#include <stdio.h>

#include <math.h>

#include <assert.h>



#include "vector.h"



float  sqr(float a) {return a*a;}



// vector (floating point) implementation



float magnitude(Vector v) {

    return float(sqrt(sqr(v.x) + sqr( v.y)+ sqr(v.z)));

}

Vector normalize(Vector v) {

    float d=magnitude(v);

    if (d==0) {

		printf("Cant normalize ZERO vector\n");

		assert(0);

		d=0.1f;

	}

    v.x/=d;

    v.y/=d;

    v.z/=d;

    return v;

}



Vector operator+(Vector v1,Vector v2) {return Vector(v1.x+v2.x,v1.y+v2.y,v1.z+v2.z);}

Vector operator-(Vector v1,Vector v2) {return Vector(v1.x-v2.x,v1.y-v2.y,v1.z-v2.z);}

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

Vector operator*(Vector v1,float s)   {return Vector(v1.x*s,v1.y*s,v1.z*s);}

Vector operator*(float s, Vector v1)  {return Vector(v1.x*s,v1.y*s,v1.z*s);}

Vector operator/(Vector v1,float s)   {return v1*(1.0f/s);}

float  operator^(Vector v1,Vector v2) {return v1.x*v2.x + v1.y*v2.y + v1.z*v2.z;}

Vector operator*(Vector v1,Vector v2) {

    return Vector(

                v1.y * v2.z - v1.z*v2.y,

                v1.z * v2.x - v1.x*v2.z,

                v1.x * v2.y - v1.y*v2.x);

}

Vector planelineintersection(Vector n,float d,Vector p1,Vector p2){

	// returns the point where the line p1-p2 intersects the plane n&d

        Vector dif  = p2-p1;

        float dn= n^dif;

        float t = -(d+(n^p1) )/dn;

        return p1 + (dif*t);

}

int concurrent(Vector a,Vector b) {

	return(a.x==b.x && a.y==b.y && a.z==b.z);

}





// Matrix Implementation

matrix transpose(matrix m) {

	return matrix(	Vector(m.x.x,m.y.x,m.z.x),

					Vector(m.x.y,m.y.y,m.z.y),

					Vector(m.x.z,m.y.z,m.z.z));

}

Vector operator*(matrix m,Vector v){

	m=transpose(m); // since column ordered

	return Vector(m.x^v,m.y^v,m.z^v);

}

matrix operator*(matrix m1,matrix m2){

	m1=transpose(m1);

	return matrix(m1*m2.x,m1*m2.y,m1*m2.z);

}



//Quaternion Implementation    

Quaternion operator*(Quaternion a,Quaternion b) {

	Quaternion c;

	c.r = a.r*b.r - a.x*b.x - a.y*b.y - a.z*b.z; 

	c.x = a.r*b.x + a.x*b.r + a.y*b.z - a.z*b.y; 

	c.y = a.r*b.y - a.x*b.z + a.y*b.r + a.z*b.x; 

	c.z = a.r*b.z + a.x*b.y - a.y*b.x + a.z*b.r; 

	return c;

}

Quaternion operator-(Quaternion q) {

	return Quaternion(q.r*-1,q.x,q.y,q.z);

}

Quaternion operator*(Quaternion a,float b) {

	return Quaternion(a.r*b, a.x*b, a.y*b, a.z*b);

}

Vector operator*(Quaternion q,Vector v) {

	return q.getmatrix() * v;

}

Vector operator*(Vector v,Quaternion q){

	assert(0);  // must multiply with the quat on the left

	return Vector(0.0f,0.0f,0.0f);

}



Quaternion operator+(Quaternion a,Quaternion b) {

	return Quaternion(a.r+b.r, a.x+b.x, a.y+b.y, a.z+b.z);

}

float operator^(Quaternion a,Quaternion b) {

	return  (a.r*b.r + a.x*b.x + a.y*b.y + a.z*b.z); 

}

Quaternion slerp(Quaternion a,Quaternion b,float interp){

	if((a^b) <0.0) {

		a.r=-a.r;

		a.x=-a.x;

		a.y=-a.y;

		a.z=-a.z;

	}

	float theta = float(acos(a^b));

	if(theta==0.0f) { return(a);}

	return a*float(sin(theta-interp*theta)/sin(theta)) + b*float(sin(interp*theta)/sin(theta));

}