Qt实现cardinal样条曲线例子

#include "spline.h" #include<math.h> void point::setPoint(float _x, float _y) { x = _x; y = _y; } void spline::initLength() { A = new float[n - 1]; B = new float[n - 1]; C = new float[n - 1]; D = new float[n - 1]; E = new float[n - 1]; for (int i = 0; i < n - 1; i++){ A[i] = 9 * (a[0][i] * a[0][i] + a[1][i] * a[1][i]); B[i] = 12 * (a[0][i] * b[0][i] + a[1][i] * b[1][i]); C[i] = 6 * (a[0][i] * c[0][i] + a[1][i] * c[1][i]) + 4 * (b[0][i] * b[0][i] + b[1][i] * b[1][i]); D[i] = 4 * (b[0][i] * c[0][i] + b[1][i] * c[1][i]); E[i] = c[0][i] * c[0][i] + c[1][i] * c[1][i]; } } float spline::f(int i, float x) { return sqrt(((((A[i] * x + B[i])*x) + C[i])*x + D[i])*x + E[i]); } float spline::simpson(int j, float x, float y) { const int n = 10; const float h = (y - x) / n; float ans = 0.0f; for (int i = 1; i <= n - 1; i++){ if (i % 2){ ans += 4 * f(j, x + 1.0f*i / n*(y - x)); } else ans += 2 * f(j, x + 1.0f*i / n*(y - x)); } ans += f(j, x) + f(j, y); ans *= h / 3; return ans; } //第i段，u float spline::getLen(int i, float u) { return simpson(i, 0, u); } float spline::getU(int i, float s, float u1, float u2) { float ms = getLen(i, (u1 + u2) / 2); if (ms - s > -1.0f && ms - s<1.0f){ return (u1 + u2) / 2; } else if (ms > s)return getU(i, s, u1, (u1 + u2) / 2); else if (ms < s)return getU(i, s, (u1 + u2) / 2, u2); } spline::spline(point* p, int _n, int _grain, float _tension) { n = _n; grain = _grain; tension = _tension; knots = new point[n + 2]; for (int i = 1; i <= n; i++) { knots[i].x = p[i - 1].x; knots[i].y = p[i - 1].y; } knots[0].x = p[0].x; knots[0].y = p[0].y; knots[n + 1].x = p[n - 1].x; knots[n + 1].y = p[n - 1].y; Spline = new point[(n - 1)* grain + 1]; a[0] = new float[n - 1]; b[0] = new float[n - 1]; c[0] = new float[n - 1]; d[0] = new float[n - 1]; a[1] = new float[n - 1]; b[1] = new float[n - 1]; c[1] = new float[n - 1]; d[1] = new float[n - 1]; count = 0; CubicSpline(); initLength(); } int spline::size() { return (n - 1)*grain + 1; } float spline::getX(int i) { return Spline[i].x; } float spline::getY(int i) { return Spline[i].y; } void spline::CubicSpline() { point *s, *k0, *kml, *k1, *k2; int i, j; float* u = new float[grain]; GetCardinalMatrix(); for (i = 0; i < grain; i++) { u[i] = ((float)i) / grain;//u [0,1] } s = Spline; kml = knots; k0 = kml + 1; k1 = k0 + 1; k2 = k1 + 1; for (i = 0; i < n - 1; i++) { init(0, i, kml->x, k0->x, k1->x, k2->x); init(1, i, kml->y, k0->y, k1->y, k2->y); for (j = 0; j < grain; j++) { s->x = Matrix(0, i, u[j]); s->y = Matrix(1, i, u[j]); s++; } k0++, kml++, k1++, k2++; } s->x = knots[n].x; s->y = knots[n].y; delete u; } //void spline::print() //{ // for (int i = 0; i < grain*(n - 1) + 1; i++) { // if (i%grain == 0) // printf("\n"); // printf("%f %f\n", Spline[i].x, Spline[i].y); // } //} void spline::GetCardinalMatrix() { float a1 = tension; m[0] = -a1, m[1] = 2 - a1, m[2] = a1 - 2, m[3] = a1; m[4] = 2 * a1, m[5] = a1 - 3, m[6] = 3 - 2 * a1, m[7] = -a1; m[8] = -a1, m[9] = 0, m[10] = a1, m[11] = 0; m[12] = 0, m[13] = 1, m[14] = 0, m[15] = 0; } void spline::init(int i, int j, float a0, float b0, float c0, float d0) { a[i][j] = m[0] * a0 + m[1] * b0 + m[2] * c0 + m[3] * d0; b[i][j] = m[4] * a0 + m[5] * b0 + m[6] * c0 + m[7] * d0; c[i][j] = m[8] * a0 + m[9] * b0 + m[10] * c0 + m[11] * d0; d[i][j] = m[12] * a0 + m[13] * b0 + m[14] * c0 + m[15] * d0; } //i为0：X，i为1：Y //u float spline::Matrix(int i, int j, float u) { return(d[i][j] + u*(c[i][j] + u*(b[i][j] + u*a[i][j]))); } float spline::getXFromU(int i, float u) { return Matrix(0, i, u); } float spline::getYFromU(int i, float u) { return Matrix(1, i, u); } spline::~spline() { delete[] knots; delete[] Spline; }