mat_vec_fns_II.h

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// 
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#ifndef MAT_VEC_FNS_II_H_INCLUDED
#define MAT_VEC_FNS_II_H_INCLUDED

#include <cmath>
#include "mat_vec_types.h"


template <class t_scalar> bool sameSign(t_scalar a, t_scalar b);

int getMissingNode(int n0, int n1, int n2);
void getRestOfNodes(int iN, int &iO0, int &iO1, int &iO2);
void getMissingPair(int in0, int in1, int &on0, int &on1); 


// template <class brr3> void arr3arr3Add(brr3 &vecA, brr3 &vecB, brr3 &res);
template <class t_scalar, class brr3> void arr3arr3Add(arr3_view<t_scalar,brr3> vecA, arr3_view<t_scalar,brr3> vecB, arr3_view<t_scalar,brr3> res);

// void arr3arr3Substract(arr3 &vecA, arr3 &vecB, arr3 &res); 
// template <class brr3> void arr3arr3Substract(brr3 &vecA, brr3 &vecB, brr3 &res);
template <class t_scalar, class brr3> void arr3arr3Substract(arr3_view<t_scalar,brr3> vecA, arr3_view<t_scalar,brr3> vecB, arr3_view<t_scalar,brr3> res);

// void arr3arr3VectorProduct(arr3 (&u), arr3 (&v), arr3 (&w));
// template <class brr3> void arr3arr3VectorProduct(brr3 (&u), brr3 (&v), brr3 (&w));
template <class t_scalar, class brr3> void arr3arr3VectorProduct(arr3_view<t_scalar,brr3> u, arr3_view<t_scalar,brr3> v, arr3_view<t_scalar,brr3> w);

// scalar arr3arr3DotProduct(arr3 &vecA, arr3 &vecB);
template <class t_scalar, class brr3> t_scalar arr3arr3DotProduct(arr3_view<t_scalar,brr3> vecA, arr3_view<t_scalar,brr3> vecB);

template <class t_scalar, class brr3> void arr3Normalise(arr3_view<t_scalar,brr3> e);

// void arr3Normalise2(arr3 &e, arr3 &n);
template <class t_scalar, class brr3> void arr3Normalise2(arr3_view<t_scalar,brr3> e, arr3_view<t_scalar,brr3> n);

template <class t_scalar, class brr3> void arr3Resize(t_scalar f, arr3_view<t_scalar,brr3> u);

// void arr3Resize2(scalar f, arr3 &u, arr3 &v);
template <class t_scalar, class brr3> void arr3Resize2(t_scalar f, arr3_view<t_scalar,brr3> u, arr3_view<t_scalar,brr3> v);

template <class t_scalar, class brr3> void arr3Resize3(t_scalar f, arr3_view<t_scalar,brr3> u, arr3_view<t_scalar,brr3> v);

template <class t_scalar, class brr3> void arr3Store(arr3_view<t_scalar,brr3> u, arr3_view<t_scalar,brr3> v);

template <class t_scalar, class brr3> t_scalar arr3arr3Distance(arr3_view<t_scalar,brr3> vecA, arr3_view<t_scalar,brr3> vecB);

template <class t_scalar, class brr3> t_scalar mag(arr3_view<t_scalar,brr3> v);

template <class t_scalar, class brr3> t_scalar mag2(arr3_view<t_scalar,brr3> v);

template <class brr3> void arr3Initialise(brr3 &v);

template <class t_scalar, class brr3> t_scalar detByRows(arr3_view<t_scalar,brr3> a, arr3_view<t_scalar,brr3> b, arr3_view<t_scalar,brr3> c); 

template <class t_scalar, class brr3> t_scalar detByCols(arr3_view<t_scalar,brr3> a, arr3_view<t_scalar,brr3> b, arr3_view<t_scalar,brr3> c); 



// void tangent(arr3 &vecA, arr3 &vecB, arr3 &t);
template <class t_scalar, class brr3> void tangent(brr3 &vecA, brr3 &vecB, brr3 &t);

// template <class t_scalar, class brr3> void getUnitNormal(brr3 &u, brr3 &v, brr3 &w);
// template <class brr3> void getUnitNormal(brr3 &u, brr3 &v, brr3 &w);
template <class t_scalar, class brr3> void getUnitNormal(brr3 &u, brr3 &v, brr3 &w);

template <class t_scalar, class brr3> void getNormal(brr3 &v1, brr3 &v2, brr3 &v3, brr3 &n);

template <class t_scalar, class brr3> void getNormalInwards(brr3 (&tetA)[4], int n0, int n1, int n2, brr3 (&n));
template <class t_scalar, class brr3> void getNormalInwards(brr3 &f0, brr3 &f1, brr3 &f2, brr3 &p3, brr3 (&n));

