0);
|
|
}
|
|
|
|
inline bool IsColinear(const Point2D& start, const Point2D& end) const {
|
|
|
|
return NumericUtil::NearlyEqual(WhichSide(start, end), 0.0);
|
|
}
|
|
|
|
bool IsLeft(const Segment2D& s) const;
|
|
|
|
bool IsRight(const Segment2D& s) const;
|
|
|
|
bool IsColinear(const Segment2D& s) const;
|
|
|
|
private:
|
|
|
|
double x;
|
|
double y;
|
|
};
|
|
|
|
/*
|
|
6 Class Point3D
|
|
|
|
This class provides a point in the euclidian space.
|
|
It's components are represented by three double values.
|
|
|
|
*/
|
|
class Point3D {
|
|
|
|
public:
|
|
|
|
/*
|
|
6.1 Constructors
|
|
|
|
*/
|
|
|
|
inline Point3D() :
|
|
x(0.0), y(0.0), z(0.0) {
|
|
|
|
}
|
|
|
|
inline Point3D(double _x, double _y, double _z) :
|
|
x(_x), y(_y), z(_z) {
|
|
|
|
}
|
|
|
|
Point3D(const Point2D& p);
|
|
|
|
/*
|
|
6.2 Getter and setter methods.
|
|
|
|
*/
|
|
|
|
inline double GetX() const {
|
|
|
|
return x;
|
|
}
|
|
|
|
inline double GetY() const {
|
|
|
|
return y;
|
|
}
|
|
|
|
inline double GetZ() const {
|
|
|
|
return z;
|
|
}
|
|
|
|
inline double GetT() const {
|
|
|
|
return z;
|
|
}
|
|
|
|
/*
|
|
6.3 Operators and Predicates
|
|
|
|
6.3.1 Operators for comparison.
|
|
|
|
*/
|
|
|
|
inline bool operator ==(const Point3D& p) const {
|
|
|
|
return NumericUtil::NearlyEqual(x, p.x) &&
|
|
NumericUtil::NearlyEqual(y, p.y) &&
|
|
NumericUtil::NearlyEqual(z, p.z);
|
|
}
|
|
|
|
inline bool operator !=(const Point3D& p) const {
|
|
|
|
return !(*this == p);
|
|
}
|
|
|
|
/*
|
|
6.3.2 operator -
|
|
|
|
Returns the Vector3D pointing from p to this.
|
|
|
|
*/
|
|
|
|
inline Vector3D operator -(const Point3D& p) const {
|
|
|
|
return Vector3D(x - p.x, y - p.y, z - p.z);
|
|
}
|
|
|
|
/*
|
|
6.3.3 operator +
|
|
|
|
Returns the translation of this along v.
|
|
|
|
*/
|
|
|
|
inline Point3D operator +(const Vector3D& v) const
|
|
{
|
|
Point3D p;
|
|
p.x = x + v.GetX();
|
|
p.y = y + v.GetY();
|
|
p.z = z + v.GetZ();
|
|
return p;
|
|
}
|
|
|
|
/*
|
|
6.3.4 operator -
|
|
|
|
Returns the translation of this along -v.
|
|
|
|
*/
|
|
|
|
inline Point3D operator -(const Vector3D& v) const
|
|
{
|
|
Point3D p;
|
|
p.x = x - v.GetX();
|
|
p.y = y - v.GetY();
|
|
p.z = z - v.GetZ();
|
|
return p;
|
|
}
|
|
|
|
/*
|
|
6.3.5 operator +
|
|
|
|
Returns the affine sum of this and p.
|
|
|
|
*/
|
|
|
|
inline Point3D operator +(const Point3D& p) const
|
|
{
|
|
Point3D sum;
|
|
sum.x = x + p.x;
|
|
sum.y = y + p.y;
|
|
sum.z = z + p.z;
|
|
return sum;
|
|
}
|
|
|
|
/*
|
|
6.3.6 operator [*]
|
|
|
|
Returns this point, scaled by the factor f.
|
|
|
|
*/
|
|
|
|
inline Point3D operator *(const double& f) const {
|
|
|
|
Point3D res;
|
|
res.x = x * f;
|
|
res.y = y * f;
|
|
res.z = z * f;
|
|
return res;
|
|
}
|
|
|
|
/*
|
|
6.3.7 Distance
|
|
|
|
Returns the distance between this and p.
|
|
|
|
*/
|
|
|
|
inline double Distance(const Point3D& p) const {
|
|
|
|
return (p - *this).Length();
|
|
}
|
|
|
|
/*
|
|
6.3.8 Distance2
|
|
|
|
Returns the quadratic distance between this and p.
|
|
|
|
*/
|
|
|
|
inline double Distance2(const Point3D& p) const {
|
|
|
|
return (p - *this).Length2();
|
|
}
|
|
|
|
/*
|
|
6.3.9 DistanceToPlane
|
|
|
|
Returns the distance between this and a plane
|
|
defined by the point p0 and the vector normal.
|
|
|
|
*/
|
|
|
|
double DistanceToPlane(const Point3D& p0, const Vector3D& normal) const {
|
|
|
|
const double sb = (- (normal * (*this - p0))) / normal.Length2();
|
|
const Point3D base = *this + (sb * normal);
|
|
|
|
return Distance(base);
|
|
}
|
|
|
|
/*
|
|
6.3.10 DistanceToPlane2
|
|
|
|
Returns the quadratic distance between this and a plane
|
|
defined by the point p0 and the vector normal.
|
|
|
|
*/
|
|
|
|
double DistanceToPlane2(const Point3D& p0, const Vector3D& normal) const {
|
|
|
|
const double sb = (- (normal * (*this - p0))) / normal.Length2();
|
|
const Point3D base = *this + (sb * normal);
|
|
|
|
return Distance2(base);
|
|
}
|
|
|
|
/*
|
|
6.3.11 GetVRMLDesc
|
|
|
|
Returns a description of this point in VRML format.
|
|
|
|
*/
|
|
|
|
inline std::string GetVRMLDesc() const {
|
|
|
|
std::ostringstream oss;
|
|
|
|
oss << std::setprecision(VRML_DOUBLE_PRECISION) << std::fixed << x
|
|
<< " " << y << " " << z << ", ";
|
|
|
|
return oss.str();
|
|
}
|
|
|
|
private:
|
|
|
|
double x;
|
|
double y;
|
|
double z;
|
|
};
|
|
|
|
/*
|
|
7 Overloaded output operators
|
|
|
|
*/
|
|
|
|
std::ostream& operator <<(std::ostream& o, const Point2D& p);
|
|
std::ostream& operator <<(std::ostream& o, const Point3D& p);
|
|
std::ostream& operator <<(std::ostream& o, const Vector2D& p);
|
|
std::ostream& operator <<(std::ostream& o, const Vector3D& p);
|
|
|
|
} // end of namespace mregionops
|
|
|
|
} // end of namespace temporalalgebra
|
|
|
|
|
|
|
|
#endif // POINTVECTOR_H_
|