Coons曲面

原理：
http://wenku.baidu.com/link?url=w2flm9and7b1cg_gPOHAi8N-TfFxeje0FVyHab4PsCpegJ9SapcDTvb22sRiBlBKz8tk96Ha_P9-XO0dO3sRe7gIRdPDtG2HV-P64xdpMyS

#define nPoints 30
//每段曲线的点数
//矩阵乘法
void mul(float *c, float *a, float *b, int row, int rc, int col)
{
for(int i=0; i<row; i++)
{
for(int j=0; j<col; j++)
{
float t = 0;
for(int k=0; k<rc; k++)
t += a[i*rc+k] * b[k*col+j];
c[i*col+j] = t;
}
}
}
void init(float *p, float *u, float *v, float *uv)
{
for(int i=0; i<4; i++)
{
p[i] = rand() % 500;
u[i] = (rand() % 2 ? -1 : 1) * (rand() % 10 + 1);
v[i] = (rand() % 2 ? -1 : 1) * (rand() % 10 + 1);
uv[i] = (rand() % 2 ? -1 : 1) * (rand() % 10 + 1);
}
}
void setM(float *C, float *p, float *u, float *v, float *uv)
{
float B[][4] =
{
{p[0], p[1], v[0],
v[1]},
{p[2], p[3], v[2],
v[3]},
{u[0], u[1], uv[0], uv[1]},
{u[2], u[3], uv[2], uv[3]}
};
for(int i=0; i<4; i++)
for(int j=0; j<4; j++)
C[i*4+j] = B[i][j];
}
//双三次Coons曲面
void Coons(CDC *pdc)
{
CPen newPen(PS_SOLID, 1, RGB(0, 0, 255));
pdc->SelectObject(&newPen);
float p1[4], pu1[4], pv1[4], puv1[4];
float p2[4], pu2[4], pv2[4], puv2[4];
init(p1, pu1, pv1, puv1);
init(p2, pu2, pv2, puv2);
float delta = 1.0 / nPoints;
float FG[1][4], FGt[4][1], Cx[4][4], Cy[4][4];
float tmp1[nPoints], tmp2[nPoints];
for(float u=0; u<nPoints; u++)
{
float t = u * delta;
float t1 = t;
float t2 = t1 * t;
float t3 = t2 * t;
FG[0][0] = 2*t3 - 3*t2 + 1;
FG[0][1] = -2*t3 + 3*t2;
FG[0][2] = t3 - 2*t2 + t1;
FG[0][3] = t3 - t2;
setM((float *)Cx, p1, pu1, pv1, puv1);
setM((float *)Cy, p2, pu2, pv2, puv2);
float tmpx[1][4], tmpy[1][4], x[nPoints], y[nPoints];
mul((float *)tmpx, (float *)FG, (float *)Cx, 1, 4, 4);
mul((float *)tmpy, (float *)FG, (float *)Cy, 1, 4, 4);
for(int v=0; v<nPoints; v++)
{
t = v * delta;
t1 = t;
t2 = t1 * t;
t3 = t2 * t;
FGt[0][0] = 2*t3 - 3*t2 + 1;
FGt[1][0] = -2*t3 + 3*t2;
FGt[2][0] = t3 - 2*t2 + t1;
FGt[3][0] = t3 - t2;
float x1[1][1], y1[1][1];
mul((float *)x1,
(float *)tmpx, (float *)FGt, 1, 4, 1);
mul((float *)y1,
(float *)tmpy, (float *)FGt, 1, 4, 1);
x[v] = x1[0][0];
y[v] = y1[0][0];
}
pdc->MoveTo(x[0], y[0]);
//连线
for(int i=1; i<nPoints; i++)
{
pdc->LineTo(x[i], y[i]);
}
//连线
for(i=1; i<nPoints; i++)
{
if(u!=0)
{
pdc->MoveTo(tmp1[i], tmp2[i]);
pdc->LineTo(x[i], y[i]);
}
tmp1[i] = x[i];
tmp2[i] = y[i];
}
}
}

最后

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