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Updated interface: all Matrix classes have now the same interface

This commit is contained in:
Paolo Cignoni 2004-10-18 15:03:14 +00:00
parent f6597baedf
commit 13190dfe88
2 changed files with 116 additions and 84 deletions
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34
vcg/math/matrix33.h
View File

@ -24,6 +24,9 @@
History History
$Log: not supported by cvs2svn $ $Log: not supported by cvs2svn $
Revision 1.2 2004/07/13 06:48:26 cignoni
removed uppercase references in include
Revision 1.1 2004/05/28 13:09:05 ganovelli Revision 1.1 2004/05/28 13:09:05 ganovelli
created created
@ -52,6 +55,7 @@ template<class S>
class Matrix33 class Matrix33
{ {
public: public:
typedef S ScalarType;
/// Default constructor /// Default constructor
inline Matrix33() {} inline Matrix33() {}
@ -69,6 +73,18 @@ public:
for(int i=0;i<9;++i) a[i] = v[i]; for(int i=0;i<9;++i) a[i] = v[i];
} }
/// Number of columns
inline unsigned int ColumnsNumber() const
{
return 3;
};
/// Number of rows
inline unsigned int RowsNumber() const
{
return 3;
};
/// Assignment operator /// Assignment operator
Matrix33 & operator = ( const Matrix33 & m ) Matrix33 & operator = ( const Matrix33 & m )
{ {
@ -181,10 +197,10 @@ public:
a[6] = row[0];a[7] = row[1];a[8] = row[2]; a[6] = row[0];a[7] = row[1];a[8] = row[2];
} }
void Zero() { void SetZero() {
for(int i=0;i<9;++i) a[i] =0; for(int i=0;i<9;++i) a[i] =0;
} }
void Identity() { void SetIdentity() {
for(int i=0;i<9;++i) a[i] =0; for(int i=0;i<9;++i) a[i] =0;
a[0]=a[4]=a[8]=1.0; a[0]=a[4]=a[8]=1.0;
} }
@ -208,7 +224,7 @@ public:
a[8] = t[2]*t[2]*q +c; a[8] = t[2]*t[2]*q +c;
} }
/// Funzione per eseguire la trasposta della matrice /// Funzione per eseguire la trasposta della matrice
Matrix33 & Trasp() Matrix33 & Transpose()
{ {
swap(a[1],a[3]); swap(a[1],a[3]);
swap(a[2],a[6]); swap(a[2],a[6]);
@ -217,7 +233,7 @@ public:
} }
/// Funzione per costruire una matrice diagonale dati i tre elem. /// Funzione per costruire una matrice diagonale dati i tre elem.
Matrix33 & SetDiag(S *v) Matrix33 & SetDiagonal(S *v)
{int i,j; {int i,j;
for(i=0;i<3;i++) for(i=0;i<3;i++)
for(j=0;j<3;j++) for(j=0;j<3;j++)
@ -228,7 +244,7 @@ public:
/// Assegna l'n-simo vettore colonna /// Assegna l'n-simo vettore colonna
void SetCol(const int n, S* v){ void SetColumn(const int n, S* v){
assert( (n>=0) && (n<3) ); assert( (n>=0) && (n<3) );
a[n]=v[0]; a[n+3]=v[1]; a[n+6]=v[2]; a[n]=v[0]; a[n+3]=v[1]; a[n+6]=v[2];
}; };
@ -241,7 +257,7 @@ public:
}; };
/// Assegna l'n-simo vettore colonna /// Assegna l'n-simo vettore colonna
void SetCol(const int n, const Point3<S> v){ void SetColumn(const int n, const Point3<S> v){
assert( (n>=0) && (n<3) ); assert( (n>=0) && (n<3) );
a[n]=v[0]; a[n+3]=v[1]; a[n+6]=v[2]; a[n]=v[0]; a[n+3]=v[1]; a[n+6]=v[2];
}; };
@ -254,7 +270,7 @@ public:
}; };
/// Restituisce l'n-simo vettore colonna /// Restituisce l'n-simo vettore colonna
Point3<S> GetCol(const int n) const { Point3<S> GetColumn(const int n) const {
assert( (n>=0) && (n<3) ); assert( (n>=0) && (n<3) );
