已知点矩阵的三个顶点坐标、行列数和行列的间距，计算得出剩余所有点的坐标

计算矩阵中每个点的坐标

给定左上角、左下角和右上角三个点的坐标，以及矩阵的行数、列数、行间距和列间距，我们可以计算出所有点的坐标。
在项目中有一个运动装置，只可按照x或y方向移动。目标是在96孔板的96个孔，而这些孔是排列整齐有序的，那么我们就可通过该方案计算出剩余的点，来简化示教人员的工作。

代码实现

public class PlateWellPoint
{
    public double X { get; }
    public double Y { get; }
    public int RowIndex { get; set; }
    public int ColumnIndex { get; set; }

    public PlateWellPoint(double x, double y)
    {
        X = x;
        Y = y;
    }

    public override string ToString()
    {
        return $"R{RowIndex}C{ColumnIndex}({X:F2}, {Y:F2})";
    }
}

public class PlatePointMatrixGenerator
{
    public static List<PlateWellPoint> GeneratePoints(PlateWellPoint topLeft, PlateWellPoint bottomLeft, PlateWellPoint topRight, int rows, int cols, double rowSpacing, double colSpacing)
    {
        // 计算右下角点坐标
        PlateWellPoint bottomRight = CalculateBottomRightPoint(topLeft, bottomLeft, topRight);
        // 验证输入的四个点是否形成矩形
        if (!IsRectangle(topLeft, bottomLeft, topRight, bottomRight))
        {
            Console.WriteLine("警告：输入的三个点无法形成矩形，计算结果可能不准确。");
        }
        // 计算矩阵中所有点的坐标
        List<PlateWellPoint> allPoints = CalculateAllPoints(topLeft, topRight, bottomLeft, rows, cols);
        // 输出所有点的坐标
        Console.WriteLine("\n矩阵中所有点的坐标:");
        int index = 0;
        for (int r = 0; r < rows; r++)
        {
            for (int c = 0; c < cols; c++)
            {
                Console.WriteLine($"点[{r},{c}]: {allPoints[index]}");
                index++;
            }
        }

        // 验证间距
        VerifySpacing(allPoints, rows, cols, rowSpacing, colSpacing);
        return allPoints;
    }
    // 计算右下角的点坐标
    static PlateWellPoint CalculateBottomRightPoint(PlateWellPoint topLeft, PlateWellPoint bottomLeft, PlateWellPoint topRight)
    {
        // 右下角的坐标可以通过向量加法计算
        // 从左上角到右上角的位移 + 从左上角到左下角的位移 = 从左上角到右下角的位移
        double bottomRightX = topLeft.X + (topRight.X - topLeft.X) + (bottomLeft.X - topLeft.X);
        double bottomRightY = topLeft.Y + (topRight.Y - topLeft.Y) + (bottomLeft.Y - topLeft.Y);

        return new PlateWellPoint(bottomRightX, bottomRightY);
    }
    // 检查四个点是否构成矩形
    static bool IsRectangle(PlateWellPoint topLeft, PlateWellPoint bottomLeft, PlateWellPoint topRight, PlateWellPoint bottomRight)
    {
        // 计算对角线长度是否相等
        double diagonal1 = Math.Sqrt(Math.Pow(topLeft.X - bottomRight.X, 2) + Math.Pow(topLeft.Y - bottomRight.Y, 2));
        double diagonal2 = Math.Sqrt(Math.Pow(topRight.X - bottomLeft.X, 2) + Math.Pow(topRight.Y - bottomLeft.Y, 2));

        // 对角线长度应该近似相等
        return Math.Abs(diagonal1 - diagonal2) < 0.001;
    }
    // 计算矩阵中所有点的坐标
    static List<PlateWellPoint> CalculateAllPoints(PlateWellPoint topLeft, PlateWellPoint topRight, PlateWellPoint bottomLeft, int rows, int cols)
    {
        List<PlateWellPoint> points = new List<PlateWellPoint>();

        // 计算行方向和列方向的单位向量
        double rowVectorX = (bottomLeft.X - topLeft.X) / (rows - 1);
        double rowVectorY = (bottomLeft.Y - topLeft.Y) / (rows - 1);

        double colVectorX = (topRight.X - topLeft.X) / (cols - 1);
        double colVectorY = (topRight.Y - topLeft.Y) / (cols - 1);

        // 计算每个点的坐标
        for (int r = 0; r < rows; r++)
        {
            for (int c = 0; c < cols; c++)
            {
                double x = topLeft.X + r * rowVectorX + c * colVectorX;
                double y = topLeft.Y + r * rowVectorY + c * colVectorY;
                points.Add(new PlateWellPoint(x, y) { RowIndex = r, ColumnIndex = c });
            }
        }

        return points;
    }
    // 验证计算的点是否符合给定的行间距和列间距
    static void VerifySpacing(List<PlateWellPoint> points, int rows, int cols, double expectedRowSpacing, double expectedColSpacing)
    {
        double totalRowSpacingError = 0;
        int rowSpacingCount = 0;
        double totalColSpacingError = 0;
        int colSpacingCount = 0;

        // 检查行间距
        for (int r = 0; r < rows - 1; r++)
        {
            for (int c = 0; c < cols; c++)
            {
                int idx1 = r * cols + c;
                int idx2 = ((r + 1) * cols) + c;

                double distance = Math.Sqrt(Math.Pow(points[idx1].X - points[idx2].X, 2) + Math.Pow(points[idx1].Y - points[idx2].Y, 2));
                totalRowSpacingError += Math.Abs(distance - expectedRowSpacing);
                rowSpacingCount++;
            }
        }

        // 检查列间距
        for (int r = 0; r < rows; r++)
        {
            for (int c = 0; c < cols - 1; c++)
            {
                int idx1 = r * cols + c;
                int idx2 = r * cols + c + 1;

                double distance = Math.Sqrt(Math.Pow(points[idx1].X - points[idx2].X, 2) + Math.Pow(points[idx1].Y - points[idx2].Y, 2));
                totalColSpacingError += Math.Abs(distance - expectedColSpacing);
                colSpacingCount++;
            }
        }

        // 打印平均误差
        if (rowSpacingCount > 0)
        {
            double avgRowError = totalRowSpacingError / rowSpacingCount;
            Console.WriteLine($"\n行间距平均误差: {avgRowError:F4} mm");
        }

        if (colSpacingCount > 0)
        {
            double avgColError = totalColSpacingError / colSpacingCount;
            Console.WriteLine($"列间距平均误差: {avgColError:F4} mm");
        }
    }
}

案例图

调用验证

var leftTop = new PlateWellPoint(2, 2);
var rightTop = new PlateWellPoint(6, 6);
var leftButtom = new PlateWellPoint(4, 0);
int rowCount = 3;
int columnCount = 5;
var points = PlatePointMatrixGenerator.GeneratePoints(leftTop, leftButtom, rightTop, rowCount, columnCount, 1, 1);

运行结果

注意：行列序号从0开始的。

从上述结果中随便选一个点，在案例图中找到进行坐标验证
例如：取索引为13的点，是R2C3即第三行第四列，在案例图中核对坐标是否为x:7,y:3。
从案例图中任选一个坐标点，在上述结果中查找，是否为指定的行和列。