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Martin Hope
Vitalii
Asked: 2024-10-22 22:46:14 +0800 CST
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我正在编写一个小型图像转换器，需要将矢量图像（在本例中为 svg）转换为光栅图像，我开始实现并陷入了贝塞尔曲线。

处理曲线的函数：

void precompute_binomial_coefficients(std::vector<std::vector<double>>& binomial_coefficients, uint32_t n) 
{
    binomial_coefficients.resize(n + 1, std::vector<double>(n + 1, 0.0));
    for (uint32_t i = 0; i <= n; ++i) 
    {
        binomial_coefficients[i][0] = 1.0;
        for (uint32_t j = 1; j <= i; ++j) 
        {
            binomial_coefficients[i][j] = binomial_coefficients[i - 1][j - 1] + binomial_coefficients[i - 1][j];
        }
    }
}

double basis(const std::vector<std::vector<double>>& binomial_coefficients, uint32_t i, uint32_t n, double t) 
{
    if (i > n - 1)
    {
        throw std::out_of_range("Index i is out of range for binomial coefficients");
    }
    return binomial_coefficients[n - 1][i] * std::pow(t, i) * std::pow(1 - t, n - 1 - i);
}

std::pair<int, int> bezier(const std::vector<std::pair<int, int>>& control_points, const std::vector<std::vector<double>>& binomial_coefficients, double t) 
{
    uint32_t n = control_points.size();
    if (n == 0) 
    {
        throw std::invalid_argument("Control points vector is empty");
    }
    double x = 0.0;
    double y = 0.0;
    double temp;

    for (uint32_t i = 0; i < n; ++i) 
    {
        temp = basis(binomial_coefficients, i, n, t);
        x += control_points[i].first * temp;
        y += control_points[i].second * temp;
    }
    return std::make_pair(static_cast<int>(std::ceil(x)), static_cast<int>(std::ceil(y)));
}

void DrawBezierCurve(Image& image_, const std::vector<std::pair<int, int>>& control_points, const Color& color) 
{
    if (control_points.empty())
    {
        return;
    }

    uint32_t n = control_points.size();
    std::vector<std::vector<double>> binomial_coefficients;
    precompute_binomial_coefficients(binomial_coefficients, n - 1);

    double step = 0.01;

    for (double t = 0.0; t <= 1.0; t += step) 
    {
        std::pair<int, int> current_point = bezier(control_points, binomial_coefficients, t);
        if (current_point.first >= 0 && current_point.first < image_.GetWidth() && current_point.second >= 0 && current_point.second < image_.GetHeight()) 
        {
            image_.SetPixel(current_point.first, current_point.second, color);
        }
    }
}

画线功能：

 void DrawLine(Image& image_, int x1_, int y1_, int x2_, int y2_, const Color& color_)
 {
     int dx = abs(x2_ - x1_);
     int dy = abs(y2_ - y1_);
     int sx = (x1_ < x2_) ? 1 : -1;
     int sy = (y1_ < y2_) ? 1 : -1;
     int err = dx - dy;

     while (true)
     {
         if (x1_ >= 0 && x1_ < image_.GetWidth() && y1_ >= 0 && y1_ < image_.GetHeight())
         {
             image_.SetPixel(x1_, y1_, color_);
         }

         if (x1_ == x2_ && y1_ == y2_)
         {
             break;
         }

         int e2 = 2 * err;

         if (e2 > -dy)
         {
             err -= dy;
             x1_ += sx;
         }

         if (e2 < dx)
         {
             err += dx;
             y1_ += sy;
         }
     }
 }

转换后，线条不会被平滑，而是简单地笔直，穿过控制点。做错了什么？

c++