639 lines
19 KiB
C++
639 lines
19 KiB
C++
/*! \file pimathvector.h
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* \ingroup Math
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* \~\brief
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* \~english Math vector
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* \~russian Математический вектор
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*/
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/*
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PIP - Platform Independent Primitives
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PIMathVector
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Ivan Pelipenko peri4ko@yandex.ru, Andrey Bychkov work.a.b@yandex.ru
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This program is free software: you can redistribute it and/or modify
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it under the terms of the GNU Lesser General Public License as published by
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the Free Software Foundation, either version 3 of the License, or
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(at your option) any later version.
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This program 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 Lesser General Public License for more details.
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You should have received a copy of the GNU Lesser General Public License
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along with this program. If not, see <http://www.gnu.org/licenses/>.
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*/
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#ifndef PIMATHVECTOR_H
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#define PIMATHVECTOR_H
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#include "pimathbase.h"
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#include "pimathcomplex.h"
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template<uint Cols, uint Rows, typename Type>
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class PIMathMatrixT;
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#define PIMATHVECTOR_ZERO_CMP (1E-100)
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/// Vector templated
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#define PIMV_FOR for (uint i = 0; i < Size; ++i)
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template<uint Size, typename Type = double>
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class PIP_EXPORT PIMathVectorT {
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typedef PIMathVectorT<Size, Type> _CVector;
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static_assert(std::is_arithmetic<Type>::value || is_complex<Type>::value, "Type must be arithmetic or complex");
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static_assert(Size > 0, "Size must be > 0");
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public:
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PIMathVectorT(const Type & v = Type()) { PIMV_FOR c[i] = v; }
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PIMathVectorT(const PIVector<Type> & val) {
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assert(Size == val.size());
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PIMV_FOR c[i] = val[i];
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}
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PIMathVectorT(std::initializer_list<Type> init_list) {
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assert(Size == init_list.size());
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PIMV_FOR c[i] = init_list.begin()[i];
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}
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static _CVector fromTwoPoints(const _CVector & st, const _CVector & fn) {
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_CVector tv;
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PIMV_FOR tv[i] = fn[i] - st[i];
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return tv;
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}
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constexpr uint size() const { return Size; }
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_CVector & fill(const Type & v) {
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PIMV_FOR c[i] = v;
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return *this;
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}
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_CVector & move(const Type & v) {
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PIMV_FOR c[i] += v;
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return *this;
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}
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_CVector & move(const _CVector & v) {
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PIMV_FOR c[i] += v[i];
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return *this;
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}
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_CVector & swapElements(uint f, uint s) {
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piSwap<Type>(c[f], c[s]);
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return *this;
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}
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Type lengthSqr() const {
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Type tv(0);
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PIMV_FOR tv += c[i] * c[i];
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return tv;
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}
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Type length() const {
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static_assert(std::is_arithmetic<Type>::value, "Unavailable for complex");
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if (std::is_arithmetic<Type>::value) return std::sqrt(lengthSqr());
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// if (is_complex<Type>::value) return 1000.; // std::sqrt(lengthSqr());
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}
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Type manhattanLength() const {
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static_assert(std::is_arithmetic<Type>::value, "Unavailable for complex");
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if (std::is_arithmetic<Type>::value) {
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Type tv(0);
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PIMV_FOR tv += piAbs<Type>(c[i]);
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return tv;
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}
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}
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Type angleCos(const _CVector & v) const {
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static_assert(std::is_arithmetic<Type>::value, "Unavailable for complex");
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if (std::is_arithmetic<Type>::value) {
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Type tv = v.length() * length();
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assert(piAbs<Type>(tv) > PIMATHVECTOR_ZERO_CMP);
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return dot(v) / tv;
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}
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}
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Type angleSin(const _CVector & v) const {
