c++ - C++ 中的 B 样条曲线

Question

谁能帮我解决 B 样条曲线错误问题？

我想用c++画B样条曲线，但是即使所有坐标都是正数，线段的坐标是负数。

这是 B 样条曲线代码。

void BSplineCurve(Dot &ControlPoint1, Dot &ControlPoint2, 
                  Dot &ControlPoint3,Dot &ControlPoint4, 
                  Dot &DrawCurve, double &t){

    double t2 = t * t;
    double t3 = t2 * t;
    double mt3 = (1 - t) * (1 - t) * (1 - t);

    double bi3 = mt3 / 6;
    double bi2 = ((3 * t3) - (6 * t2) + 4) / 6;
    double bi1 = ((-3 * t3) + (3 * t2) + (3 * t) + 1) / 6;
    double bi  = mt3 / 6;

    DrawCurve.x = ControlPoint1.x * bi3;
    DrawCurve.x += ControlPoint2.x * bi2;
    DrawCurve.x += ControlPoint3.x * bi1;
    DrawCurve.x += ControlPoint4.x * bi;

    DrawCurve.y = ControlPoint1.y * bi3;
    DrawCurve.y += ControlPoint2.y * bi2;
    DrawCurve.y += ControlPoint3.y * bi1;
    DrawCurve.y += ControlPoint4.y * bi;
}

这是绘图代码。

double t = 3.f;
do{

    if ((3 < t) && (t <= 4)) {
    BSplineCurve(ControlPoint1, ControlPoint2, ControlPoint3, ControlPoint4, DrawCurve, t);
    Draw1Dot(DrawCurve.x, DrawCurve.y, DrawCurve.R, DrawCurve.G, DrawCurve.B);
    }
    else if ((4 < t) && (t <= 5)) {
    BSplineCurve(ControlPoint2, ControlPoint3, ControlPoint4, ControlPoint5, DrawCurve, t);
    Draw1Dot(DrawCurve.x, DrawCurve.y, DrawCurve.R, DrawCurve.G, DrawCurve.B);
    }
    else if ((5 < t) && (t <= 6)) {
    BSplineCurve(ControlPoint3, ControlPoint4, ControlPoint5, ControlPoint6, DrawCurve, t);
    Draw1Dot(DrawCurve.x, DrawCurve.y, DrawCurve.R, DrawCurve.G, DrawCurve.B);
    }
    t += 0.001;
} while(t < 6.001);

这是控制点的坐标。

第 1 点:50、50

第 2 点:50、100

第 3 点:200、100

第 4 点:200、50

第 5 点:350、50

第 6 点:350、100

但这是第一段的坐标。

Q3:-1543，-349

Answer 1

您的绘图代码看起来不对。

在函数 BSplineCurve 中，t 参数的值应在 [0, 1] 范围内。通过将 t 从 0 更改为 1，将在点 ControlPoint2 和 ControlPoint3 之间构建三次 B 样条曲线。

你可以尝试这样的事情:

Dot points[6] = {ControlPoint1, ControlPoint2, ControlPoint3, ControlPoint4, ControlPoint5, ControlPoint6};
for(double t = 3.0; t < 6.0; t += 0.001)
{
    const int start = static_cast<int>(t);
    BSplineCurve(points[start - 3], 
                 points[start - 2], 
                 points[start - 1], 
                 points[start], 
                 DrawCurve, 
                 t - start);
    Draw1Dot(DrawCurve.x, DrawCurve.y, DrawCurve.R, DrawCurve.G, DrawCurve.B);
}

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更新

您的 B 样条计算代码看起来也不对:-)

bi 应该是 t3/6.0 而不是 mt3/6.0。参见 here (幻灯片 25)。

---

固定函数看起来像这样(我没有测试):

void BSplineCurve(const Dot &point1, 
                  const Dot &point2, 
                  const Dot &point3,
                  const Dot &point4, 
                  const double t,
                  Dot &result)
{
    const double t2 = t * t;
    const double t3 = t2 * t;
    const double mt = 1.0 - t;
    const double mt3 = mt * mt * mt;

    const double bi3 = mt3;
    const double bi2 = 3 * t3 - 6 * t2 + 4;
    const double bi1 =-3 * t3 + 3 * t2 + 3 * t + 1;
    const double bi  = t3;

    result.x = point1.x * bi3 + 
               point2.x * bi2 +
               point3.x * bi1 +
               point4.x * bi;
    result.x /= 6.0;

    result.y = point1.y * bi3 + 
               point2.y * bi2 +
               point3.y * bi1 +
               point4.y * bi;
    result.y /= 6.0;
}