AffineTransform.hpp

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/* 
 * AffineTransform.hpp 
 *
 * Copyright (C) 2003 Thomas Seidel <thomas.seidel@univie.ac.at>
 *
 * This library is free software; you can redistribute it and/or
 * modify it under the terms of the GNU Lesser General Public
 * License as published by the Free Software Foundation; either
 * version 2 of the License, or (at your option) any later version.
 *
 * This library is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
 * Lesser General Public License for more details.
 *
 * You should have received a copy of the GNU Lesser General Public License
 * along with this library; see the file COPYING. If not, write to
 * the Free Software Foundation, Inc., 59 Temple Place - Suite 330,
 * Boston, MA 02111-1307, USA.
 */
 
#ifndef CDPL_MATH_AFFINETRANSFORM_HPP
#define CDPL_MATH_AFFINETRANSFORM_HPP
 
#include <algorithm>
#include <cmath>
#include <limits>
#include <cstddef>
#include <vector>
#include <utility>
 
#include "CDPL/Math/Check.hpp"
#include "CDPL/Math/Expression.hpp"
#include "CDPL/Base/Exceptions.hpp"
 
 
namespace CDPL
{
 
    namespace Math
    {
 
        template <typename V>
        class MatrixReference;
        template <typename T, typename A>
        class Vector;
        template <typename T, typename A>
        class Matrix;
 
        template <typename T>
        class RotationMatrix : public MatrixContainer<RotationMatrix<T> >
        {
 
            typedef RotationMatrix<T> SelfType;
 
          public:
            typedef T                                     ValueType;
 
            typedef const T                               Reference;
 
            typedef const T                               ConstReference;
 
            typedef std::size_t                           SizeType;
 
            typedef std::ptrdiff_t                        DifferenceType;
 
            typedef MatrixReference<SelfType>             ClosureType;
 
            typedef const MatrixReference<const SelfType> ConstClosureType;
 
            typedef Matrix<T, std::vector<T> >            MatrixTemporaryType;
 
            typedef Vector<T, std::vector<T> >            VectorTemporaryType;
 
            template <typename E>
            RotationMatrix(SizeType n, const QuaternionExpression<E>& q):
                size(n)
            {
                set(q);
            }
 
            template <typename T1, typename T2, typename T3, typename T4>
            RotationMatrix(SizeType n, const T1& w, const T2& ux, const T3& uy, const T4& uz):
                size(n)
            {
                set(w, ux, uy, uz);
            }
 
            RotationMatrix(const RotationMatrix& m):
                size(m.size)
            {
                std::copy(m.data, m.data + 4, data);
            }
 
            template <typename E>
            void set(const QuaternionExpression<E>& q)
            {
                data[0] = q().getC1();
                data[1] = q().getC2();
                data[2] = q().getC3();
                data[3] = q().getC4();
            }
 
            template <typename T1, typename T2, typename T3, typename T4>
            void set(const T1& w, const T2& ux, const T3& uy, const T4& uz)
            {
                data[0] = std::cos(w / 2.0);
                data[1] = std::sin(w / 2.0) * ux;
                data[2] = std::sin(w / 2.0) * uy;
                data[3] = std::sin(w / 2.0) * uz;
            }
 
            ConstReference operator()(SizeType i, SizeType j) const
            {
                CDPL_MATH_CHECK(i < getSize1() && j < getSize2(), "Index out of range", Base::IndexError);
 
                if (i >= 3 || i >= size || j >= 3 || j >= size)
                    return (i == j ? ValueType(1) : ValueType());
 
                switch (i) {
 
                    case 0:
                        switch (j) {
 
                            case 0:
                                // a2 + b2 - c2 - d2
                                return (data[0] * data[0] + data[1] * data[1] - data[2] * data[2] - data[3] * data[3]);
 
                            case 1:
                                // 2(bc - ad)
                                return 2 * (data[1] * data[2] - data[0] * data[3]);
 
                            case 2:
                                // 2(bd + ac)
                                return 2 * (data[1] * data[3] + data[0] * data[2]);
 
                            default:
                                return ValueType();
                        }
 
                    case 1:
                        switch (j) {
 
                            case 0:
                                // 2(bc + ad)
                                return 2 * (data[1] * data[2] + data[0] * data[3]);
 