Point3<S> t; Point3<S> t;
t[0]=a[n]; t[1]=a[n+3]; t[2]=a[n+6]; t[0]=a[n]; t[1]=a[n+3]; t[2]=a[n+6];
@ -273,14 +289,14 @@ public:
/// Funzione per il calcolo del determinante /// Funzione per il calcolo del determinante
S Det() const S Determinant() const
{ {
return a[0]*(a[4]*a[8]-a[5]*a[7]) - return a[0]*(a[4]*a[8]-a[5]*a[7]) -
a[1]*(a[3]*a[8]-a[5]*a[6]) + a[1]*(a[3]*a[8]-a[5]*a[6]) +
a[2]*(a[3]*a[7]-a[4]*a[6]) ; a[2]*(a[3]*a[7]-a[4]*a[6]) ;
} }
Matrix33 & invert() Matrix33 & Invert()
{ {
// Maple produsse: // Maple produsse:
S t4 = a[0]*a[4]; S t4 = a[0]*a[4];

166
vcg/math/matrix44.h
View File

@ -24,6 +24,10 @@
History History
$Log: not supported by cvs2svn $ $Log: not supported by cvs2svn $
Revision 1.19 2004/10/07 14:23:57 ganovelli
added function to take rows and comlumns. Added toMatrix and fromMatrix to comply
RotationTYpe prototype in Similarity.h
Revision 1.18 2004/05/28 13:01:50 ganovelli Revision 1.18 2004/05/28 13:01:50 ganovelli
changed scalar to ScalarType changed scalar to ScalarType
@ -111,8 +115,20 @@ public:
Matrix44(const Matrix44 &m); Matrix44(const Matrix44 &m);
Matrix44(const T v[]); Matrix44(const T v[]);
T &element(const int row, const int col); /// Number of columns
T element(const int row, const int col) const; inline unsigned int ColumnsNumber() const
{
return 4;
};
/// Number of rows
inline unsigned int RowsNumber() const
{
return 4;
};
T &ElementAt(const int row, const int col);
T ElementAt(const int row, const int col) const;
//T &operator[](const int i); //T &operator[](const int i);
//const T &operator[](const int i) const; //const T &operator[](const int i) const;
T *V(); T *V();
@ -122,7 +138,7 @@ public:
const T *operator[](const int i) const; const T *operator[](const int i) const;
// return a copy of the i-th column // return a copy of the i-th column
Point4<T> Column(const int& i)const{ Point4<T> GetColumn(const int& i)const{
assert(i >=0); assert(i >=0);
assert(i<4); assert(i<4);
int first = i<<2; int first = i<<2;
@ -130,7 +146,7 @@ public:
} }
// return the i-th row // return the i-th row
Point4<T> & Column4(const int& i)const{ Point4<T> & GetColumn4(const int& i)const{
assert(i >=0); assert(i >=0);
assert(i<4); assert(i<4);
int first = i<<2; int first = i<<2;
@ -144,7 +160,7 @@ public:
return *((Point4<T>*)(&_a[i<<2])); return *((Point4<T>*)(&_a[i<<2]));
} }
Point3<T> Column3(const int& i)const{ Point3<T> GetColumn3(const int& i)const{
assert(i >=0); assert(i >=0);
assert(i<4); assert(i<4);
int first = i <<2; int first = i <<2;
@ -235,13 +251,13 @@ template <class T> Matrix44<T>::Matrix44(const T v[]) {
memcpy((T *)_a, v, 16 * sizeof(T)); memcpy((T *)_a, v, 16 * sizeof(T));
} }
template <class T> T &Matrix44<T>::element(const int row, const int col) { template <class T> T &Matrix44<T>::ElementAt(const int row, const int col) {
assert(row >= 0 && row < 4); assert(row >= 0 && row < 4);
assert(col >= 0 && col < 4); assert(col >= 0 && col < 4);
return _a[(row<<2) + col]; return _a[(row<<2) + col];
} }
