一次，二次、三次多项式系数解算是工程项目里最常用到的方法，就是常用的数学公式，如果从头写还是比较费劲，涉及到高斯解方程等，这里将源码分享给大家，已经经过大量的测试，解算算法是完全正确的。直接复制即可使用，如果能帮到大家，希望能点赞。
//solve one order polynomial
void PolynCal1(double *x1, double *y1, double *x2,
double *y2, int n, double *cofx, double *cofy)
{
for(int i=0; i<n; i++)
{
x1[i]=(cofx[0]+cofx[1]*x2[i]+cofx[2]*y2[i]);
y1[i]=(cofy[0]+cofy[1]*x2[i]+cofy[2]*y2[i]);
}
}
void PolynCoff3(double *x1, double *y1, double *x2,
double *y2, int n, double *cofx, double *cofy,
double *rmsx, double *rmsy)
{
double a[10],aa[100],al[10];
int i;
//x
memset(aa,0,sizeof(double)*100);
memset(al,0,sizeof(double)*10);
for(i=0; i<n; i++)
{
a[0] = 1.0;
a[1] = x2[i]; a[2] = y2[i];
a[3] = x2[i]*x2[i]; a[4] = x2[i]*y2[i]; a[5] = y2[i]*y2[i];
a[6] = x2[i]*x2[i]*x2[i]; a[7] = x2[i]*x2[i]*y2[i];
a[8] = x2[i]*y2[i]*y2[i]; a[9] = y2[i]*y2[i]*y2[i];
EquationNorm(a,10,x1[i],aa,al,1.0);
}
Agaus(aa, al, 10);
memcpy(cofx, al, sizeof(double)*10);
//y
memset(aa,0,sizeof(double)*100);
memset(al,0,sizeof(double)*10);
for(i=0; i<n; i++)
{
a[0] = 1.0;
a[1] = x2[i]; a[2] = y2[i];
a[3] = x2[i]*x2[i]; a[4] = x2[i]*y2[i]; a[5] = y2[i]*y2[i];
a[6] = x2[i]*x2[i]*x2[i]; a[7] = x2[i]*x2[i]*y2[i];
a[8] = x2[i]*y2[i]*y2[i]; a[9] = y2[i]*y2[i]*y2[i];
EquationNorm(a,10,y1[i],aa,al,1.0);
}
Agaus(aa, al, 10);
memcpy(cofy, al, sizeof(double)*10);
if(rmsx)
{
for(i=0; i<n; i++)
{
rmsx[i]=(cofx[0]+
cofx[1]*x2[i]+cofx[2]*y2[i]+
cofx[3]*x2[i]*x2[i]+cofx[4]*x2[i]*y2[i]+
cofx[5]*y2[i]*y2[i] + cofx[6]*x2[i]*x2[i]*x2[i] + cofx[7]*x2[i]*x2[i]*y2[i]+
cofx[8]*x2[i]*y2[i]*y2[i] + cofx[9]*y2[i]*y2[i]*y2[i])-x1[i];
}
}
if(rmsy)
{
for(i=0; i<n; i++)
{
rmsy[i]=(cofy[0]+
cofy[1]*x2[i]+cofy[2]*y2[i]+
cofy[3]*x2[i]*x2[i]+cofy[4]*x2[i]*y2[i]+
cofy[5]*y2[i]*y2[i] + cofy[6]*x2[i]*x2[i]*x2[i] + cofy[7]*x2[i]*x2[i]*y2[i]+
cofy[8]*x2[i]*y2[i]*y2[i] + cofy[9]*y2[i]*y2[i]*y2[i])-y1[i];
}
}
}
//solve one order polynomial
void PolynCoff2(double *x1, double *y1, double *x2,
double *y2, int n, double *cofx, double *cofy,
double *rmsx, double *rmsy)
{
double a[6],aa[36],al[6];
int i;
//x
memset(aa,0,sizeof(double)*36);
memset(al,0,sizeof(double)*6);
for(i=0; i<n; i++)
{
a[0] = 1.0;
a[1] = x2[i]; a[2] = y2[i];
a[3] = x2[i]*x2[i]; a[4] = x2[i]*y2[i]; a[5] = y2[i]*y2[i];
EquationNorm(a,6,x1[i],aa,al,1.0);
}
Agaus(aa, al, 6);
memcpy(cofx, al, sizeof(double)*6);
//y
memset(aa,0,sizeof(double)*36);
memset(al,0,sizeof(double)*6);
for(i=0; i<n; i++)
{
a[0] = 1.0;
a[1] = x2[i]; a[2] = y2[i];
a[3] = x2[i]*x2[i]; a[4] = x2[i]*y2[i]; a[5] = y2[i]*y2[i];
EquationNorm(a,6,y1[i],aa,al,1.0);
}
Agaus(aa, al, 6);
memcpy(cofy, al, sizeof(double)*6);
if(rmsx)
{
for(i=0; i<n; i++)
{
rmsx[i]=(cofx[0]+
cofx[1]*x2[i]+cofx[2]*y2[i]+
cofx[3]*x2[i]*x2[i]+cofx[4]*x2[i]*y2[i]+
cofx[5]*y2[i]*y2[i])-x1[i];
}
}
if(rmsy)
{
for(i=0; i<n; i++)
{
rmsy[i]=(cofy[0]+
cofy[1]*x2[i]+cofy[2]*y2[i]+
cofy[3]*x2[i]*x2[i]+cofy[4]*x2[i]*y2[i]+
cofy[5]*y2[i]*y2[i])-y1[i];
}
}
}
void PolynCal2(double *x1, double *y1, double *x2,
