具体的代码还是线性代数.
主要是旋转和平移.
这个例子的中模型是在世界原点建立. 所以旋转会以自身轴心旋转.
如果不在世界原点建立模型, 还想以自身为旋转轴旋转.
则是需要以下步骤:
模型的中心点为 V1(100,100,0)假设中心为轴(平行于 Y 轴), 旋转 A 度, 也就是说自身中心点的 Y 轴旋转.
步骤:
(1)v1 平移到世界原点后其他八个顶点的坐标.(中心点坐标的三个参数如果是大于 0 就是 (每个) 顶点减去相对应 XYZ, 如果中心点坐标的三个参数如果是小于 0, 则是 (每个) 顶点加上相对应 XYZ, 或者使用平移矩阵)
(2)(每个)顶点先是平移到 V1 在原点时的所在的位置, 再使用旋转矩阵经行旋转
(3) (每个)旋转后的顶点在平移回中心点原先所在位置.
ATP 附加属性类
- using System;
- using System.Collections.Generic;
- using System.Linq;
- using System.Text;
- using System.Threading.Tasks;
- using System.Windows;
- using System.Windows.Controls;
- using System.Windows.Data;
- using System.Windows.Media;
- using System.Windows.Media.Media3D;
- using System.Windows.Shapes;
- namespace ATP
- {
- public class ATP_Y
- {
- public static readonly DependencyProperty P_YProperty = DependencyProperty.RegisterAttached("P_Y", typeof(double), typeof(ATP.ATP_Y), new PropertyMetadata(0.0, new PropertyChangedCallback(OnP_YChanged)));
- private static void OnP_YChanged(DependencyObject d, DependencyPropertyChangedEventArgs e)
- {
- PY = (double)e.NewValue;
- Draw(d, X, Y, Z);
- }
- public static void SetP_Y(DependencyObject d, double v) => d.SetValue(P_YProperty, v);
- public static double GetP_Y(DependencyObject d) => (double)d.GetValue(P_YProperty);
- public static readonly DependencyProperty P_XProperty = DependencyProperty.RegisterAttached("P_X", typeof(double), typeof(ATP.ATP_Y), new PropertyMetadata(0.0, new PropertyChangedCallback(OnP_XChanged)));
- private static void OnP_XChanged(DependencyObject d, DependencyPropertyChangedEventArgs e)
- {
- PX= (double)e.NewValue;
- Draw(d, X, Y, Z);
- }
- public static void SetP_X(DependencyObject d, double v) => d.SetValue(P_XProperty, v);
- public static double GetP_X(DependencyObject d) => (double)d.GetValue(P_XProperty);
- public static readonly DependencyProperty P_ZProperty = DependencyProperty.RegisterAttached("P_Z", typeof(double), typeof(ATP.ATP_Y), new PropertyMetadata(0.0, new PropertyChangedCallback(OnP_ZChanged)));
- private static void OnP_ZChanged(DependencyObject d, DependencyPropertyChangedEventArgs e)
- {
- PZ = (double)e.NewValue;
- Draw(d, X, Y, Z);
- }
- public static void SetP_Z(DependencyObject d, double v) => d.SetValue(P_ZProperty, v);
- public static double GetP_Z(DependencyObject d) => (double)d.GetValue(P_ZProperty);
- public static readonly DependencyProperty ModeDataProperty = DependencyProperty.RegisterAttached("ModeData", typeof(Point3D), typeof(ATP_Y), new PropertyMetadata(new Point3D(10, 10, 10), new PropertyChangedCallback(OnModeDataChanged)));
- public static void SetModeData(DependencyObject d, Point3D v) => d.SetValue(ModeDataProperty, v);
- public static Point3D GetModeData(DependencyObject d) => (Point3D)d.GetValue(ModeDataProperty);
- private static void OnModeDataChanged(DependencyObject d, DependencyPropertyChangedEventArgs e)
- {
- var data = (Point3D)e.NewValue;
- ModeWidth = data.X;
- ModeHeight = data.Y;
- ModeZWidth = data.Z;
- Draw(d,X,Y,Z);
- }
- public static readonly DependencyProperty YProperty = DependencyProperty.RegisterAttached("Y", typeof(double), typeof(ATP.ATP_Y), new PropertyMetadata(-1.0, new PropertyChangedCallback(OnYChanged)));