                            case 1:
                                // a2 - b2 + c2 - d2
                                return (data[0] * data[0] - data[1] * data[1] + data[2] * data[2] - data[3] * data[3]);
 
                            case 2:
                                // 2(cd - ab)
                                return 2 * (data[2] * data[3] - data[0] * data[1]);
 
                            default:
                                return ValueType();
                        }
 
                    case 2:
                        switch (j) {
 
                            case 0:
                                // 2(bd - ac)
                                return 2 * (data[1] * data[3] - data[0] * data[2]);
 
                            case 1:
                                // 2(cd + ab)
                                return 2 * (data[2] * data[3] + data[0] * data[1]);
 
                            case 2:
                                // a2 - b2 - c2 + d2
                                return (data[0] * data[0] - data[1] * data[1] - data[2] * data[2] + data[3] * data[3]);
 
                            default:
                                return ValueType();
                        }
 
                    default:
                        return (i == j ? ValueType(1) : ValueType());
                }
            }
 
            bool isEmpty() const
            {
                return (size == 0);
            }
 
            SizeType getSize1() const
            {
                return size;
            }
 
            SizeType getSize2() const
            {
                return size;
            }
 
            SizeType getMaxSize1() const
            {
                return std::numeric_limits<SizeType>::max();
            }
 
            SizeType getMaxSize2() const
            {
                return std::numeric_limits<SizeType>::max();
            }
 
            RotationMatrix& operator=(const RotationMatrix& m)
            {
                if (this != &m) {
                    std::copy(m.data, m.data + 4, data);
                    size = m.size;
                }
 
                return *this;
            }
 
            void swap(RotationMatrix& m)
            {
                if (this != &m) {
                    std::swap_ranges(data, data + 4, m.data);
                    std::swap(size, m.size);
                }
            }
 
            friend void swap(RotationMatrix& m1, RotationMatrix& m2)
            {
                m1.swap(m2);
            }
 
            void resize(SizeType n)
            {
                size = n;
            }
 
          private:
            typedef ValueType ArrayType[4];
 
            SizeType  size;
            ArrayType data;
        };
 
        template <typename T>
        class ScalingMatrix : public MatrixContainer<ScalingMatrix<T> >
        {
 
            typedef ScalingMatrix<T> SelfType;
 
          public:
            typedef T                                     ValueType;
 
            typedef const T                               Reference;
 
            typedef const T                               ConstReference;
 
            typedef std::size_t                           SizeType;
 
            typedef std::ptrdiff_t                        DifferenceType;
 
            typedef MatrixReference<SelfType>             ClosureType;
 
            typedef const MatrixReference<const SelfType> ConstClosureType;
 
            typedef Matrix<T, std::vector<T> >            MatrixTemporaryType;
 
            typedef Vector<T, std::vector<T> >            VectorTemporaryType;
 
            explicit ScalingMatrix(SizeType n, const ValueType& sx = ValueType(1),
                                   const ValueType& sy = ValueType(1), const ValueType& sz = ValueType(1)):
                size(n)
            {
                set(sx, sy, sz);
            }
 
            ScalingMatrix(const ScalingMatrix& m):
                size(m.size)
            {
                std::copy(m.data, m.data + 3, data);
            }
 
            void set(const ValueType& sx = ValueType(1), const ValueType& sy = ValueType(1),
                     const ValueType& sz = ValueType(1))
            {
                data[0] = sx;
                data[1] = sy;
                data[2] = sz;
            }
 
            ConstReference operator()(SizeType i, SizeType j) const
            {
                CDPL_MATH_CHECK(i < getSize1() && j < getSize2(), "Index out of range", Base::IndexError);
 
                if (i != j)
                    return ValueType();
 
                if (i < size && i < 3)
                    return data[i];
 
                return ValueType(1);
            }
 
            bool isEmpty() const
            {
                return (size == 0);
            }
 
            SizeType getSize1() const
            {
                return size;
            }
 
            SizeType getSize2() const
            {
                return size;
            }
 
            SizeType getMaxSize1() const
            {
                return std::numeric_limits<SizeType>::max();
            }
 
            SizeType getMaxSize2() const
            {
                return std::numeric_limits<SizeType>::max();
            }
 
