CoordGeom.cpp

/* 
 *      Copyright (C) 2003-2005 Gabest
 *      http://www.gabest.org
 *
 *  This Program is free software; you can redistribute it and/or modify
 *  it under the terms of the GNU General Public License as published by
 *  the Free Software Foundation; either version 2, or (at your option)
 *  any later version.
 *   
 *  This Program 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 General Public License for more details.
 *   
 *  You should have received a copy of the GNU General Public License
 *  along with GNU Make; see the file COPYING.  If not, write to
 *  the Free Software Foundation, 675 Mass Ave, Cambridge, MA 02139, USA. 
 *  http://www.gnu.org/copyleft/gpl.html
 *
 */

#include "stdafx.h"
#include <math.h>
#include "CoordGeom.h"

#define EPSILON (1e-7)
#define BIGNUMBER (1e+9)
#define IsZero(d) (fabs(d) < EPSILON)

//
// Vector
//

Vector::Vector(double x, double y, double z)
{
        this->x = x;
        this->y = y;
        this->z = z;
}

void Vector::Set(double x, double y, double z)
{
        this->x = x;
        this->y = y;
        this->z = z;
}

double Vector::Length()
{
        return(sqrt(x * x + y * y + z * z));
}

double Vector::Sum()
{
        return(x + y + z);
}

double Vector::CrossSum()
{
        return(x*y + x*z + y*z);
}

Vector Vector::Cross()
{
        return(Vector(x*y, x*z, y*z));
}

Vector Vector::Pow(double exp)
{
        return(exp == 0 ? Vector(1, 1, 1) : exp == 1 ? *this : Vector(pow(x, exp), pow(y, exp), pow(z, exp)));
}

Vector Vector::Unit()
{
        double l = Length();
        if(!l || l == 1) return(*this);
        return(*this * (1 / l));
}

Vector& Vector::Unitalize()
{
        return(*this = Unit());
}

Vector Vector::Normal(Vector& a, Vector& b)
{
        return((a - *this) % (b - a));
}

double Vector::Angle(Vector& a, Vector& b)
{
        return(((a - *this).Unit()).Angle((b - *this).Unit()));
}

double Vector::Angle(Vector& a)
{
        double angle = *this | a;
        return((angle > 1) ? 0 : (angle < -1) ? PI : acos(angle));
}

void Vector::Angle(double& u, double& v)
{
        Vector n = Unit();

        u = asin(n.y);

        if(IsZero(n.z)) v = PI/2 * Sgn(n.x);
        else if(n.z > 0) v = atan(n.x / n.z);
        else if(n.z < 0) v = IsZero(n.x) ? PI : (PI * Sgn(n.x) + atan(n.x / n.z));
}

Vector Vector::Angle()
{
        Vector ret;
        Angle(ret.x, ret.y);
        ret.z = 0;
        return(ret);
}

Vector& Vector::Min(Vector& a)
{
        x = (x < a.x) ? x : a.x;
        y = (y < a.y) ? y : a.y;
        z = (z < a.z) ? z : a.z;
        return(*this);
}

Vector& Vector::Max(Vector& a)
{
        x = (x > a.x) ? x : a.x;
        y = (y > a.y) ? y : a.y;
        z = (z > a.z) ? z : a.z;
        return(*this);
}

Vector Vector::Abs()
{
        return(Vector(fabs(x), fabs(y), fabs(z)));
}

Vector Vector::Reflect(Vector& n)
{
        return(n * ((-*this) | n) * 2 - (-*this));
}

Vector Vector::Refract(Vector& N, double nFront, double nBack, double* nOut)
{
        Vector D = -*this;

        double N_dot_D = (N | D);
        double n = N_dot_D >= 0 ? (nFront / nBack) : (nBack / nFront);

        Vector cos_D = N * N_dot_D;
        Vector sin_T = (cos_D - D) * n;

        double len_sin_T = sin_T | sin_T;

        if(len_sin_T > 1) 
        {
                if(nOut) {*nOut = N_dot_D >= 0 ? nFront : nBack;}
                return((*this).Reflect(N));
        }

        double N_dot_T = sqrt(1.0 - len_sin_T);
        if(N_dot_D < 0) N_dot_T = -N_dot_T;

        if(nOut) {*nOut = N_dot_D >= 0 ? nBack : nFront;}

        return(sin_T - (N * N_dot_T));
}

Vector Vector::Refract2(Vector& N, double nFrom, double nTo, double* nOut)
{
        Vector D = -*this;

        double N_dot_D = (N | D);
        double n = nFrom / nTo;