- public static void SetY(DependencyObject d, double v) => d.SetValue(YProperty, v);
- public static double GetY(DependencyObject d) => (double)d.GetValue(YProperty);
- public static readonly DependencyProperty XProperty = DependencyProperty.RegisterAttached("X", typeof(double), typeof(ATP.ATP_Y), new PropertyMetadata(-1.0, new PropertyChangedCallback(OnXChanged)));
- private static void OnXChanged(DependencyObject d, DependencyPropertyChangedEventArgs e)
- {
- var deg = Math.PI / 180 * (double)e.NewValue;
- X = deg;
- Draw(d, deg, Y, Z);
- }
- public static void SetX(DependencyObject d, double v) => d.SetValue(XProperty, v);
- public static double GetX(DependencyObject d) => (double)d.GetValue(XProperty);
- public static readonly DependencyProperty ZProperty = DependencyProperty.RegisterAttached("Z", typeof(double), typeof(ATP.ATP_Y), new PropertyMetadata(-1.0, new PropertyChangedCallback(OnZChanged)));
- private static void OnZChanged(DependencyObject d, DependencyPropertyChangedEventArgs e)
- {
- var deg = Math.PI / 180 * (double)e.NewValue;
- Z = deg;
- Draw(d, X, Y, deg);
- }
- public static void SetZ(DependencyObject d, double v) => d.SetValue(ZProperty, v);
- public static double GetZ(DependencyObject d) => (double)d.GetValue(ZProperty);
- private static void OnYChanged(DependencyObject d, DependencyPropertyChangedEventArgs e)
- {
- var deg = Math.PI / 180 * (double)e.NewValue;
- Y = deg;
- Draw(d, X, deg, Z);
- }
- private static double PX, PY, PZ;
- private static double X, Y, Z;
- private static double ModeHeight, ModeWidth, ModeZWidth;
- private static void Draw(DependencyObject d, double X, double Y, double Z)
- {
- var ui = d as Grid;
- ui.Children.Clear();
- var rect = new Rect(new Size(ModeWidth,ModeHeight));
- Group[0] = new Point3D(rect.Width / 2, rect.Height / 2, -(ModeZWidth/2));
- Group[1] = new Point3D(0 - (rect.Width / 2), rect.Height / 2, -(ModeZWidth / 2));
- Group[2] = new Point3D(0 - (rect.Width / 2), 0 - (rect.Height / 2), -(ModeZWidth / 2));
- Group[3] = new Point3D((rect.Width / 2), 0 - (rect.Height / 2), -(ModeZWidth / 2));
- Group[4] = new Point3D(rect.Width / 2, rect.Height / 2, (ModeZWidth / 2));
- Group[5] = new Point3D(0 - (rect.Width / 2), rect.Height / 2, (ModeZWidth / 2));
- Group[6] = new Point3D(0 - (rect.Width / 2), 0 - (rect.Height / 2), (ModeZWidth / 2));
- Group[7] = new Point3D((rect.Width / 2), 0 - (rect.Height / 2), (ModeZWidth / 2));
- for (var i = 0; i <8; i++)
- PP[i] = PSP(ReturnP3D(Y 轴转置矩阵(X, Y, Z) * GetMatrixMP(Group[i])), new Rect(new Size(Math.Max(rect.Height, rect.Width),ModeZWidth)));
- Set(0, 1, ui,Colors.Black);
- Set(1, 2, ui,Colors.Blue);
- Set(2, 3, ui, Colors.Red);
- Set(3, 0, ui, Colors.Fuchsia);
- Set(4, 5, ui, Colors.DarkSlateBlue);
- Set(5, 6, ui, Colors.Red);
- Set(6, 7, ui, Colors.Red);
- Set(7, 4, ui, Colors.Red);
- Set(0, 4, ui, Colors.Red);
- Set(1, 5, ui, Colors.Red);
- Set(2, 6, ui, Colors.Red);
- Set(3, 7, ui, Colors.Red);
- }
- private static void Set(int g1, int g2, Grid g,Color A)
- {
- var c1 = new Line();
- c1.Stroke = new SolidColorBrush(A);