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static_assert(std::is_arithmetic<Type>::value, "Unavailable for complex");
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if (std::is_arithmetic<Type>::value) {
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Type tv = angleCos(v);
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return std::sqrt(Type(1) - tv * tv);
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}
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}
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Type angleRad(const _CVector & v) const {
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static_assert(std::is_arithmetic<Type>::value, "Unavailable for complex");
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if (std::is_arithmetic<Type>::value) {
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return std::acos(angleCos(v));
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}
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}
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Type angleDeg(const _CVector & v) const {
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static_assert(std::is_arithmetic<Type>::value, "Unavailable for complex");
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if (std::is_arithmetic<Type>::value) {
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return toDeg(angleRad(v));
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}
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}
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Type angleElevation(const _CVector & v) const {
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static_assert(std::is_arithmetic<Type>::value, "Unavailable for complex");
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if (std::is_arithmetic<Type>::value) {
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return 90.0 - angleDeg(v - *this);
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}
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}
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_CVector projection(const _CVector & v) {
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static_assert(std::is_arithmetic<Type>::value, "Unavailable for complex");
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if (std::is_arithmetic<Type>::value) {
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Type tv = v.length();
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assert(piAbs<Type>(tv) > PIMATHVECTOR_ZERO_CMP);
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return v * (dot(v) / tv);
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}
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}
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_CVector & normalize() {
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static_assert(std::is_arithmetic<Type>::value, "Unavailable for complex");
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if (std::is_arithmetic<Type>::value) {
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Type tv = length();
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assert(piAbs<Type>(tv) > PIMATHVECTOR_ZERO_CMP);
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if (tv == Type(1)) return *this;
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PIMV_FOR c[i] /= tv;
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return *this;
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}
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}
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_CVector normalized() {
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_CVector tv(*this);
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tv.normalize();
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return tv;
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}
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bool isNull() const {
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PIMV_FOR if (c[i] != Type{}) return false;
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return true;
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}
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bool isOrtho(const _CVector & v) const { return ((*this) ^ v) == Type{}; }
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Type & operator[](uint index) { return c[index]; }
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const Type & operator[](uint index) const { return c[index]; }
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Type at(uint index) const { return c[index]; }
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inline Type & element(uint index) { return c[index]; }
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inline const Type & element(uint index) const { return c[index]; }
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_CVector & operator=(const Type & v) {
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PIMV_FOR c[i] = v;
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return *this;
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}
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bool operator==(const _CVector & v) const {
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PIMV_FOR if (c[i] != v[i]) return false;
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return true;
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}
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bool operator!=(const _CVector & v) const { return !(*this == c); }
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void operator+=(const _CVector & v) { PIMV_FOR c[i] += v[i]; }
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void operator-=(const _CVector & v) { PIMV_FOR c[i] -= v[i]; }
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void operator*=(const Type & v) { PIMV_FOR c[i] *= v; }
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void operator/=(const Type & v) {
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assert(std::abs(v) > PIMATHVECTOR_ZERO_CMP);
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PIMV_FOR c[i] /= v;
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}
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_CVector operator-() const {
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_CVector tv;
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PIMV_FOR tv[i] = -c[i];
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return tv;
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}
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_CVector operator+(const _CVector & v) const {
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_CVector tv(*this);
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PIMV_FOR tv[i] += v[i];
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return tv;
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}
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_CVector operator-(const _CVector & v) const {
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_CVector tv(*this);
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PIMV_FOR tv[i] -= v[i];
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return tv;
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}
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_CVector operator*(const Type & v) const {
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_CVector tv(*this);
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PIMV_FOR tv[i] *= v;
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return tv;
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}
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_CVector operator/(const Type & v) const {