// bool sameSidePlane(arr3 &vec, arr3 &test, arr3 &p1, arr3 &p2, arr3 &p3);
template <class t_scalar, class brr3> bool sameSidePlane(brr3 &vec, brr3 &test, brr3 &p1, brr3 &p2, brr3 &p3);

template <class t_scalar, class brr3> bool sameSideLine(brr3 &e, brr3 &p1, brr3 &p2, brr3 &p3);

template <class t_scalar, class brr3> bool nodeInTet(brr3 &vec, brr3 (tet)[4]);
template <class t_scalar, class brr3> bool nodeInTet(brr3 &vec, brr3 &tet0, brr3 &tet1, brr3 &tet2, brr3 &tet3);

// void linePlaneIntersectionPoint(arr3 &ip, arr3 &e1, arr3 &e2, arr3 &p1, arr3 &p2, arr3 &p3);
template <class t_scalar, class brr3> void linePlaneIntersectionPoint(brr3 &ip, brr3 &e1, brr3 &e2, brr3 &p1, brr3 &p2, brr3 &p3);

template <class t_scalar, class brr3> bool safeLinePlaneIntersectionPoint(brr3 &ip, brr3 &e1, brr3 &e2, brr3 &p1, brr3 &p2, brr3 &p3);

template <class t_scalar,class brr3> bool lineFaceIntersectionPoint(brr3 (&ip), brr3 (&e1), brr3 (&e2), brr3 (&p1), brr3 (&p2), brr3 (&p3));


// bool isPointInFace(arr3 &ip, arr3 &p1, arr3 &p2, arr3 &p3);
template <class t_scalar, class brr3> bool isPointInFace(brr3 &ip, brr3 &p1, brr3 &p2, brr3 &p3);

// bool intersectionPoint(arr3 &(ip), arr3 (&e1), arr3 (&e2), arr3 (&tet)[4], int f1, int f2, int f3);
template <class t_scalar, class brr3> bool intersectionPoint(brr3 &(ip), brr3 (&e1), brr3 (&e2), brr3 (&tet)[4], int f1, int f2, int f3);
template <class t_scalar, class brr3> bool intersectionPoint(brr3 &ip, brr3 &e1, brr3 &e2, brr3 &f1, brr3 &f2, brr3 &f3);

// void faceCentroid(arr3 &p1, arr3 &p2, arr3 &p3, arr3 &c);
template <class brr3> void faceCentroid(brr3 &p1, brr3 &p2, brr3 &p3, brr3 &c);

template <class t_scalar, class brr3> bool samePlane(brr3 &p1, brr3 &p2, brr3 &p3, brr3 &p4);

template <class t_scalar, class brr3> void intersectingPointToLine(arr3_view<t_scalar,brr3> p0, arr3_view<t_scalar,brr3> p1, arr3_view<t_scalar,brr3> p2p1, arr3_view<t_scalar,brr3> p3);
template <class t_scalar, class brr3> void intersectingPointToLine(vector3 &p0, arr3_view<t_scalar,brr3> p1, arr3_view<t_scalar,brr3> p2p1, arr3_view<t_scalar,brr3> p3);
// template <class t_scalar, class brr3> void intersectingPointToLine(brr3 &p0, brr3 &p1, brr3 &p2, brr3 &p3);

template <class t_scalar, class brr3> t_scalar distanceFromPointToLine(arr3_view<t_scalar,brr3> p0, arr3_view<t_scalar,brr3> p1, arr3_view<t_scalar,brr3> p2);

template <class t_scalar, class brr3> t_scalar getTetrahedraVolume(arr3_view<t_scalar,brr3> p0, arr3_view<t_scalar,brr3> p1, arr3_view<t_scalar,brr3> p2, arr3_view<t_scalar,brr3> p3);

template <class brr3> void getTetrahedraCM(brr3 &p1, brr3 &p2, brr3 &p3, brr3 &p4, brr3 &c);


template <class t_scalar, class brr3, class brr4> void getLocalCoordinatesForLinTet(arr3_view<t_scalar,brr3> t0, arr3_view<t_scalar,brr3> t1, arr3_view<t_scalar,brr3> t2, arr3_view<t_scalar,brr3> t3, arr3_view<t_scalar,brr3> p, brr4 &phi);

template <class brr3> void vec3Vec3SubsToArr3(vector3 &u, vector3 &v, brr3 (&w));
void vec3Arr3SubsToArr3(vector3 &u, arr3 &v, arr3 &w);
void arr3Vec3SubsToArr3(arr3 (&u), vector3 &v, arr3 (&w));


void vec3Arr3AddToArr3(vector3 &u, arr3 (&v), arr3 (&w));
void vec3Vec3AddToArr3(vector3 &u, vector3 &v, arr3 (&w));

void vec3ResizeToArr3(scalar f, vector3 &u, arr3 &v);

scalar vec3Arr3DotProduct(vector3 &u, arr3 &v);

#endif