- c1.X1 = PP[g1].X;
- c1.Y1 = PP[g1].Y;
- c1.X2 = PP[g2].X;
- c1.Y2 = PP[g2].Y;
- g.Children.Add(c1);
- }
- private static Matrix GetMatrixMP(Point3D MP)
- {
- var D = new double[4, 1];
- D[0, 0] = MP.X;
- D[1, 0] = MP.Y;
- D[2, 0] = MP.Z;
- D[3, 0] = 1;
- return new Matrix(D);
- }
- private static Point3D ReturnP3D(Matrix MP) => new Point3D(MP[0, 0], MP[1, 0], MP[2, 0]);
- private static Point PSP(Point3D ModePoint, Rect rect)
- {
- Point3D vp = new Point3D(PX, PY, Math.Max(rect.Height, rect.Width)+PZ);
- Point p;
- int x, y;
- x = (int)(vp.X + (ModePoint.X - vp.X) * vp.Z / (vp.Z - ModePoint.Z + 0.5));
- y = (int)(vp.Y + (ModePoint.Y - vp.Y) * vp.Z / (vp.Z - ModePoint.Z + 0.5));
- p = new Point(x, y);
- return p;
- }
- private static Point3D[] Group = new Point3D[8];
- private static Point[] PP = new Point[8];
private static Matrix Y 轴转置矩阵(double DegX, double DegY, double DegZ)
- {
- var A = new double[4, 4];
- A[0, 0] = 1;
- A[0, 1] = 0;
- A[0, 2] = 0;
- A[1, 0] = 0;
- A[1, 1] = Math.Cos(X);
- A[1, 2] = Math.Sin(X);
- A[2, 0] = 0;
- A[2, 1] = 0 - Math.Sin(X);
- A[2, 2] = Math.Cos(X);
- A[0, 3] = 0;
- A[1, 3] = 0;
- A[2, 3] = 0;
- A[3, 0] = 1;
- A[3, 1] = 1;
- A[3, 2] = 1;
- A[3, 3] = 1;
- var B = new double[4, 4];
- B[0, 0] = Math.Cos(Y);
- B[0, 1] = 0;
- B[0, 2] = -Math.Sin(Y);
- B[1, 0] = 0;
- B[1, 1] = 1;
- B[1, 2] = 0;
- B[2, 0] = Math.Sin(Y);
- B[2, 1] = 0;
- B[2, 2] = Math.Cos(Y);
- B[0, 3] = 1;
- B[1, 3] = 1;
- B[2, 3] = 1;
- B[3, 0] = 1;
- B[3, 1] = 1;
- B[3, 2] = 1;
- B[3, 3] = 1;
- var C = new double[4, 4];
- C[0, 0] = Math.Cos(Z);
- C[0, 1] = Math.Sin(Z);
- C[0, 2] = 0;
- C[1, 0] = 0 - Math.Sin(Z);
- C[1, 1] = Math.Cos(Z);
- C[1, 2] = 0;
- C[2, 0] = 0;
- C[2, 1] = 0;
- C[2, 2] = 1;
- C[0, 3] = 1;
- C[1, 3] = 1;
- C[2, 3] = 1;
- B[3, 0] = 1;
- B[3, 1] = 1;
- B[3, 2] = 1;
- C[3, 3] = 1;
- Matrix MT1 = new Matrix(A);
- Matrix MT2 = new Matrix(B);
- Matrix MT3 = new Matrix(C);
- var MT4 = MT1 * MT2;
- return MT4 * MT3;
- }
- }
- }
xaml 代码
- // 其中 ModeData 的三个参数为矩形的长高宽
- //X,Y,Z 为轴的旋转角度
- <Windows x:Class="ATP.MainWindow"
- xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
- xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
- xmlns:d="http://schemas.microsoft.com/expression/blend/2008"
- xmlns:mc="http://schemas.openxmlformats.org/markup-compatibility/2006"
- xmlns:local="clr-namespace:ATP"
- mc:Ignorable="d"
- Title="MainWindow" Height="450" Width="800">
- <Grid> <Grid.RowDefinitions>
- <RowDefinition Height="*"/>
- <RowDefinition Height="auto"/>
- </Grid.RowDefinitions>
- <Grid x:Name="G" local:ATP_Y.P_Z="{Binding ElementName=s4,Path=Value}" local:ATP_Y.ModeData="100,100,100" HorizontalAlignment="Center" VerticalAlignment="Center" local:ATP_Y.Y="{Binding ElementName=s2,Path=Value}" local:ATP_Y.X="{Binding ElementName=s1,Path=Value}" local:ATP_Y.Z="{Binding ElementName=s3,Path=Value}"/>
- <StackPanel Grid.Row="1">
- <!--X 轴旋转 -->
- <Slider Minimum="0" Maximum="360" x:Name="s1"/>
- <!--Y 轴旋转 -->
- <Slider Minimum="0" Maximum="360" x:Name="s2"/>
- <!--Z 轴旋转 -->
- <Slider Minimum="0" Maximum="360" x:Name="s3"/>
- <!-- 视野远近 -->