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assert(std::abs(v) > PIMATHVECTOR_ZERO_CMP);
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_CVector tv = _CVector(*this);
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PIMV_FOR tv[i] /= v;
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return tv;
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}
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_CVector cross(const _CVector & v) const {
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static_assert(Size == 3, "cross product avalible only for 3D vectors");
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_CVector tv;
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tv[0] = c[1] * v[2] - v[1] * c[2];
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tv[1] = v[0] * c[2] - c[0] * v[2];
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tv[2] = c[0] * v[1] - v[0] * c[1];
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return tv;
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}
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Type dot(const _CVector & v) const {
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Type tv{};
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PIMV_FOR tv += c[i] * v[i];
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return tv;
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}
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_CVector mul(const _CVector & v) const {
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_CVector tv(*this);
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PIMV_FOR tv[i] *= v[i];
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return tv;
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}
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_CVector mul(const Type & v) const { return (*this) * v; }
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_CVector div(const _CVector & v) const {
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_CVector tv(*this);
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PIMV_FOR {
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assert(std::abs(v[i]) > PIMATHVECTOR_ZERO_CMP);
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tv[i] /= v[i];
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}
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return tv;
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}
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_CVector div(const Type & v) const { return (*this) / v; }
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PIMathMatrixT<1, Size, Type> transposed() const {
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PIMathMatrixT<1, Size, Type> ret;
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PIMV_FOR ret[0][i] = c[i];
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return ret;
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}
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Type distToLine(const _CVector & lp0, const _CVector & lp1) {
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static_assert(std::is_arithmetic<Type>::value, "Unavailable for complex");
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if (std::is_arithmetic<Type>::value) {
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_CVector a(lp0, lp1);
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Type tv = a.length();
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assert(std::abs(tv) > PIMATHVECTOR_ZERO_CMP);
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_CVector b(lp0, *this);
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return piAbs<Type>(a[0] * b[1] - a[1] * b[0]) / tv;
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}
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}
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template<uint Size1, typename Type1> /// vector {Size, Type} to vector {Size1, Type1}
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PIMathVectorT<Size1, Type1> turnTo() const {
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PIMathVectorT<Size1, Type1> tv;
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uint sz = piMin<uint>(Size, Size1);
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for (uint i = 0; i < sz; ++i)
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tv[i] = c[i];
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return tv;
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}
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//! \~english
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//! \brief Returns this vector with another element type.
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//! \~russian
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//! \brief Возвращает этот вектор с другим типом элементов.
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template<typename T>
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PIMathVectorT<Size, T> toType() const {
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PIMathVectorT<Size, T> ret;
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PIMV_FOR ret[i] = element(i);
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return ret;
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}
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//! \~english
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//! \brief Returns the subvector with size SubSize. Elements takes from coordinates "offset".
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//! \details
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//! \~russian
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//! \brief Возвращает подвектор с размерами SubSize. Элементы берутся с координат "offset".
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//! \details Координаты могут быть отрицательными. Возвращаемый подвектор может быть любого размера. Если исходные элементы выходят
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//! за границы исходного подвектора, то в подвекторе будут нули.
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template<uint SubSize>
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PIMathVectorT<SubSize, Type> subvector(int offset = 0) const {
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PIMathVectorT<SubSize, Type> ret;
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for (int i = 0; i < (int)SubSize; ++i) {
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int si = i + offset;
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if (si < 0 || si >= (int)Size) continue;
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ret[i] = element(si);
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}
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return ret;
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}
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//! \~english
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//! \brief Set the subvector "v" in coordinates "index".
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//! \details
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//! \~russian
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//! \brief Устанавливает подвектор "v" в координаты "index".
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//! \details Присваивает значения из вектора "v" в область текущиего вектора, ограниченную
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//! размерами "v", самого вектор и границами, исходя из координат установки. Координаты могут быть отрицательными.
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//! Вектор "v" может быть любого размера. Возвращает ссылку на этот вектор.
