UT/UT_Vector2.h

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/*
 * PROPRIETARY INFORMATION.  This software is proprietary to
 * Side Effects Software Inc., and is not to be reproduced,
 * transmitted, or disclosed in any way without written permission.
 *
 * Produced by:
 *      Rob Bairos
 *      Side Effects Software Inc.
 *      123 Front Street West, Suite 1401
 *      Toronto, Ontario
 *      Canada   M5J 2M2
 *      416-504-9876
 *
 * NAME:        UT_Vector2.h (C++)
 *
 *
 * COMMENTS:
 *      This class handles fpreal vectors of dimension 2.
 *
 * WARNING:
 *      This class should NOT contain any virtual methods, nor should it
 *      define more member data. The size of UT_VectorF2 must always be 
 *      8 bytes (2 floats).
 */

#ifndef __UT_Vector2_h__
#define __UT_Vector2_h__

#include "UT_API.h"
#include <iostream.h>
#include <limits.h>
#include "UT_Math.h"
#include "UT_Assert.h"

class UT_IStream;
class UT_JSONWriter;
class UT_JSONValue;
class UT_JSONParser;

#include "UT_VectorTypes.h"

// Free floating functions:

// Operators that involve a UT_Vector2 object:
template <typename T>
inline UT_Vector2T<T>   operator+(const UT_Vector2T<T> &v1, const UT_Vector2T<T> &v2);
template <typename T>
inline UT_Vector2T<T>   operator-(const UT_Vector2T<T> &v1, const UT_Vector2T<T> &v2);
template <typename T>
inline bool             operator<(const UT_Vector2T<T> &v1, const UT_Vector2T<T> &v2);
template <typename T>
inline bool             operator<=(const UT_Vector2T<T> &v1, const UT_Vector2T<T> &v2);
template <typename T>
inline bool             operator>(const UT_Vector2T<T> &v1, const UT_Vector2T<T> &v2);
template <typename T>
inline bool             operator>=(const UT_Vector2T<T> &v1, const UT_Vector2T<T> &v2);
template <typename T, typename S>
inline UT_Vector2T<T>   operator+(const UT_Vector2T<T> &v, S scalar);
template <typename T, typename S>
inline UT_Vector2T<T>   operator-(const UT_Vector2T<T> &v, S scalar);
template <typename T, typename S>
inline UT_Vector2T<T>   operator*(const UT_Vector2T<T> &v, S scalar);
template <typename T, typename S>
inline UT_Vector2T<T>   operator/(const UT_Vector2T<T> &v, S scalar);
template <typename T, typename S>
inline UT_Vector2T<T>   operator+(S scalar, const UT_Vector2T<T> &v);
template <typename T, typename S>
inline UT_Vector2T<T>   operator-(S scalar, const UT_Vector2T<T> &v);
template <typename T, typename S>
inline UT_Vector2T<T>   operator*(S scalar, const UT_Vector2T<T> &v);
template <typename T, typename S>
inline UT_Vector2T<T>   operator/(S scalar, const UT_Vector2T<T> &v);
template <typename T, typename S>
inline UT_Vector2T<T>   operator*(const UT_Vector2T<T> &v, 
                                  const UT_Matrix2T<S> &mat);

/// The dot product
template <typename T>
inline T                dot      (const UT_Vector2T<T> &v1, const UT_Vector2T<T> &v2);
/// Cross product, which for 2d vectors results in a fpreal.
template <typename T>
inline T                cross    (const UT_Vector2T<T> &v1, const UT_Vector2T<T> &v2);

/// The orthogonal projection of a vector u onto a vector v
template <typename T>
inline UT_Vector2T<T>   project  (const UT_Vector2T<T> &u, const UT_Vector2T<T> &v);