- <Slider Minimum="0" Maximum="360" x:Name="s4" />
- </StackPanel>
- </Grid>
- </Windows>
矩阵类
- using System;
- using System.Collections.Generic;
- using System.Linq;
- using System.Text;
- using System.Threading.Tasks;
- namespace ATP
- {
- [Serializable]
- public class Matrix
- {
- public double[] element;
- private int rows = 0;
- private int cols = 0;
- /// <summary>
- /// 获取矩阵行数
- /// </summary>
- public int Rows
- {
- get
- {
- return rows;
- }
- }
- /// <summary>
- /// 获取矩阵列数
- /// </summary>
- public int Cols
- {
- get
- {
- return cols;
- }
- }
- /// <summary>
- /// 获取或设置第 i 行第 j 列的元素值
- /// </summary>
- /// <param name="i">第 i 行</param>
- /// <param name="j">第 j 列</param>
- /// <returns > 返回第 i 行第 j 列的元素值</returns>
- public double this[int i, int j]
- {
- get
- {
- if (i <Rows && j < Cols)
- {
- return element[i * cols + j];
- }
- else
- {
- throw new Exception("索引越界");
- }
- }
- set
- {
- element[i * cols + j] = value;
- }
- }
- /// <summary>
- /// 用二维数组初始化 Matrix
- /// </summary>
- /// <param name="m">二维数组</param>
- public Matrix(double[][] m)
- {
- this.rows = m.GetLength(0);
- this.cols = m.GetLength(1);
- int count = 0;
- this.element = new double[Rows * Cols];
- for (int i = 0; i <rows; i++)
- {
- for (int j = 0; j < cols; j++)
- {
- element[count++] = m[i][j];
- }
- }
- }
- public Matrix(double[,] m)
- {
- this.rows = m.GetLength(0);
- this.cols = m.GetLength(1);
- this.element = new double[this.rows * this.cols];
- int count = 0;
- for (int i = 0; i < rows; i++)
- {
- for (int j = 0; j < cols; j++)
- {
- element[count++] = m[i, j];
- }
- }
- }
- public Matrix(List<List<double>> m)
- {
- this.rows = m.Count;
- this.cols = m[0].Count;
- this.element = new double[Rows * Cols];
- for (int i = 0; i <rows; i++)
- {
- for (int j = 0; j < cols; j++)
- {
- this[i, j] = m[i][j];
- }
- }
- }
- #region 矩阵数学运算
- public static Matrix MAbs(Matrix a)
- {
- Matrix _thisCopy = a.DeepCopy();
- for (int i = 0; i < a.Rows; i++)
- {
- for (int j = 0; j < a.Cols; j++)
- {
- _thisCopy[i, j] = Math.Abs(a[i, j]);
- }
- }
- return _thisCopy;
- }
- /// <summary>
- /// 矩阵相加
- /// </summary>
- /// <param name="a">第一个矩阵, 和 b 矩阵必须同等大小</param>
- /// <param name="b">第二个矩阵</param>
- /// <returns > 返回矩阵相加后的结果</returns>
- public static Matrix operator +(Matrix a, Matrix b)
- {
- if (a.cols == b.cols && a.rows == b.rows)
- {
- double[,] res = new double[a.rows, a.cols];
- for (int i = 0; i <a.Rows; i++)
- {
- for (int j = 0; j < a.Cols; j++)
- {
- res[i, j] = a[i, j] + b[i, j];
- }
- }
- return new Matrix(res);
- }
- else
- {
- throw new Exception("两个矩阵行列不相等");
- }
- }
- /// <summary>
- /// 矩阵相减
- /// </summary>
- /// <param name="a">第一个矩阵, 和 b 矩阵必须同等大小</param>
- /// <param name="b">第二个矩阵</param>
- /// <returns > 返回矩阵相减后的结果</returns>
- public static Matrix operator -(Matrix a, Matrix b)
- {
- if (a.cols == b.cols && a.rows == b.rows)
- {
- double[,] res = new double[a.rows, a.cols];
- for (int i = 0; i <a.Rows; i++)
- {
- for (int j = 0; j < a.Cols; j++)
- {
- res[i, j] = a[i, j] - b[i, j];
- }
- }
- return new Matrix(res);
- }
- else
- {
- throw new Exception("两个矩阵行列不相等");
- }
- }