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template<uint SubSize>
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PIMathVectorT<Size, Type> & setSubvector(int index, const PIMathVectorT<SubSize, Type> & v) {
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for (int i = 0; i < (int)SubSize; ++i) {
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int si = i + index;
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if (si < 0 || si >= (int)Size) continue;
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element(si) = v[i];
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}
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return *this;
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}
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static _CVector cross(const _CVector & v1, const _CVector & v2) { return v1.cross(v2); }
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static _CVector dot(const _CVector & v1, const _CVector & v2) { return v1.dot(v2); }
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static _CVector mul(const _CVector & v1, const _CVector & v2) { return v1.mul(v2); }
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static _CVector mul(const Type & v1, const _CVector & v2) { return v2 * v1; }
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static _CVector mul(const _CVector & v1, const Type & v2) { return v1 * v2; }
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static _CVector div(const _CVector & v1, const _CVector & v2) { return v1.div(v2); }
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static _CVector div(const _CVector & v1, const Type & v2) { return v1 / v2; }
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private:
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Type c[Size];
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};
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template<uint Size, typename Type>
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inline PIMathVectorT<Size, Type> operator*(const Type & x, const PIMathVectorT<Size, Type> & v) {
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return v * x;
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}
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template<uint Size, typename Type>
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inline PICout operator<<(PICout s, const PIMathVectorT<Size, Type> & v) {
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s << "Vector{";
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PIMV_FOR {
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s << v[i];
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if (i < Size - 1) s << ", ";
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}
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s << "}";
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return s;
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}
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typedef PIMathVectorT<2u, int> PIMathVectorT2i;
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typedef PIMathVectorT<3u, int> PIMathVectorT3i;
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typedef PIMathVectorT<4u, int> PIMathVectorT4i;
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typedef PIMathVectorT<2u, double> PIMathVectorT2d;
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typedef PIMathVectorT<3u, double> PIMathVectorT3d;
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typedef PIMathVectorT<4u, double> PIMathVectorT4d;
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#undef PIMV_FOR
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/// Vector
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#define PIMV_FOR for (uint i = 0; i < c.size(); ++i)
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template<typename Type>
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class PIP_EXPORT PIMathVector {
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typedef PIMathVector<Type> _CVector;
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template<typename P, typename Type1>
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friend PIBinaryStream<P> & operator<<(PIBinaryStream<P> & s, const PIMathVector<Type1> & v);
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template<typename P, typename Type1>
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friend PIBinaryStream<P> & operator>>(PIBinaryStream<P> & s, PIMathVector<Type1> & v);
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public:
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PIMathVector(const uint size = 0, const Type & new_value = Type()) { c.resize(size, new_value); }
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PIMathVector(const PIVector<Type> & val) { c = val; }
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PIMathVector(PIVector<Type> && val): c(std::move(val)) {}
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PIMathVector(std::initializer_list<Type> init_list) { c = PIVector<Type>(init_list); }
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template<uint Size>
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PIMathVector(const PIMathVectorT<Size, Type> & val) {
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c.resize(Size);
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PIMV_FOR c[i] = val[i];
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}
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static PIMathVector fromTwoPoints(const _CVector & st, const _CVector & fn) {