/// Multiplication of a row or column vector by a matrix (ie. right vs. left
/// multiplication respectively). The operator*() declared above is an alias 
/// for rowVecMult().
// @{
//
// Notes on optimisation of matrix/vector multiplies:
// - multiply(dest, mat) functions have been deprecated in favour of
// rowVecMult/colVecMult routines, which produce temporaries. For these to
// offer comparable performance, the compiler has to optimize away the
// temporary, but most modern compilers can do this. Performance tests with
// gcc3.3 indicate that this is a realistic expectation for modern
// compilers.
// - since matrix/vector multiplies cannot be done without temporary data,
// the "primary" functions are the global matrix/vector
// rowVecMult/colVecMult routines, rather than the member functions.

template <typename T, typename S>
inline UT_Vector2T<T>   rowVecMult(const UT_Vector2T<T> &v, 
                                   const UT_Matrix2T<S> &m);
template <typename T, typename S>
inline UT_Vector2T<T>   colVecMult(const UT_Matrix2T<S> &m, 
                                   const UT_Vector2T<T> &v);
// @}

template <typename T>
inline T                distance2d(const UT_Vector2T<T> &v1, const UT_Vector2T<T> &v2);

/// 2D Vector class.
template <typename T>
class UT_API UT_Vector2T {
public:
    /// Default constructor.
    /// No data is initialized! Use it for extra speed.
    inline       UT_Vector2T(void)
                 {
                 }
    inline       UT_Vector2T(T vx, T vy)
                 {
                    vec[0] = vx; vec[1] = vy;
                 }
    explicit     UT_Vector2T(const fpreal32 v[2])
                 { vec[0] = v[0]; vec[1] = v[1]; }
    explicit     UT_Vector2T(const fpreal64 v[2])
                 { vec[0] = v[0]; vec[1] = v[1]; }
    explicit     UT_Vector2T(const UT_Vector3T<T> &v);
    explicit     UT_Vector2T(const UT_Vector4T<T> &v);

    template <typename S> UT_Vector2T(const UT_Vector2T<S> &v)
    { vec[0] = v.x(); vec[1] = v.y(); }

    // Default assignment operator is fine.
    template <typename S>
    UT_Vector2T<T>      &operator=(const UT_Vector2T<S> &v)
    { vec[0] = v.x(); vec[1] = v.y();  return *this; }

    // TODO: remove these. They should require an explicit UT_Vector2()
    // construction, since they're unsafe.

    /// Assignment operator that truncates a V3 to a V2. 
    UT_Vector2T<T>      &operator=(const UT_Vector3T<T> &v);
    /// Assignment operator that truncates a V4 to a V2. 
    UT_Vector2T<T>      &operator=(const UT_Vector4T<T> &v);
    UT_Vector2T<T>      operator-() const
                {
                    return UT_Vector2T<T>(-vec[0], -vec[1]);
                }
    UT_Vector2T<T>      &operator+=(const UT_Vector2T<T> &v)
                {
                    vec[0] += v.vec[0];
                    vec[1] += v.vec[1];
                    return *this;
                }
    UT_Vector2T<T>      &operator-=(const UT_Vector2T<T> &v)
                {
                    vec[0] -= v.vec[0];
                    vec[1] -= v.vec[1];
                    return *this;
                }
    unsigned    operator==(const UT_Vector2T<T> &v) const
                {
                    return (vec[0] == v.vec[0] && vec[1] == v.vec[1]); 
                }
    unsigned    operator!=(const UT_Vector2T<T> &v) const { return !(*this == v); }     
    int         equalZero(T tol = 0.00001f) const
                {
                    return (vec[0] >= -tol && vec[0] <= tol) &&
                           (vec[1] >= -tol && vec[1] <= tol);
                }
    int         isEqual(const UT_Vector2T<T> &v, T tol = 0.00001f) const
                {
                    return ((vec[0]>=v.vec[0]-tol) && (vec[0]<=v.vec[0]+tol) &&
                            (vec[1]>=v.vec[1]-tol) && (vec[1]<=v.vec[1]+tol));
                }

    bool        isNan() const
                { return SYSisNan(vec[0]) || SYSisNan(vec[1]); }

    void        negate() { operator=(operator-()); }

    void        multiplyComponents(const UT_Vector2T<T> &v)
                {
                    vec[0] *= v.vec[0];
                    vec[1] *= v.vec[1];
                }