- /// <summary>
- /// 对矩阵每个元素取相反数
- /// </summary>
- /// <param name="a">二维矩阵</param>
- /// <returns > 得到矩阵的相反数</returns>
- public static Matrix operator -(Matrix a)
- {
- Matrix res = a;
- for (int i = 0; i <a.rows; i++)
- {
- for (int j = 0; j < a.cols; j++)
- {
- res.element[i * a.cols + j] = -res.element[i * a.cols + j];
- }
- }
- return res;
- }
- /// <summary>
- /// 矩阵相乘
- /// </summary>
- /// <param name="a">第一个矩阵</param>
- /// <param name="b">第二个矩阵, 这个矩阵的行要与第一个矩阵的列相等</param>
- /// <returns > 返回相乘后的一个新的矩阵</returns>
- public static Matrix operator *(Matrix a, Matrix b)
- {
- if (a.cols == b.rows)
- {
- double[,] res = new double[a.rows, b.cols];
- for (int i = 0; i <a.rows; i++)
- {
- for (int j = 0; j < b.cols; j++)
- {
- for (int k = 0; k < a.cols; k++)
- {
- res[i, j] += a[i, k] * b[k, j];
- }
- }
- }
- return new Matrix(res);
- }
- else
- {
- throw new Exception("两个矩阵行和列不等");
- }
- }
- /// <summary>
- /// 矩阵与数相乘
- /// </summary>
- /// <param name="a">第一个矩阵</param>
- /// <param name="num">一个实数</param>
- /// <returns > 返回相乘后的新的矩阵</returns>
- public static Matrix operator *(Matrix a, double num)
- {
- Matrix res = a;
- for (int i = 0; i <a.rows; i++)
- {
- for (int j = 0; j < a.cols; j++)
- {
- res.element[i * a.cols + j] *= num;
- }
- }
- return res;
- }
- /// <summary>
- /// 矩阵转置
- /// </summary>
- /// <returns > 返回当前矩阵转置后的新矩阵</returns>
- public Matrix Transpose()
- {
- double[,] res = new double[cols, rows];
- {
- for (int i = 0; i <cols; i++)
- {
- for (int j = 0; j < rows; j++)
- {
- res[i, j] = this[j, i];
- }
- }
- }
- return new Matrix(res);
- }
- /// <summary>
- /// 矩阵求逆
- /// </summary>
- /// <returns > 返回求逆后的新的矩阵</returns>
- public Matrix Inverse()
- {
- // 最后原始矩阵并不变, 所以需要深拷贝一份
- Matrix _thisCopy = this.DeepCopy();
- if (cols == rows && this.Determinant() != 0)
- {
- // 初始化一个同等大小的单位阵
- Matrix res = _thisCopy.EMatrix();
- for (int i = 0; i <rows; i++)
- {
- // 首先找到第 i 列的绝对值最大的数, 并将该行和第 i 行互换
- int rowMax = i;
- double max = Math.Abs(_thisCopy[i, i]);
- for (int j = i; j < rows; j++)
- {
- if (Math.Abs(_thisCopy[j, i])> max)
- {
- rowMax = j;
- max = Math.Abs(_thisCopy[j, i]);
- }
- }
- // 将第 i 行和找到最大数那一行 rowMax 交换
- if (rowMax != i)
- {
- _thisCopy.Exchange(i, rowMax);
- res.Exchange(i, rowMax);
- }
- // 将第 i 行做初等行变换, 将第一个非 0 元素化为 1
- double r = 1.0 / _thisCopy[i, i];
- _thisCopy.Exchange(i, -1, r);
- res.Exchange(i, -1, r);
- // 消元
- for (int j = 0; j <rows; j++)
- {
- // 到本行后跳过
- if (j == i)
- continue;
- else
- {
- r = -_thisCopy[j, i];
- _thisCopy.Exchange(i, j, r);
- res.Exchange(i, j, r);
- }
- }
- }
- return res;
- }
- else
- {
- throw new Exception("矩阵不是方阵无法求逆");
- }
- }
- #region 重载比较运算符
- public static bool operator <(Matrix a, Matrix b)
- {
- bool issmall = true;
- for (int i = 0; i < a.Rows; i++)
- {
- for (int j = 0; j < a.Cols; j++)
- {
- if (a[i, j]>= b[i, j]) issmall = false;
- }
- }
- return issmall;
- }
- public static bool operator>(Matrix a, Matrix b)
- {
- bool issmall = true;
- for (int i = 0; i <a.Rows; i++)
- {
- for (int j = 0; j < a.Cols; j++)
- {
- if (a[i, j] <= b[i, j]) issmall = false;
- }
- }
- return issmall;