template <class T> T Matrix44<T>::element(const int row, const int col) const { template <class T> T Matrix44<T>::ElementAt(const int row, const int col) const {
assert(row >= 0 && row < 4); assert(row >= 0 && row < 4);
assert(col >= 0 && col < 4); assert(col >= 0 && col < 4);
return _a[(row<<2) + col]; return _a[(row<<2) + col];
@ -287,8 +303,8 @@ template <class T> Matrix44<T> Matrix44<T>::operator*(const Matrix44 &m) const {
for(int j = 0; j < 4; j++) { for(int j = 0; j < 4; j++) {
T t = 0.0; T t = 0.0;
for(int k = 0; k < 4; k++) for(int k = 0; k < 4; k++)
t += element(i, k) * m.element(k, j); t += ElementAt(i, k) * m.ElementAt(k, j);
ret.element(i, j) = t; ret.ElementAt(i, j) = t;
} }
return ret; return ret;
} }
@ -298,7 +314,7 @@ template <class T> Point4<T> Matrix44<T>::operator*(const Point4<T> &v) const {
for(int i = 0; i < 4; i++){ for(int i = 0; i < 4; i++){
T t = 0.0; T t = 0.0;
for(int k = 0; k < 4; k++) for(int k = 0; k < 4; k++)
t += element(i,k) * v[k]; t += ElementAt(i,k) * v[k];
ret[i] = t; ret[i] = t;
} }
return ret; return ret;
@ -347,11 +363,11 @@ template <class T> void Matrix44<T>::operator*=( const Matrix44 & m ) {
Point4<T> t(0, 0, 0, 0); Point4<T> t(0, 0, 0, 0);
for(int k = 0; k < 4; k++) { for(int k = 0; k < 4; k++) {
for(int j = 0; j < 4; j++) { for(int j = 0; j < 4; j++) {
t[k] += element(i, k) * m.element(k, j); t[k] += ElementAt(i, k) * m.ElementAt(k, j);
} }
} }
for(int l = 0; l < 4; l++) for(int l = 0; l < 4; l++)
element(i, l) = t[l]; ElementAt(i, l) = t[l];
} */ } */
} }
@ -371,18 +387,18 @@ template <class T> void Matrix44<T>::SetIdentity() {
template <class T> void Matrix44<T>::SetDiagonal(const T k) { template <class T> void Matrix44<T>::SetDiagonal(const T k) {
SetZero(); SetZero();
element(0, 0) = k; ElementAt(0, 0) = k;
element(1, 1) = k; ElementAt(1, 1) = k;
element(2, 2) = k; ElementAt(2, 2) = k;
element(3, 3) = 1; ElementAt(3, 3) = 1;
} }
template <class T> Matrix44<T> &Matrix44<T>::SetScale(const T sx, const T sy, const T sz) { template <class T> Matrix44<T> &Matrix44<T>::SetScale(const T sx, const T sy, const T sz) {
SetZero(); SetZero();
element(0, 0) = sx; ElementAt(0, 0) = sx;
element(1, 1) = sy; ElementAt(1, 1) = sy;
element(2, 2) = sz; ElementAt(2, 2) = sz;
element(3, 3) = 1; ElementAt(3, 3) = 1;
return *this; return *this;
} }
@ -392,9 +408,9 @@ template <class T> Matrix44<T> &Matrix44<T>::SetTranslate(const Point3<T> &t) {
} }
template <class T> Matrix44<T> &Matrix44<T>::SetTranslate(const T sx, const T sy, const T sz) { template <class T> Matrix44<T> &Matrix44<T>::SetTranslate(const T sx, const T sy, const T sz) {
SetIdentity(); SetIdentity();
element(0, 3) = sx; ElementAt(0, 3) = sx;
element(1, 3) = sy; ElementAt(1, 3) = sy;
element(2, 3) = sz; ElementAt(2, 3) = sz;
return *this; return *this;
} }
template <class T> Matrix44<T> &Matrix44<T>::SetRotate(T AngleRad, const Point3<T> & axis) { template <class T> Matrix44<T> &Matrix44<T>::SetRotate(T AngleRad, const Point3<T> & axis) {
@ -404,22 +420,22 @@ template <class T> Matrix44<T> &Matrix44<T>::SetRotate(T AngleRad, const Point3<
T q = 1-c; T q = 1-c;