    /// Given an oriented line from e1 passing through e2, determine on which
    /// side of the line the point p lies.  Alternatively, determine in which
    /// half plane, positive or negative, the point lies.  If the segment
    /// degenerates to a point, then the point is always on it.
    // (Moret and Shapiro 1991)
    
    T      whichSide(const UT_Vector2T<T> &e1, const UT_Vector2T<T> &e2) const
                { 
                    return (vec[0] - e1.vec[0]) * (e2.vec[1] - e1.vec[1]) -
                           (vec[1] - e1.vec[1]) * (e2.vec[0] - e1.vec[0]);
                }

    UT_Vector2T<T>  &operator=(T scalar)
                {
                    vec[0] = vec[1] = scalar;
                    return *this;
                }
    UT_Vector2T<T>  &operator+=(T scalar)
                {
                    vec[0] += scalar;
                    vec[1] += scalar;
                    return *this;
                }
    UT_Vector2T<T>  &operator-=(T scalar)
                {
                    return operator+=(-scalar);
                }
    UT_Vector2T<T>  &operator*=(T scalar)
                {
                    vec[0] *= scalar;
                    vec[1] *= scalar;
                    return *this;
                }
    UT_Vector2T<T>  &operator*=(const UT_Vector2T<T> &v)
                 {
                    vec[0] *= v.vec[0];
                    vec[1] *= v.vec[1];
                    return *this;
                 }
    UT_Vector2T<T>  &operator/=(T scalar)
                {
                    return operator*=( 1.0f/scalar );
                }
    UT_Vector2T<T>  &operator/=(const UT_Vector2T<T> &v)
                 {
                    vec[0] /= v.vec[0];
                    vec[1] /= v.vec[1];
                    return *this;
                 }

    template <typename S>
    inline UT_Vector2T<T> &operator*=(const UT_Matrix2T<S> &mat)
                 { return operator=(*this * mat); }

    inline
    T    dot(const UT_Vector2T<T> &v) const
                 {
                    return ::dot(*this, v);
                 }
    T    normalize (void)
                 {
                    T dn   = vec[0]*vec[0] + vec[1]*vec[1];
                    if (dn > FLT_MIN && dn != 1.0F)
                    {
                        dn = SYSsqrt(dn);
                        (*this) /= dn;
                    }

                    return dn;
                 }

    /// These allow you to find out what indices to use for different axes
    // @{
    int                 findMinAbsAxis() const
                        {
                            if (SYSabs(x()) < SYSabs(y()))
                                return 0;
                            else
                                return 1;
                        }
    int                 findMaxAbsAxis() const
                        {
                            if (SYSabs(x()) >= SYSabs(y()))
                                return 0;
                            else
                                return 1;
                        }
    // @}

    /// The vector length (not to be confused with the vector dimension).
    inline T    length(void) const { return SYSsqrt(dot(*this)); }
    /// The vector length squared.
    inline T    length2(void) const { return dot(*this); }

    /// Calculates the orthogonal projection of a vector u on the *this vector 
    UT_Vector2T<T>              project(const UT_Vector2T<T> &u);


    /// Vector p (representing a point in 2-space) and vector v define
    /// a line. This member returns the projection of "this" onto the
    /// line (the point on the line that is closest to this point).
    UT_Vector2T<T>              projection(const UT_Vector2T<T> &p, const UT_Vector2T<T> &v) const;