double *y2, int n, const double *cofx, const double *cofy)
{
for(int i=0; i<n; i++)
{
x1[i]=(cofx[0]+
cofx[1]*x2[i]+cofx[2]*y2[i]+
cofx[3]*x2[i]*x2[i]+cofx[4]*x2[i]*y2[i]+cofx[5]*y2[i]*y2[i]);
y1[i]=(cofy[0]+
cofy[1]*x2[i]+cofy[2]*y2[i]+
cofy[3]*x2[i]*x2[i]+cofy[4]*x2[i]*y2[i]+cofy[5]*y2[i]*y2[i]);
}
}
void PolynCal3(double *x1, double *y1, double *x2,
double *y2, int n, const double *cofx, const double *cofy)
{
for(int i=0; i<n; i++)
{
x1[i]=(cofx[0]+
cofx[1]*x2[i]+cofx[2]*y2[i]+
cofx[3]*x2[i]*x2[i]+cofx[4]*x2[i]*y2[i]+
cofx[5]*y2[i]*y2[i] + cofx[6]*x2[i]*x2[i]*x2[i] + cofx[7]*x2[i]*x2[i]*y2[i]+
cofx[8]*x2[i]*y2[i]*y2[i] + cofx[9]*y2[i]*y2[i]*y2[i]);
y1[i]=(cofy[0]+
cofy[1]*x2[i]+cofy[2]*y2[i]+
cofy[3]*x2[i]*x2[i]+cofy[4]*x2[i]*y2[i]+
cofy[5]*y2[i]*y2[i] + cofy[6]*x2[i]*x2[i]*x2[i] + cofy[7]*x2[i]*x2[i]*y2[i]+
cofy[8]*x2[i]*y2[i]*y2[i] + cofy[9]*y2[i]*y2[i]*y2[i]);
}
}
//solve one order polynomial
void PolynCoff1(double *x1, double *y1, double *x2,
double *y2, int n, double *cofx, double *cofy,
double *rmsx, double *rmsy)
{
double a[3],aa[9],al[3];
int i;
//x
memset(aa,0,sizeof(double)*9);
memset(al,0,sizeof(double)*3);
for(i=0; i<n; i++)
{
a[0] = 1.0;
a[1] = x2[i]; a[2] = y2[i];
EquationNorm(a,3,x1[i],aa,al,1.0);
}
Agaus(aa, al, 3);
memcpy(cofx, al, sizeof(double)*3);
//y
memset(aa,0,sizeof(double)*9);
memset(al,0,sizeof(double)*3);
for(i=0; i<n; i++)
{
a[0] = 1.0;
a[1] = x2[i]; a[2] = y2[i];
EquationNorm(a,3,y1[i],aa,al,1.0);
}
Agaus(aa, al, 3);
memcpy(cofy, al, sizeof(double)*3);
//rmsx
if(rmsx)
{
for(i=0; i<n; i++)
rmsx[i]=(cofx[0]+cofx[1]*x2[i]+cofx[2]*y2[i])-x1[i];
}
//rmsy
if(rmsy)
{
for(i=0; i<n; i++)
rmsy[i]=(cofy[0]+cofy[1]*x2[i]+cofy[2]*y2[i])-y1[i];
}
}
void EquationNorm(double *a, int n, double b,
double *aa, double *ab, double p)
{
int i,j;
for (i=0; i<n; i++)
{
for (j=0; j<n; j++)
*aa++ += p* a[i] * a[j];
*ab++ += p* a[i] * b;
}
}
int Agaus(double *a, double *b, int n)
{
int l = 1, k, i, j, is = 0, p, q;
boost::scoped_array<int> js(new int[n]);
double d,t;
for (k=0; k<=n-2; k++) {
d=0.0;
for (i=k; i<=n-1; i++) {
for (j=k; j<=n-1; j++) {
t = std::fabs(a[i*n+j]);
if (t>d) {
d = t;
js[k] = j;
is = i;
}
}
}
if (d+1.0 == 1.0)
l = 0;
else {
if (js[k] != k)
for (i=0; i<=n-1; i++) {
p = i*n+k;
q = i*n+js[k];
t = a[p];
a[p] = a[q];
a[q] = t;
}
if (is != k) {
for (j=k; j<=n-1; j++) {
p = k*n+j;
q = is*n+j;
t = a[p];
a[p] = a[q];
a[q] = t;
}
t = b[k];
b[k] = b[is];
b[is] = t;
}
}
if (l == 0)
return 0;
d = a[k*n+k];
for (j=k+1; j<=n-1; j++) {
p = k*n+j;
a[p] = a[p]/d;
}
b[k] = b[k]/d;
for (i=k+1; i<=n-1; i++) {
for (j=k+1; j<=n-1; j++) {
p = i*n+j;
a[p] = a[p]-a[i*n+k]*a[k*n+j];
}
b[i] = b[i]-a[i*n+k]*b[k];
}
}
d = a[(n-1)*n+n-1];
if (std::fabs(d)+1.0 == 1.0)
return 0;
b[n-1] = b[n-1]/d;
for (i=n-2; i>=0; i--) {
t = 0.0;
for (j=i+1; j<=n-1; j++)
t = t+a[i*n+j]*b[j];
b[i] = b[i]-t;
}
js[n-1] = n-1;
for (k=n-1; k>=0; k--) {
if (js[k] != k) {
t = b[k];
b[k] = b[js[k]];
b[js[k]] = t;
}
}
return 1;
}