Trigonometric.cpp

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/*
 * Trigonometric.cpp
 *
 *  Created on: Jan 9, 2020
 *      Author: Nikhil
 */

#include "Trigonometric.h"
#include "typedef.h"
#include <math.h>

Trigonometric::Trigonometric(){}

Trigonometric::~Trigonometric(){}

double Trigonometric::operator()(const double& t)  const
{
    // Trigonometric weighting function
    if (t <= -1 || t >= 1)
    {
        return 0.0;
    } 
    else
    {
        return 0.5 * (1.0 + cos(t * M_PI));
    }
}

double Trigonometric::integrate(const Vector3d& vec1_pull_seg, const Vector3d& vec2_pull_seg) const
{
    Vector3d a, b;
    double result = 1.0;
    a = (vec1_pull_seg - vec2_pull_seg) * M_PI;
    b = vec2_pull_seg * M_PI;

    // 0
    // 1
    // 2
    for (int i = 0; i <= 2; i++)
    {
        if (fabs(a(i)) < epsilon)
        {
            result = result + cos(b(i));
        }
        else
        {
            result = result + (sin(a(i) + b(i)) - sin(b(i))) / a(i);
        }
    }

    // 01
    if (fabs(a(0) - a(1)) < epsilon)
    {
        result = result + cos(b(0) - b(1)) / 2.0;
    }
    else
    {
        result = result + (sin(b(0) - b(1) + a(0) - a(1)) - sin(b(0) - b(1))) / ((a(0) - a(1)) * 2.0);
    }

    if (fabs(a(0) + a(1)) < epsilon)
    {
        result = result + cos(b(0) + b(1)) / 2.0;
    }
    else
    {
        result = result + (sin(b(0) + b(1) + a(0) + a(1)) - sin(b(0) + b(1))) / ((a(0) + a(1)) * 2.0);
    }

    // 02
    if (fabs(a(0) - a(2)) < epsilon)
    {
        result = result + cos(b(0) - b(2)) / 2.0;
    }
    else
    {
        result = result + (sin(b(0) - b(2) + a(0) - a(2)) - sin(b(0) - b(2))) / ((a(0) - a(2)) * 2.0);
    }

    if (fabs(a(0) + a(2)) < epsilon)
    {
        result = result + cos(b(0) + b(2)) / 2.0;
    }
    else
    {
        result = result + (sin(b(0) + b(2) + a(0) + a(2)) - sin(b(0) + b(2))) / ((a(0) + a(2)) * 2.0);
    }

    // 12
    if (fabs(a(1) - a(2)) < epsilon)
    {
        result = result + cos(b(1) - b(2)) / 2.0;
    }
    else
    {
        result = result + (sin(b(1) - b(2) + a(1) - a(2)) - sin(b(1) - b(2))) / ((a(1) - a(2)) * 2.0);
    }

    if (fabs(a(1) + a(2)) < epsilon)
    {
        result = result + cos(b(1) + b(2)) / 2.0;
    }
    else
    {
        result = result + (sin(b(1) + b(2) + a(1) + a(2)) - sin(b(1) + b(2))) / ((a(1) + a(2)) * 2.0);
    }

    // 012
    if (fabs(a(0) - a(1) - a(2)) < epsilon)
    {
        result = result + cos(b(0) - b(1) - b(2)) / 4.0;
    }
    else
    {
        result = result + (sin(b(0) - b(1) - b(2) + a(0) - a(1) - a(2)) - sin(b(0) - b(1) - b(2))) / ((a(0) - a(1) - a(2)) * 4.0);
    }
    
    if (fabs(a(0) + a(1) - a(2)) < epsilon)
    {
        result = result + cos(b(0) + b(1) - b(2)) / 4.0;
    }
    else
    {
        result = result + (sin(b(0) + b(1) - b(2) + a(0) + a(1) - a(2)) - sin(b(0) + b(1) - b(2))) / ((a(0) + a(1) - a(2)) * 4.0);
    }

    if (fabs(a(0) - a(1) + a(2)) < epsilon)
    {
        result = result + cos(b(0) - b(1) + b(2)) / 4.0;
    }
    else
    {
        result = result + (sin(b(0) - b(1) + b(2) + a(0) - a(1) + a(2)) - sin(b(0) - b(1) + b(2))) / ((a(0) - a(1) + a(2)) * 4.0);
    }

    if (fabs(a(0) + a(1) + a(2)) < epsilon)
    {
        result = result + cos(b(0) + b(1) + b(2)) / 4.0;
    }
    else
    {
        result = result + (sin(b(0) + b(1) + b(2) + a(0) + a(1) + a(2)) - sin(b(0) + b(1) + b(2))) / ((a(0) + a(1) + a(2)) * 4.0);
    }
    
    return result;
}