            ScalingMatrix& operator=(const ScalingMatrix& m)
            {
                if (this != &m) {
                    std::copy(m.data, m.data + 3, data);
                    size = m.size;
                }
 
                return *this;
            }
 
            void swap(ScalingMatrix& m)
            {
                if (this != &m) {
                    std::swap_ranges(data, data + 3, m.data);
                    std::swap(size, m.size);
                }
            }
 
            friend void swap(ScalingMatrix& m1, ScalingMatrix& m2)
            {
                m1.swap(m2);
            }
 
            void resize(SizeType n)
            {
                size = n;
            }
 
          private:
            typedef ValueType ArrayType[3];
 
            SizeType  size;
            ArrayType data;
        };
 
        template <typename T>
        class TranslationMatrix : public MatrixContainer<TranslationMatrix<T> >
        {
 
            typedef TranslationMatrix<T> SelfType;
 
          public:
            typedef T                                     ValueType;
 
            typedef const T                               Reference;
 
            typedef const T                               ConstReference;
 
            typedef std::size_t                           SizeType;
 
            typedef std::ptrdiff_t                        DifferenceType;
 
            typedef MatrixReference<SelfType>             ClosureType;
 
            typedef const MatrixReference<const SelfType> ConstClosureType;
 
            typedef Matrix<T, std::vector<T> >            MatrixTemporaryType;
 
            typedef Vector<T, std::vector<T> >            VectorTemporaryType;
 
            explicit TranslationMatrix(SizeType n, const ValueType& tx = ValueType(),
                                       const ValueType& ty = ValueType(), const ValueType& tz = ValueType()):
                size(n)
            {
                set(tx, ty, tz);
            }
 
            TranslationMatrix(const TranslationMatrix& m):
                size(m.size)
            {
                std::copy(m.data, m.data + 3, data);
            }
 
            void set(const ValueType& tx = ValueType(), const ValueType& ty = ValueType(),
                     const ValueType& tz = ValueType())
            {
                data[0] = tx;
                data[1] = ty;
                data[2] = tz;
            }
 
            ConstReference operator()(SizeType i, SizeType j) const
            {
                CDPL_MATH_CHECK(i < getSize1() && j < getSize2(), "Index out of range", Base::IndexError);
 
                if (i == j)
                    return ValueType(1);
 
                if (j == (size - 1) && i < size && i < 3)
                    return data[i];
 
                return ValueType();
            }
 
            bool isEmpty() const
            {
                return (size == 0);
            }
 
            SizeType getSize1() const
            {
                return size;
            }
 
            SizeType getSize2() const
            {
                return size;
            }
 
            SizeType getMaxSize1() const
            {
                return std::numeric_limits<SizeType>::max();
            }
 
            SizeType getMaxSize2() const
            {
                return std::numeric_limits<SizeType>::max();
            }
 
            TranslationMatrix& operator=(const TranslationMatrix& m)
            {
                if (this != &m) {
                    std::copy(m.data, m.data + 3, data);
                    size = m.size;
                }
 
                return *this;
            }
 
            void swap(TranslationMatrix& m)
            {
                if (this != &m) {
                    std::swap_ranges(data, data + 3, m.data);
                    std::swap(size, m.size);
                }
            }
 
            friend void swap(TranslationMatrix& m1, TranslationMatrix& m2)
            {
                m1.swap(m2);
            }
 
            void resize(SizeType n)
            {
                size = n;
            }
 
          private:
            typedef ValueType ArrayType[3];
 
            SizeType  size;
            ArrayType data;
        };
 
        typedef ScalingMatrix<float>         FScalingMatrix;
        
        typedef ScalingMatrix<double>        DScalingMatrix;
        
        typedef ScalingMatrix<long>          LScalingMatrix;
        
        typedef ScalingMatrix<unsigned long> ULScalingMatrix;
 
        typedef RotationMatrix<float>         FRotationMatrix;
        
        typedef RotationMatrix<double>        DRotationMatrix;
        
        typedef RotationMatrix<long>          LRotationMatrix;
        
        typedef RotationMatrix<unsigned long> ULRotationMatrix;
 
        typedef TranslationMatrix<float>         FTranslationMatrix;
        
        typedef TranslationMatrix<double>        DTranslationMatrix;
        
        typedef TranslationMatrix<long>          LTranslationMatrix;
        
        typedef TranslationMatrix<unsigned long> ULTranslationMatrix;
    } // namespace Math
} // namespace CDPL
 
#endif // CDPL_MATH_AFFINETRANSFORM_HPP