Point3<T> t = axis; Point3<T> t = axis;
t.Normalize(); t.Normalize();
element(0,0) = t[0]*t[0]*q + c; ElementAt(0,0) = t[0]*t[0]*q + c;
element(0,1) = t[0]*t[1]*q - t[2]*s; ElementAt(0,1) = t[0]*t[1]*q - t[2]*s;
element(0,2) = t[0]*t[2]*q + t[1]*s; ElementAt(0,2) = t[0]*t[2]*q + t[1]*s;
element(0,3) = 0; ElementAt(0,3) = 0;
element(1,0) = t[1]*t[0]*q + t[2]*s; ElementAt(1,0) = t[1]*t[0]*q + t[2]*s;
element(1,1) = t[1]*t[1]*q + c; ElementAt(1,1) = t[1]*t[1]*q + c;
element(1,2) = t[1]*t[2]*q - t[0]*s; ElementAt(1,2) = t[1]*t[2]*q - t[0]*s;
element(1,3) = 0; ElementAt(1,3) = 0;
element(2,0) = t[2]*t[0]*q -t[1]*s; ElementAt(2,0) = t[2]*t[0]*q -t[1]*s;
element(2,1) = t[2]*t[1]*q +t[0]*s; ElementAt(2,1) = t[2]*t[1]*q +t[0]*s;
element(2,2) = t[2]*t[2]*q +c; ElementAt(2,2) = t[2]*t[2]*q +c;
element(2,3) = 0; ElementAt(2,3) = 0;
element(3,0) = 0; ElementAt(3,0) = 0;
element(3,1) = 0; ElementAt(3,1) = 0;
element(3,2) = 0; ElementAt(3,2) = 0;
element(3,3) = 1; ElementAt(3,3) = 1;
return *this; return *this;
} }
@ -433,10 +449,10 @@ template <class T> T Matrix44<T>::Determinant() const {
template <class T> Point3<T> operator*(const Matrix44<T> &m, const Point3<T> &p) { template <class T> Point3<T> operator*(const Matrix44<T> &m, const Point3<T> &p) {
T w; T w;
Point3<T> s; Point3<T> s;
s[0] = m.element(0, 0)*p[0] + m.element(0, 1)*p[1] + m.element(0, 2)*p[2] + m.element(0, 3); s[0] = m.ElementAt(0, 0)*p[0] + m.ElementAt(0, 1)*p[1] + m.ElementAt(0, 2)*p[2] + m.ElementAt(0, 3);
s[1] = m.element(1, 0)*p[0] + m.element(1, 1)*p[1] + m.element(1, 2)*p[2] + m.element(1, 3); s[1] = m.ElementAt(1, 0)*p[0] + m.ElementAt(1, 1)*p[1] + m.ElementAt(1, 2)*p[2] + m.ElementAt(1, 3);
s[2] = m.element(2, 0)*p[0] + m.element(2, 1)*p[1] + m.element(2, 2)*p[2] + m.element(2, 3); s[2] = m.ElementAt(2, 0)*p[0] + m.ElementAt(2, 1)*p[1] + m.ElementAt(2, 2)*p[2] + m.ElementAt(2, 3);
w = m.element(3, 0)*p[0] + m.element(3, 1)*p[1] + m.element(3, 2)*p[2] + m.element(3, 3); w = m.ElementAt(3, 0)*p[0] + m.ElementAt(3, 1)*p[1] + m.ElementAt(3, 2)*p[2] + m.ElementAt(3, 3);
if(w!= 0) s /= w; if(w!= 0) s /= w;
return s; return s;
} }
@ -444,10 +460,10 @@ template <class T> Point3<T> operator*(const Matrix44<T> &m, const Point3<T> &p)
//template <class T> Point3<T> operator*(const Point3<T> &p, const Matrix44<T> &m) { //template <class T> Point3<T> operator*(const Point3<T> &p, const Matrix44<T> &m) {
// T w; // T w;
// Point3<T> s; // Point3<T> s;
// s[0] = m.element(0, 0)*p[0] + m.element(1, 0)*p[1] + m.element(2, 0)*p[2] + m.element(3, 0); // s[0] = m.ElementAt(0, 0)*p[0] + m.ElementAt(1, 0)*p[1] + m.ElementAt(2, 0)*p[2] + m.ElementAt(3, 0);
// s[1] = m.element(0, 1)*p[0] + m.element(1, 1)*p[1] + m.element(2, 1)*p[2] + m.element(3, 1); // s[1] = m.ElementAt(0, 1)*p[0] + m.ElementAt(1, 1)*p[1] + m.ElementAt(2, 1)*p[2] + m.ElementAt(3, 1);
// s[2] = m.element(0, 2)*p[0] + m.element(1, 2)*p[1] + m.element(2, 2)*p[2] + m.element(3, 2); // s[2] = m.ElementAt(0, 2)*p[0] + m.ElementAt(1, 2)*p[1] + m.ElementAt(2, 2)*p[2] + m.ElementAt(3, 2);