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assert(st.size() == fn.size());
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_CVector v(st.size());
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for (uint i = 0; i < v.size(); ++i)
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v.c[i] = fn[i] - st[i];
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}
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static PIMathVector zeros(const uint size) { return PIMathVector(size, Type()); }
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static PIMathVector ones(const uint size) { return PIMathVector(size, Type(1)); }
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static PIMathVector arange(const Type start, const Type stop, const Type step = Type(1)) {
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PIVector<Type> v;
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for (Type i = start; i < stop; i += step)
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v << i;
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return PIMathVector(std::move(v));
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}
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uint size() const { return c.size(); }
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_CVector & resize(uint size, const Type & new_value = Type()) {
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c.resize(size, new_value);
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return *this;
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}
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_CVector resized(uint size, const Type & new_value = Type()) {
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_CVector tv = _CVector(*this);
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tv.resize(size, new_value);
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return tv;
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}
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_CVector & fill(const Type & v) {
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c.fill(v);
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return *this;
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}
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_CVector & move(const Type & v) {
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PIMV_FOR c[i] += v;
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return *this;
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}
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_CVector & move(const _CVector & v) {
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assert(c.size() == v.size());
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PIMV_FOR c[i] += v[i];
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return *this;
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}
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_CVector & swapElements(uint f, uint s) {
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piSwap<Type>(c[f], c[s]);
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return *this;
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}
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Type lengthSqr() const {
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Type tv(0);
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PIMV_FOR tv += c[i] * c[i];
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return tv;
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}
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Type length() const { return std::sqrt(lengthSqr()); }
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Type manhattanLength() const {
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Type tv(0);
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PIMV_FOR tv += piAbs<Type>(c[i]);
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return tv;
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}
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Type angleCos(const _CVector & v) const {
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assert(c.size() == v.size());
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Type tv = v.length() * length();
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assert(std::abs(tv) > PIMATHVECTOR_ZERO_CMP);
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return dot(v) / tv;
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}
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Type angleSin(const _CVector & v) const {
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assert(c.size() == v.size());
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Type tv = angleCos(v);
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return std::sqrt(Type(1) - tv * tv);
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}
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Type angleRad(const _CVector & v) const { return std::acos(angleCos(v)); }
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Type angleDeg(const _CVector & v) const { return toDeg(angleRad(v)); }
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_CVector projection(const _CVector & v) {
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assert(c.size() == v.size());
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Type tv = v.length();
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assert(std::abs(tv) > PIMATHVECTOR_ZERO_CMP);
|
||
return v * (dot(v) / tv);
|
||
}
|
||
_CVector & normalize() {
|
||
Type tv = length();
|
||