        Vector cos_D = N * N_dot_D;
        Vector sin_T = (cos_D - D) * n;

        double len_sin_T = sin_T | sin_T;

        if(len_sin_T > 1) 
        {
                if(nOut) {*nOut = nFrom;}
                return((*this).Reflect(N));
        }

        double N_dot_T = sqrt(1.0 - len_sin_T);
        if(N_dot_D < 0) N_dot_T = -N_dot_T;

        if(nOut) {*nOut = nTo;}

        return(sin_T - (N * N_dot_T));
}

double Vector::operator | (Vector& v)
{
        return(x * v.x + y * v.y + z * v.z);
}

Vector Vector::operator % (Vector& v)
{
        return(Vector(y * v.z - z * v.y, z * v.x - x * v.z, x * v.y - y * v.x));
}

double& Vector::operator [] (int i)
{
        return(!i ? x : (i == 1) ? y : z);
}

Vector Vector::operator - ()
{
        return(Vector(-x, -y, -z));
}

bool Vector::operator == (const Vector& v) const
{
        if(IsZero(x - v.x) && IsZero(y - v.y) && IsZero(z - v.z)) return(true);
        return(false);
}

bool Vector::operator != (const Vector& v) const
{
        return((*this == v) ? false : true);
}

Vector Vector::operator + (double d)
{
        return(Vector(x + d, y + d, z + d));
}

Vector Vector::operator + (Vector& v)
{
        return(Vector(x + v.x, y + v.y, z + v.z));
}

Vector Vector::operator - (double d)
{
        return(Vector(x - d, y - d, z - d));
}

Vector Vector::operator - (Vector& v)
{
        return(Vector(x - v.x, y - v.y, z - v.z));
}

Vector Vector::operator * (double d)
{
        return(Vector(x * d, y * d, z * d));
}

Vector Vector::operator * (Vector& v)
{
        return(Vector(x * v.x, y * v.y, z * v.z));
}

Vector Vector::operator / (double d)
{
        return(Vector(x / d, y / d, z / d));
}

Vector Vector::operator / (Vector& v)
{
        return(Vector(x / v.x, y / v.y, z / v.z));
}

Vector& Vector::operator += (double d)
{
        x += d; y += d; z += d;
        return(*this);
}

Vector& Vector::operator += (Vector& v)
{
        x += v.x; y += v.y; z += v.z;
        return(*this);
}

Vector& Vector::operator -= (double d)
{
        x -= d; y -= d; z -= d;
        return(*this);
}

Vector& Vector::operator -= (Vector& v)
{
        x -= v.x; y -= v.y; z -= v.z;
        return(*this);
}

Vector& Vector::operator *= (double d)
{
        x *= d; y *= d; z *= d;
        return(*this);
}

Vector& Vector::operator *= (Vector& v)
{
        x *= v.x; y *= v.y; z *= v.z;
        return(*this);
}

Vector& Vector::operator /= (double d)
{
        x /= d; y /= d; z /= d;
        return(*this);
}

Vector& Vector::operator /= (Vector& v)
{
        x /= v.x; y /= v.y; z /= v.z;
        return(*this);
}

//
// Ray
//

Ray::Ray(Vector& p, Vector& d)
{
        this->p = p;
        this->d = d;
}

void Ray::Set(Vector& p, Vector& d)
{
        this->p = p;
        this->d = d;
}

double Ray::GetDistanceFrom(Ray& r)
{
        double t = (d | r.d);
        if(IsZero(t)) return(-BIGNUMBER); // plane is paralell to the ray, return -infinite
        return(((r.p - p) | r.d) / t);
}

double Ray::GetDistanceFrom(Vector& v)
{
        double t = ((v - p) | d) / (d | d);
        return(((p + d*t) - v).Length());
}

Vector Ray::operator [] (double t)
{
        return(p + d*t);
}

//
// XForm
//

XForm::XForm(Ray& r, Vector& s, bool isWorldToLocal)
{
        Initalize(r, s, isWorldToLocal);
}

void XForm::Initalize()
{
        m.Initalize();
}

void XForm::Initalize(Ray& r, Vector& s, bool isWorldToLocal)
{
        Initalize();

        if(m_isWorldToLocal = isWorldToLocal)
        {
                *this -= r.p;
                *this >>= r.d;
                *this /= s;