// w = m.element(0, 3)*p[0] + m.element(1, 3)*p[1] + m.element(2, 3)*p[2] + m.element(3, 3); // w = m.ElementAt(0, 3)*p[0] + m.ElementAt(1, 3)*p[1] + m.ElementAt(2, 3)*p[2] + m.ElementAt(3, 3);
// if(w != 0) s /= w; // if(w != 0) s /= w;
// return s; // return s;
//} //}
@ -455,9 +471,9 @@ template <class T> Point3<T> operator*(const Matrix44<T> &m, const Point3<T> &p)
template <class T> Matrix44<T> &Transpose(Matrix44<T> &m) { template <class T> Matrix44<T> &Transpose(Matrix44<T> &m) {
for(int i = 1; i < 4; i++) for(int i = 1; i < 4; i++)
for(int j = 0; j < i; j++) { for(int j = 0; j < i; j++) {
T t = m.element(i, j); T t = m.ElementAt(i, j);
m.element(i, j) = m.element(j, i); m.ElementAt(i, j) = m.ElementAt(j, i);
m.element(j, i) = t; m.ElementAt(j, i) = t;
} }
return m; return m;
} }
@ -473,7 +489,7 @@ template <class T> Matrix44<T> &Invert(Matrix44<T> &m) {
col[j] = 1.0; col[j] = 1.0;
col = solve.Solve(col); col = solve.Solve(col);
for(int i = 0; i < 4; i++) for(int i = 0; i < 4; i++)
m.element(i, j) = col[i]; m.ElementAt(i, j) = col[i];
} }
return m; return m;
} }
@ -486,7 +502,7 @@ template <class T> Matrix44<T> Inverse(const Matrix44<T> &m) {
col[j] = 1.0; col[j] = 1.0;
col = solve.Solve(col); col = solve.Solve(col);
for(int i = 0; i < 4; i++) for(int i = 0; i < 4; i++)
res.element(i, j) = col[i]; res.ElementAt(i, j) = col[i];
} }
return res; return res;
} }
@ -507,7 +523,7 @@ template <class T> LinearSolve<T>::LinearSolve(const Matrix44<T> &m): Matrix44<T
template <class T> T LinearSolve<T>::Determinant() const { template <class T> T LinearSolve<T>::Determinant() const {
T det = d; T det = d;
for(int j = 0; j < 4; j++) for(int j = 0; j < 4; j++)
det *= element(j, j); det *= ElementAt(j, j);
return det; return det;
} }
@ -528,7 +544,7 @@ template <class T> bool LinearSolve<T>::Decompose() {
index[i] = i; // Initialize row index list index[i] = i; // Initialize row index list
T scalemax = (T)0.0; T scalemax = (T)0.0;
for(int j = 0; j < 4; j++) for(int j = 0; j < 4; j++)
scalemax = (scalemax > math::Abs(A.element(i,j))) ? scalemax : math::Abs(A.element(i,j)); scalemax = (scalemax > math::Abs(A.ElementAt(i,j))) ? scalemax : math::Abs(A.ElementAt(i,j));
scale[i] = scalemax; scale[i] = scalemax;
} }
@ -539,7 +555,7 @@ template <class T> bool LinearSolve<T>::Decompose() {
T ratiomax = (T)0.0; T ratiomax = (T)0.0;
int jPivot = k; int jPivot = k;
for(int i = k; i < 4; i++ ) { for(int i = k; i < 4; i++ ) {
T ratio = math::Abs(A.element(index[i], k))/scale[index[i]]; T ratio = math::Abs(A.ElementAt(index[i], k))/scale[index[i]];
if(ratio > ratiomax) { if(ratio > ratiomax) {
jPivot = i; jPivot = i;
ratiomax = ratio; ratiomax = ratio;
@ -555,12 +571,12 @@ template <class T> bool LinearSolve<T>::Decompose() {
} }
// Perform forward elimination // Perform forward elimination
for(int i=k+1; i < 4; i++ ) { for(int i=k+1; i < 4; i++ ) {
T coeff = A.element(index[i],k)/A.element(indexJ,k); T coeff = A.ElementAt(index[i],k)/A.ElementAt(indexJ,k);
for(int j=k+1; j < 4; j++ ) for(int j=k+1; j < 4; j++ )
