genesis-3d_engine/Engine/foundation/math/polar.h

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#pragma once
#ifndef MATH_POLAR_H
#define MATH_POLAR_H
//------------------------------------------------------------------------------
/**
    @class Math::polar

    A polar coordinate inline class, consisting of 2 angles theta (latitude)
    and rho (longitude). Also offers conversion between cartesian and 
    polar space.

    Allowed range for theta is 0..180 degree (in rad!) and for rho 0..360 degree
    (in rad).

*/
#include "math/scalar.h"
#include "math/vector.h"
#include "math/float2.h"

//------------------------------------------------------------------------------
namespace Math
{
class polar
{
public:
    /// the default constructor
    polar();
    /// constructor, theta and rho args
    polar(scalar t, scalar r);
    /// constructor, normalized cartesian vector as arg
    polar(const vector& v);
    /// the copy constructor
    polar(const polar& src);
    /// the assignment operator
    void operator=(const polar& rhs);
    /// convert to normalized cartesian coords 
    vector get_cartesian() const;
    /// set to polar object
    void set(const polar& p);
    /// set to theta and rho
    void set(scalar t, scalar r);
    /// set to cartesian 
    void set(const vector& v);

    scalar theta;
    scalar rho;
};

//------------------------------------------------------------------------------
/**
*/
inline
polar::polar() :
    theta(0.0f),
    rho(0.0f)
{
    // empty
}

//------------------------------------------------------------------------------
/**
*/
inline
polar::polar(scalar t, scalar r) :
    theta(t),
    rho(r)
{
    // empty
}

//------------------------------------------------------------------------------
/**
*/
inline
polar::polar(const vector& v)
{
    this->set(v);
}

//------------------------------------------------------------------------------
/**
*/
inline
polar::polar(const polar& src) :
    theta(src.theta),
    rho(src.rho)
{
    // empty
}

//------------------------------------------------------------------------------
/**
*/
inline void
polar::operator=(const polar& rhs)
{
    this->theta = rhs.theta;
    this->rho = rhs.rho;
}

//------------------------------------------------------------------------------
/**
*/
inline void
polar::set(const polar& p)
{
    this->theta = p.theta;
    this->rho = p.rho;
}

//------------------------------------------------------------------------------
/**
*/
inline void
polar::set(scalar t, scalar r)
{
    this->theta = t;
    this->rho = r;
}

//------------------------------------------------------------------------------
/**
    Convert cartesian to polar.
*/
inline void
polar::set(const vector& vec)
{
    vector normVec3d = vector::normalize(vec);
    this->theta = n_acos(normVec3d.y());

    // build a normalized 2d vector of the xz component
    float2 normVec2d(normVec3d.x(), normVec3d.z());
    if (normVec2d.length() > TINY)
    {
        normVec2d = float2::normalize(normVec2d);
    }
    else
    {
        normVec2d.set(1.0f, 0.0f);
    }

    // adjust dRho based on the quadrant we are in
    if ((normVec2d.x() >= 0.0f) && (normVec2d.y() >= 0.0f))
    {
        // quadrant 1
        this->rho = n_asin(normVec2d.x());
    }
    else if ((normVec2d.x() < 0.0f) && (normVec2d.y() >= 0.0f))
    {
        // quadrant 2 
        this->rho = n_asin(normVec2d.y()) + n_deg2rad(270.0f);
    }
    else if ((normVec2d.x() < 0.0f) && (normVec2d.y() < 0.0f))
    {
        // quadrant 3
        this->rho = n_asin(-normVec2d.x()) + n_deg2rad(180.0f);
    }
    else
    {
        // quadrant 4
        this->rho = n_asin(-normVec2d.y()) + n_deg2rad(90.0f);
    }
}
    
//------------------------------------------------------------------------------
/**
    Convert polar to cartesian.
*/
inline vector
polar::get_cartesian() const
{
    scalar sinTheta = n_sin(this->theta);
    scalar cosTheta = n_cos(this->theta);
    scalar sinRho   = n_sin(this->rho);
    scalar cosRho   = n_cos(this->rho);
    vector v(sinTheta * sinRho, cosTheta, sinTheta * cosRho);
    return v;
}

} // namespace Math
//------------------------------------------------------------------------------
#endif