        }
        else
        {
                *this *= s;
                *this <<= r.d;
                *this += r.p;
        }
}

void XForm::operator *= (Vector& v)
{
        Matrix s;
        s.mat[0][0] = v.x;
        s.mat[1][1] = v.y;
        s.mat[2][2] = v.z;
        m *= s;
}

void XForm::operator += (Vector& v)
{
        Matrix t;
        t.mat[3][0] = v.x;
        t.mat[3][1] = v.y;
        t.mat[3][2] = v.z;
        m *= t;
}

void XForm::operator <<= (Vector& v)
{
        Matrix x;
        x.mat[1][1] = cos(v.x); x.mat[1][2] = -sin(v.x);
        x.mat[2][1] = sin(v.x); x.mat[2][2] = cos(v.x);

        Matrix y;
        y.mat[0][0] = cos(v.y); y.mat[0][2] = -sin(v.y);
        y.mat[2][0] = sin(v.y); y.mat[2][2] = cos(v.y);

        Matrix z;
        z.mat[0][0] = cos(v.z); z.mat[0][1] = -sin(v.z);
        z.mat[1][0] = sin(v.z); z.mat[1][1] = cos(v.z);

        m = m_isWorldToLocal ? (m * y * x * z) : (m * z * x * y);
}

void XForm::operator /= (Vector& v)
{
        Vector s;
        s.x = IsZero(v.x) ? 0 : 1 / v.x;
        s.y = IsZero(v.y) ? 0 : 1 / v.y;
        s.z = IsZero(v.z) ? 0 : 1 / v.z;
        *this *= s;
}

void XForm::operator -= (Vector& v)
{
        *this += -v;
}

void XForm::operator >>= (Vector& v)
{
        *this <<= -v;
}

Vector XForm::operator < (Vector& n)
{
        Vector ret;

        ret.x = n.x * m.mat[0][0] +
                        n.y * m.mat[1][0] +
                        n.z * m.mat[2][0];
        ret.y = n.x * m.mat[0][1] +
                        n.y * m.mat[1][1] +
                        n.z * m.mat[2][1];
        ret.z = n.x * m.mat[0][2] +
                        n.y * m.mat[1][2] +
                        n.z * m.mat[2][2];

        return(ret);
}

Vector XForm::operator << (Vector& v)
{
        Vector ret;

        ret.x = v.x * m.mat[0][0] +
                        v.y * m.mat[1][0] +
                        v.z * m.mat[2][0] +
                        m.mat[3][0];
        ret.y = v.x * m.mat[0][1] +
                        v.y * m.mat[1][1] +
                        v.z * m.mat[2][1] +
                        m.mat[3][1];
        ret.z = v.x * m.mat[0][2] +
                        v.y * m.mat[1][2] +
                        v.z * m.mat[2][2] +
                        m.mat[3][2];

        return(ret);
}

Ray XForm::operator << (Ray& r)
{
        return(Ray(*this << r.p, *this < r.d));
}

//
// XForm::Matrix
//

XForm::Matrix::Matrix()
{
        Initalize();
}

void XForm::Matrix::Initalize()
{
        mat[0][0] = 1; mat[0][1] = 0; mat[0][2] = 0; mat[0][3] = 0;
        mat[1][0] = 0; mat[1][1] = 1; mat[1][2] = 0; mat[1][3] = 0;
        mat[2][0] = 0; mat[2][1] = 0; mat[2][2] = 1; mat[2][3] = 0;
        mat[3][0] = 0; mat[3][1] = 0; mat[3][2] = 0; mat[3][3] = 1;
}

XForm::Matrix XForm::Matrix::operator * (Matrix& m)
{
        Matrix ret;

        for(int i = 0; i < 4; i++)
        {
                for(int j = 0; j < 4; j++)
                {
                        ret.mat[i][j] = mat[i][0] * m.mat[0][j] +
                                                        mat[i][1] * m.mat[1][j] +
                                                        mat[i][2] * m.mat[2][j] +
                                                        mat[i][3] * m.mat[3][j];

                        if(IsZero(ret.mat[i][j])) ret.mat[i][j] = 0;
                }
        }

        return(ret);
}

XForm::Matrix& XForm::Matrix::operator *= (XForm::Matrix& m)
{
        return(*this = *this * m);
}

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