A.element(index[i],j) -= coeff*A.element(indexJ,j); A.ElementAt(index[i],j) -= coeff*A.ElementAt(indexJ,j);
A.element(index[i],k) = coeff; A.ElementAt(index[i],k) = coeff;
//for( j=1; j< 4; j++ ) //for( j=1; j< 4; j++ )
// element(index[i],j) -= A.element(index[i], k)*element(indexJ, j); // ElementAt(index[i],j) -= A.ElementAt(index[i], k)*ElementAt(indexJ, j);
} }
} }
for(int i = 0; i < 16; i++) for(int i = 0; i < 16; i++)
@ -578,7 +594,7 @@ template <class T> bool LinearSolve<T>::Decompose() {
for(i = 0; i < 4; i++) { for(i = 0; i < 4; i++) {
T largest = 0.0; T largest = 0.0;
for(j = 0; j < 4; j++) { for(j = 0; j < 4; j++) {
T t = math::Abs(element(i, j)); T t = math::Abs(ElementAt(i, j));
if (t > largest) largest = t; if (t > largest) largest = t;
} }
@ -591,17 +607,17 @@ template <class T> bool LinearSolve<T>::Decompose() {
int imax; int imax;
for(j = 0; j < 4; j++) { for(j = 0; j < 4; j++) {
for(i = 0; i < j; i++) { for(i = 0; i < j; i++) {
T sum = element(i,j); T sum = ElementAt(i,j);
for(int k = 0; k < i; k++) for(int k = 0; k < i; k++)
sum -= element(i,k)*element(k,j); sum -= ElementAt(i,k)*ElementAt(k,j);
element(i,j) = sum; ElementAt(i,j) = sum;
} }
T largest = 0.0; T largest = 0.0;
for(i = j; i < 4; i++) { for(i = j; i < 4; i++) {
T sum = element(i,j); T sum = ElementAt(i,j);
for(k = 0; k < j; k++) for(k = 0; k < j; k++)
sum -= element(i,k)*element(k,j); sum -= ElementAt(i,k)*ElementAt(k,j);
element(i,j) = sum; ElementAt(i,j) = sum;
T t = scaling[i] * math::Abs(sum); T t = scaling[i] * math::Abs(sum);
if(t >= largest) { if(t >= largest) {
largest = t; largest = t;
@ -610,19 +626,19 @@ template <class T> bool LinearSolve<T>::Decompose() {
} }
if (j != imax) { if (j != imax) {
for (int k = 0; k < 4; k++) { for (int k = 0; k < 4; k++) {
T dum = element(imax,k); T dum = ElementAt(imax,k);
element(imax,k) = element(j,k); ElementAt(imax,k) = ElementAt(j,k);
element(j,k) = dum; ElementAt(j,k) = dum;
} }
d = -(d); d = -(d);
scaling[imax] = scaling[j]; scaling[imax] = scaling[j];
} }
index[j]=imax; index[j]=imax;
if (element(j,j) == 0.0) element(j,j) = (T)TINY; if (ElementAt(j,j) == 0.0) ElementAt(j,j) = (T)TINY;
if (j != 3) { if (j != 3) {
T dum = (T)1.0 / (element(j,j)); T dum = (T)1.0 / (ElementAt(j,j));
for (i = j+1; i < 4; i++) for (i = j+1; i < 4; i++)
element(i,j) *= dum; ElementAt(i,j) *= dum;
} }
} }
return true; return true;
@ -638,7 +654,7 @@ template <class T> Point4<T> LinearSolve<T>::Solve(const Point4<T> &b) {
x[ip] = x[i]; x[ip] = x[i];
if(first!= -1) if(first!= -1)
for(int j = first; j <= i-1; j++) for(int j = first; j <= i-1; j++)
sum -= element(i,j) * x[j]; sum -= ElementAt(i,j) * x[j];
else else
if(sum) first = i; if(sum) first = i;
x[i] = sum; x[i] = sum;
@ -646,8 +662,8 @@ template <class T> Point4<T> LinearSolve<T>::Solve(const Point4<T> &b) {
for (int i = 3; i >= 0; i--) { for (int i = 3; i >= 0; i--) {
T sum = x[i]; T sum = x[i];
for (int j = i+1; j < 4; j++) for (int j = i+1; j < 4; j++)
sum -= element(i, j) * x[j]; sum -= ElementAt(i, j) * x[j];
x[i] = sum / element(i, i); x[i] = sum / ElementAt(i, i);
} }
return x; return x;
} }