此方法用于三角形栅格化，需要传入的点有A,B,C三点的整数坐标。
本文主要考虑了以下四种情况对三角形进行栅格化遍历。
在这里插入图片描述
相对于传统逐像素扫描算法大概提高一倍的效率。

步骤如下：

  1. 根据X坐标对A，B,C进行排序交换，使得C.X<= B.X <=A.X
  2. 计算BC,AC,AB的斜率为k1,k2,k3,截距为b1,b2,b3
  3. 讨论是否有任意一个斜率不存在(趋于无穷大)
    1. 如果斜率存在，则以B.X作为分界线，用在逐X遍历通过解析式之差计算逐Y遍历范围
    2. 如果斜率不存在，则以矩形边界为范围逐X遍历，以斜率存在两线进行做差得到逐Y遍历范围
  4. 根据逐像素范围调用坐标回调传出结果

注意：该算法可能在矩形外的1像素范围内扩展，如果假定栅格化范围是10个格子，则11格内均可能有位置被回调。

using System;


/// <summary>
/// 整形向量
/// </summary>
public struct IntVector2 : IEquatable<IntVector2>, IFormattable
{
    public int x;
    public int y;

    public IntVector2(int x, int y)
    {
        this.x = x;
        this.y = y;
    }

    public static IntVector2 operator +(IntVector2 a, IntVector2 b)
    {
        return new IntVector2(a.x + b.x, a.y + b.y);
    }
    public static IntVector2 operator -(IntVector2 a, IntVector2 b)
    {
        return new IntVector2(a.x - b.x, a.y - b.y);
    }

    public bool Equals(IntVector2 other)
    {
        return x == other.x && y == other.y;
    }

    public string ToString(string? format, IFormatProvider? formatProvider)
    {
        return $"({x},{y})";
    }

    public static bool operator ==(IntVector2 left, IntVector2 right)
    {
        return left.x == right.x && left.y == right.y;
    }
    public static bool operator !=(IntVector2 left, IntVector2 right)
    {
        return left.x != right.x && left.y != right.y;
    }


}



public static class TriSteper
{
    static void Swap<T>(ref T a, ref T b)
    {
        T temp = a;
        a = b;
        b = temp;
    }
    static float GetK(ref IntVector2 a, ref IntVector2 b)
    {
        if (a.x == b.x) return float.MaxValue;
        return ((float)a.y - (float)b.y) / ((float)a.x - (float)b.x);
    }
    static float GetB(ref float k, ref IntVector2 a)
    {
        return a.y - k * a.x;
    }
    public static void ForeachTri(IntVector2 a, IntVector2 b, IntVector2 c, Action<int, int> callback)
    {

        //排序 a> b > c
        if (b.x > a.x) Swap(ref a, ref b);
        if (c.x > b.x) Swap(ref b, ref c);
        if (b.x > a.x) Swap(ref a, ref b);


        //斜率
        float k1 = GetK(ref c, ref b);
        float k2 = GetK(ref a, ref c);
        float k3 = GetK(ref a, ref b);
        //截距
        float b1 = GetB(ref k1, ref c);
        float b2 = GetB(ref k2, ref a);
        float b3 = GetB(ref k3, ref b);

        //解析式
        //c -b
        Func<int, int> anal1 = (x) => (int)Math.Round(k1 * x + b1);
        //a - c
        Func<int, int> anal2 = (x) => (int)Math.Round(k2 * x + b2);
        // a b
        Func<int, int> anal3 = (x) => (int)Math.Round(k3 * x + b3);

        //非极端三角形
        if (k1 != float.MaxValue && k2 != float.MaxValue && k3 != float.MaxValue)
        {
            //斜率分区遍历
            if (k1 > k2)
            {
                //从c到b的遍历
                for (int i = c.x; i <= b.x; ++i)
                {
                    int end = anal1(i);
                    int start = anal2(i);
                    for (int j = start; j <= end; ++j) callback(i, j);
                }
                //从b到a的遍历
                for (int i = b.x + 1; i <= a.x; ++i)
                {
                    int end = anal3(i);
                    int start = anal2(i);
                    for (int j = start; j <= end; ++j) callback(i, j);
                }
            }
            else
            {
                //从c到b的遍历
                for (int i = c.x; i <= b.x; ++i)
                {
                    int start = anal1(i);
                    int end = anal2(i);
                    for (int j = start; j <= end; ++j) callback(i, j);
                }
                //从b到a的遍历
                for (int i = b.x + 1; i <= a.x; ++i)
                {
                    int end = anal2(i);
                    int start = anal3(i);
                    for (int j = start; j <= end; ++j) callback(i, j);
                }
            }

        }
        //极端三角型
        else
        {
            //cb 斜率极限
            if (k1 == float.MaxValue)
            {
                for (int i = c.x; i <= a.x; ++i)
                {
                    int end = anal2(i);
                    int start = anal3(i);
                    if (end < start) Swap<int>(ref start, ref end);
                    for (int j = start; j <= end; ++j) callback(i, j);
                }
            }
            //ab斜率极限
            else if (k3 == float.MaxValue)
            {
                for (int i = c.x; i <= a.x; ++i)
                {
                    int end = anal2(i);
                    int start = anal1(i);
                    if (end < start) Swap<int>(ref start, ref end);
                    for (int j = start; j <= end; ++j) callback(i, j);
                }
            }
        }



    }


}

例程如下，此程序实现了简单的三角形栅格化，生成bitmap并保存

using System.Drawing;
using System.Drawing.Imaging;


class Pro
{

   //例程

    public static void Main()
    {
        IntVector2 a = new IntVector2(0, 5);
        IntVector2 b = new IntVector2(10, 0);
        IntVector2 c = new IntVector2(5, 10);

        Bitmap bitMap = new(11, 11);
        for (int i = 0; i < 11; i++) for (int j = 0; j < 11; j++) bitMap.SetPixel(i, j, Color.White);
        TriSteper.ForeachTri(a, b, c, (x, y) =>
        {
            bitMap.SetPixel(x, y, Color.Red);
            Console.WriteLine($"{new IntVector2(x, y)}");
        });

       
        Stream writer = new FileStream("haha.bmp", FileMode.OpenOrCreate);
        bitMap.Save(writer, ImageFormat.Bmp);
        writer.Close();
    }
}

注：图是使用例程指出方法绘制三次所得
在这里插入图片描述