    /// Compute (homogeneous) barycentric co-ordinates of this point
    /// relative to the triangle defined by t0, t1 and t2. (The point is
    /// projected into the triangle's plane.)
    UT_Vector3T<T> getBary(const UT_Vector2T<T> &t0, const UT_Vector2T<T> &t1,
                        const UT_Vector2T<T> &t2, bool *degen = NULL) const;


    /// Return the components of the vector. The () operator does NOT check
    /// for the boundary condition.
    // @{
    const T     *data(void) const       { return &vec[0]; }
    T           *data(void)             { return &vec[0]; }
    T           &x(void)                { return vec[0]; } 
    T            x(void) const          { return vec[0]; } 
    T           &y(void)                { return vec[1]; } 
    T            y(void) const          { return vec[1]; } 
    T           &operator()(unsigned i)
                 {
                     UT_ASSERT_P(i < 2);
                     return vec[i];
                 }
    T            operator()(unsigned i) const
                 {
                     UT_ASSERT_P(i < 2);
                     return vec[i];
                 }
    T           &operator[](unsigned i)
                 {
                     UT_ASSERT_P(i < 2);
                     return vec[i];
                 }
    T            operator[](unsigned i) const
                 {
                     UT_ASSERT_P(i < 2);
                     return vec[i];
                 }
    // @}

    /// Compute a hash
    unsigned    hash() const    { return SYSvector_hash(data(), 2); }

    // TODO: eliminate these methods. They're redundant, given good inline
    // constructors.
    /// Set the values of the vector components
    void         assign(T xx = 0.0f, T yy = 0.0f)
                 {
                    vec[0] = xx; vec[1] = yy;
                 }
    /// Set the values of the vector components
    void         assign(const T *v) {vec[0]=v[0]; vec[1]=v[1];}

    /// Express the point in homogeneous coordinates or vice-versa
    // @{
    void         homogenize  (void)     { vec[0] *= vec[1]; }
    void         dehomogenize(void)     { if (vec[1] != 0) vec[0] /= vec[1]; }
    // @}

    /// Protected I/O methods
    // @{
    void        save(ostream &os, int binary = 0) const;
    bool        load(UT_IStream &is);
    // @}

    /// @{
    /// Methods to serialize to a JSON stream.  The vector is stored as an
    /// array of 2 reals.
    bool                save(UT_JSONWriter &w) const;
    bool                save(UT_JSONValue &v) const;
    bool                load(UT_JSONParser &p);
    /// @}

    /// Returns the vector size
    static int          entries()       { return 2; }

    /// The data.
    T    vec[2];

private:
    /// I/O friends
    // @{
    friend ostream      &operator<<(ostream &os, const UT_Vector2T<T> &v)
                        {
                            v.save(os);
                            return os;
                        }
    // @}
};

#include "UT_Matrix2.h"