assert(std::abs(tv) > PIMATHVECTOR_ZERO_CMP);
|
||
if (tv == Type(1)) return *this;
|
||
PIMV_FOR c[i] /= tv;
|
||
return *this;
|
||
}
|
||
_CVector normalized() {
|
||
_CVector tv(*this);
|
||
tv.normalize();
|
||
return tv;
|
||
}
|
||
bool isNull() const {
|
||
PIMV_FOR if (c[i] != Type(0)) return false;
|
||
return true;
|
||
}
|
||
bool isValid() const { return !c.isEmpty(); }
|
||
bool isOrtho(const _CVector & v) const { return dot(v) == Type(0); }
|
||
|
||
Type & operator[](uint index) { return c[index]; }
|
||
const Type & operator[](uint index) const { return c[index]; }
|
||
Type at(uint index) const { return c[index]; }
|
||
|
||
_CVector & operator=(const Type & v) {
|
||
PIMV_FOR c[i] = v;
|
||
return *this;
|
||
}
|
||
|
||
bool operator==(const _CVector & v) const { return c == v.c; }
|
||
bool operator!=(const _CVector & v) const { return c != v.c; }
|
||
|
||
void operator+=(const _CVector & v) {
|
||
assert(c.size() == v.size());
|
||
PIMV_FOR c[i] += v[i];
|
||
}
|
||
void operator-=(const _CVector & v) {
|
||
assert(c.size() == v.size());
|
||
PIMV_FOR c[i] -= v[i];
|
||
}
|
||
void operator*=(const Type & v) { PIMV_FOR c[i] *= v; }
|
||
void operator/=(const Type & v) {
|
||
assert(std::abs(v) > PIMATHVECTOR_ZERO_CMP);
|
||
PIMV_FOR c[i] /= v;
|
||
}
|
||
_CVector operator-() const {
|
||
_CVector tv(c.size());
|
||
PIMV_FOR tv[i] = -c[i];
|
||
return tv;
|
||
}
|
||
_CVector operator+(const _CVector & v) const {
|
||
assert(c.size() == v.size());
|
||
_CVector tv(*this);
|
||
PIMV_FOR tv[i] += v[i];
|
||
return tv;
|
||
}
|
||
_CVector operator-(const _CVector & v) const {
|
||
assert(c.size() == v.size());
|
||
_CVector tv(*this);
|
||
PIMV_FOR tv[i] -= v[i];
|
||
return tv;
|
||
}
|
||
_CVector operator*(const Type & v) const {
|
||
_CVector tv(*this);
|
||
PIMV_FOR tv[i] *= v;
|
||
return tv;
|
||
}
|
||
_CVector operator/(const Type & v) const {
|
||
assert(std::abs(v) > PIMATHVECTOR_ZERO_CMP);
|
||
_CVector tv(*this);
|
||
PIMV_FOR tv[i] /= v;
|
||
return tv;
|
||
}
|
||
_CVector cross(const _CVector & v) const {
|
||
assert(c.size() == 3);
|
||
assert(v.size() == 3);
|
||
_CVector tv(3);
|
||
tv[0] = c[1] * v[2] - v[1] * c[2];
|
||
tv[1] = c[2] * v[0] - v[2] * c[0];
|
||
tv[2] = c[0] * v[1] - v[0] * c[1];
|
||
return tv;
|
||
}
|
||
Type dot(const _CVector & v) const {
|
||
assert(c.size() == v.size());
|
||
Type tv(0);
|
||
PIMV_FOR tv += c[i] * v[i];
|
||
return tv;
|
||
}
|
||
_CVector mul(const _CVector & v) const {
|
||
assert(c.size() == v.size());
|
||
_CVector tv(*this);
|
||
PIMV_FOR tv[i] *= v[i];
|
||
return tv;
|
||
}
|
||
_CVector mul(const Type & v) const { return (*this) * v; }
|
||
_CVector div(const _CVector & v) const {
|
||
assert(c.size() == v.size());
|
||
_CVector tv(*this);
|
||
PIMV_FOR {
|
||
assert(std::abs(v[i]) > PIMATHVECTOR_ZERO_CMP);
|
||
tv[i] /= v[i];
|
||
}
|
||
return tv;
|
||
}
|
||
_CVector div(const Type & v) const { return (*this) / v; }
|
||
|
||
Type distToLine(const _CVector & lp0, const _CVector & lp1) {
|
||
assert(c.size() == lp0.size());
|
||
assert(c.size() == lp1.size());
|
||
_CVector a = _CVector::fromTwoPoints(lp0, lp1);
|
||
Type tv = a.length();
|
||
assert(std::abs(tv) > PIMATHVECTOR_ZERO_CMP);
|
||
_CVector b = _CVector::fromTwoPoints(lp0, *this);
|
||
return piAbs<Type>(a[0] * b[1] - a[1] * b[0]) / tv;
|
||
}
|
||
|
||
PIVector<Type> toVector() const { return c; }
|
||
|
||
void forEach(std::function<void(const Type &)> f) const { c.forEach(f); }
|
||
_CVector & forEach(std::function<void(Type &)> f) {
|
||
c.forEach(f);
|
||
return *this;
|
||
}
|
||
|
||
inline Type * data() { return c.data(); }
|
||
inline const Type * data() const { return c.data(); }
|
||
|
||
|
||
static _CVector cross(const _CVector & v1, const _CVector & v2) { return v1.cross(v2); }
|
||
static _CVector dot(const _CVector & v1, const _CVector & v2) { return v1.dot(v2); }
|
||
static _CVector mul(const _CVector & v1, const _CVector & v2) { return v1.mul(v2); }
|
||
static _CVector mul(const Type & v1, const _CVector & v2) { return v2 * v1; }
|
||
static _CVector mul(const _CVector & v1, const Type & v2) { return v1 * v2; }
|
||
static _CVector div(const _CVector & v1, const _CVector & v2) { return v1.div(v2); }
|
||
static _CVector div(const _CVector & v1, const Type & v2) { return v1 / v2; }
|
||
|
||
private:
|
||
PIVector<Type> c;
|
||
};
|
||
|
||
template<typename Type>
|
||
inline PIMathVector<Type> operator*(const Type & x, const PIMathVector<Type> & v) {
|
||
return v * x;
|
||
}
|
||
|
||
#undef PIMV_FOR
|
||
|
||
#ifdef PIP_STD_IOSTREAM
|
||
template<typename Type>
|
||
inline std::ostream & operator<<(std::ostream & s, const PIMathVector<Type> & v) {
|
||
s << "{";
|
||
for (uint i = 0; i < v.size(); ++i) {
|
||
s << v[i];
|
||
if (i < v.size() - 1) s << ", ";
|
||
}
|
||
s << "}";
|
||
return s;
|
||
}
|
||
#endif
|
||
|
||
template<typename Type>
|
||
inline PICout operator<<(PICout s, const PIMathVector<Type> & v) {
|
||
s << "Vector{";
|
||
for (uint i = 0; i < v.size(); ++i) {
|
||
s << v[i];
|
||
if (i < v.size() - 1) s << ", ";
|
||
}
|
||
s << "}";
|
||
return s;
|
||
}
|
||
|
||
template<typename P, typename T>
|
||
inline PIBinaryStream<P> & operator<<(PIBinaryStream<P> & s, const PIMathVector<T> & v) {
|
||
s << v.c;
|
||
return s;
|
||
}
|
||
template<typename P, typename T>
|
||
inline PIBinaryStream<P> & operator>>(PIBinaryStream<P> & s, PIMathVector<T> & v) {
|
||
s >> v.c;
|
||
return s;
|
||
}
|
||
|
||
|
||
typedef PIMathVector<int> PIMathVectori;
|
||
typedef PIMathVector<double> PIMathVectord;
|
||
|
||
#endif // PIMATHVECTOR_H
|