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b0,..,b3是贝塞尔，c-1, c2是catmull rom控制点
[b0] = 1 [ 0 6 0 0] [c_1] [b1] - [-1 6 1 0] [c0] [b2] 6 [ 0 1 6 -1] [c1] [b3] [ 0 0 6 0] [c2]
Qt版本代码：
QList<QPointF> cps; cps.append(QPointF(0, 100)); cps.append(QPointF(75, 75)); cps.append(QPointF(200, 150)); cps.append(QPointF(325, 25)); cps.append(QPointF(400, 100)); QPainter p(this); //draw control point foreach(const QPointF& pos, cps) p.drawEllipse(pos, 5, 5); QPainterPath path; //create bezier from catrull-rom /* full conversion matrix (inverse bezier * catmull-rom): 4*4(matrix, 4* 1(catrull-rom control points) 0.000, 1.000, 0.000, 0.000, -0.167, 1.000, 0.167, 0.000, 0.000, 0.167, 1.000, -0.167, 0.000, 0.000, 1.000, 0.000 conversion doesn‘t require full matrix multiplication, so below we simplify */ QPointF prevFar, prev, point, next; for(int i = 0; i < cps.size(); i ++) { int prevFarIdx = i - 2; int prevIdx = i - 1; int nextIdx = i + 1; point = cps[i]; if(prevIdx >= 0) prev = cps[prevIdx]; else prev = point; if(prevFarIdx >= 0) prevFar = cps[prevFarIdx]; else prevFar = prev; if(nextIdx < cps.size()) next = cps[nextIdx]; else next = point; QPointF control1(prevFar.x() * qreal(-0.167) + prev.x() + point.x() * qreal(0.167), prevFar.y() * qreal(-0.167) + prev.y() + point.y() * qreal(0.167)); QPointF control2(prev.x() * qreal(0.167) + point.x() + next.x() * qreal(-0.167), prev.y() * qreal(0.167) + point.y() + next.y() * qreal(-0.167)); path.cubicTo(control1, control2, point); } p.drawPath(path);
参考：
1. http://stackoverflow.com/questions/1030596/drawing-hermite-curves-in-opengl
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原文地址：http://www.cnblogs.com/yanhuiw/p/4385685.html