// Free floating functions:
template <typename T>
inline UT_Vector2T<T>   operator+(const UT_Vector2T<T> &v1, const UT_Vector2T<T> &v2)
{
    return UT_Vector2T<T>(v1.x()+v2.x(), v1.y()+v2.y());
}
template <typename T>
inline UT_Vector2T<T>   operator-(const UT_Vector2T<T> &v1, const UT_Vector2T<T> &v2)
{
    return UT_Vector2T<T>(v1.x()-v2.x(), v1.y()-v2.y());
}
template <typename T>
inline UT_Vector2T<T>   operator*(const UT_Vector2T<T> &v1, const UT_Vector2T<T> &v2)
{
    return UT_Vector2T<T>(v1.x()*v2.x(), v1.y()*v2.y());
}
template <typename T>
inline UT_Vector2T<T>   operator/(const UT_Vector2T<T> &v1, const UT_Vector2T<T> &v2)
{
    return UT_Vector2T<T>(v1.x()/v2.x(), v1.y()/v2.y());
}
template <typename T>
inline bool             operator<(const UT_Vector2T<T> &v1, const UT_Vector2T<T> &v2)
{
    return ((v1.x() < v2.x()) || (v1.x() == v2.x() && v1.y() < v2.y()));
}
template <typename T>
inline bool             operator<=(const UT_Vector2T<T> &v1, const UT_Vector2T<T> &v2)
{
    return (v1 < v2) || (v1 == v2);
}
template <typename T>
inline bool             operator>(const UT_Vector2T<T> &v1, const UT_Vector2T<T> &v2)
{
    return v2 < v1;
}
template <typename T>
inline bool             operator>=(const UT_Vector2T<T> &v1, const UT_Vector2T<T> &v2)
{
    return v2 <= v1;
}
template <typename T, typename S>
inline UT_Vector2T<T>   operator+(const UT_Vector2T<T> &v, S scalar)
{
    return UT_Vector2T<T>(v.x()+scalar, v.y()+scalar);
}
template <typename T, typename S>
inline UT_Vector2T<T>   operator+(S scalar, const UT_Vector2T<T> &v)
{
    return UT_Vector2T<T>(v.x()+scalar, v.y()+scalar);
}
template <typename T, typename S>
inline UT_Vector2T<T>   operator-(const UT_Vector2T<T> &v, S scalar)
{
    return UT_Vector2T<T>(v.x()-scalar, v.y()-scalar);
}
template <typename T, typename S>
inline UT_Vector2T<T>   operator-(S scalar, const UT_Vector2T<T> &v)
{
    return UT_Vector2T<T>(scalar-v.x(), scalar-v.y());
}
template <typename T, typename S>
inline UT_Vector2T<T>   operator*(const UT_Vector2T<T> &v, S scalar)
{
    return UT_Vector2T<T>(v.x()*scalar, v.y()*scalar);
}
template <typename T, typename S>
inline UT_Vector2T<T>   operator*(S scalar, const UT_Vector2T<T> &v)
{
    return UT_Vector2T<T>(v.x()*scalar, v.y()*scalar);
}
template <typename T, typename S>
inline UT_Vector2T<T>   operator/(const UT_Vector2T<T> &v, S scalar)
{
    return UT_Vector2T<T>(v.x()/scalar, v.y()/scalar);
}
template <typename T, typename S>
inline UT_Vector2T<T>   operator/(S scalar, const UT_Vector2T<T> &v)
{
    return UT_Vector2T<T>(scalar/v.x(), scalar/v.y());
}
template <typename T>
inline T                dot(const UT_Vector2T<T> &v1, const UT_Vector2T<T> &v2)
{
    return v1.x()*v2.x() + v1.y()*v2.y();
}
template <typename T>
inline T                cross(const UT_Vector2T<T> &v1, const UT_Vector2T<T> &v2)
{
    return v1.x() * v2.y() - v1.y() * v2.x();
}
template <typename T>
inline UT_Vector2T<T>   project(const UT_Vector2T<T> &u, const UT_Vector2T<T> &v)
{
    return dot(u, v) / v.length2() * v;
}
template <typename T, typename S>
inline UT_Vector2T<T>   rowVecMult(const UT_Vector2T<T> &v, const UT_Matrix2T<S> &m)
{
    return UT_Vector2T<T>(v.x()*m(0,0) + v.y()*m(1,0),
                      v.x()*m(0,1) + v.y()*m(1,1));
}
template <typename T, typename S>
inline UT_Vector2T<T>   colVecMult(const UT_Matrix2T<S> &m, const UT_Vector2T<T> &v)
{
    return UT_Vector2T<T>(m(0,0)*v.x() + m(0,1)*v.y(),
                      m(1,0)*v.x() + m(1,1)*v.y());
}
template <typename T, typename S>
inline UT_Vector2T<T>   operator*(const UT_Vector2T<T> &v, const UT_Matrix2T<S> &m)
{
    return rowVecMult(v, m);
}
template <typename T>
inline T                distance2d(const UT_Vector2T<T> &v1, const UT_Vector2T<T> &v2)
{
    return (v1 - v2).length();
}

#endif

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