- }
- public static bool operator <=(Matrix a, Matrix b)
- {
- bool issmall = true;
- for (int i = 0; i < a.Rows; i++)
- {
- for (int j = 0; j < a.Cols; j++)
- {
- if (a[i, j]> b[i, j]) issmall = false;
- }
- }
- return issmall;
- }
- public static bool operator>=(Matrix a, Matrix b)
- {
- bool issmall = true;
- for (int i = 0; i <a.Rows; i++)
- {
- for (int j = 0; j < a.Cols; j++)
- {
- if (a[i, j] < b[i, j]) issmall = false;
- }
- }
- return issmall;
- }
- public static bool operator !=(Matrix a, Matrix b)
- {
- bool issmall = true;
- issmall = ReferenceEquals(a, b);
- if (issmall) return issmall;
- for (int i = 0; i < a.Rows; i++)
- {
- for (int j = 0; j < a.Cols; j++)
- {
- if (a[i, j] == b[i, j]) issmall = false;
- }
- }
- return issmall;
- }
- public static bool operator ==(Matrix a, Matrix b)
- {
- bool issmall = true;
- issmall = ReferenceEquals(a, b);
- if (issmall) return issmall;
- for (int i = 0; i < a.Rows; i++)
- {
- for (int j = 0; j < a.Cols; j++)
- {
- if (a[i, j] != b[i, j]) issmall = false;
- }
- }
- return issmall;
- }
- public override bool Equals(object obj)
- {
- Matrix b = obj as Matrix;
- return this == b;
- }
- public override int GetHashCode()
- {
- return base.GetHashCode();
- }
- #endregion
- public double Determinant()
- {
- if (cols == rows)
- {
- Matrix _thisCopy = this.DeepCopy();
- // 行列式每次交换行, 都需要乘以 - 1
- double res = 1;
- for (int i = 0; i < rows; i++)
- {
- // 首先找到第 i 列的绝对值最大的数
- int rowMax = i;
- double max = Math.Abs(_thisCopy[i, i]);
- for (int j = i; j < rows; j++)
- {
- if (Math.Abs(_thisCopy[j, i])> max)
- {
- rowMax = j;
- max = Math.Abs(_thisCopy[j, i]);
- }
- }
- // 将第 i 行和找到最大数那一行 rowMax 交换, 同时将单位阵做相同初等变换
- if (rowMax != i)
- {
- _thisCopy.Exchange(i, rowMax);
- res *= -1;
- }
- // 消元
- for (int j = i + 1; j <rows; j++)
- {
- double r = -_thisCopy[j, i] / _thisCopy[i, i];
- _thisCopy.Exchange(i, j, r);
- }
- }
- // 计算对角线乘积
- for (int i = 0; i < rows; i++)
- {
- res *= _thisCopy[i, i];
- }
- return res;
- }
- else
- {
- throw new Exception("不是行列式");
- }
- }
- #endregion
- #region 初等变换
- /// <summary>
- /// 初等变换: 交换第 r1 和第 r2 行
- /// </summary>
- /// <param name="r1">第 r1 行</param>
- /// <param name="r2">第 r2 行</param>
- /// <returns > 返回交换两行后的新的矩阵</returns>
- public Matrix Exchange(int r1, int r2)
- {
- if (Math.Min(r2, r1)>= 0 && Math.Max(r1, r2) <rows)
- {
- for (int j = 0; j < cols; j++)
- {
- double temp = this[r1, j];
- this[r1, j] = this[r2, j];
- this[r2, j] = temp;
- }
- return this;
- }
- else
- {
- throw new Exception("超出索引");
- }
- }
- /// <summary>
- /// 初等变换: 将 r1 行乘以某个数加到 r2 行
- /// </summary>
- /// <param name="r1">第 r1 行乘以 num</param>
- /// <param name="r2">加到第 r2 行, 若第 r2 行为负, 则直接将 r1 乘以 num 并返回</param>
- /// <param name="num">某行放大的倍数</param>
- /// <returns></returns>
- public Matrix Exchange(int r1, int r2, double num)
- {
- if (Math.Min(r2, r1)>= 0 && Math.Max(r1, r2) <rows)
- {
- for (int j = 0; j < cols; j++)
- {
- this[r2, j] += this[r1, j] * num;
- }
- return this;
- }
- else if (r2 < 0)
- {
- for (int j = 0; j < cols; j++)
- {
- this[r1, j] *= num;
- }
- return this;
- }
- else
- {
- throw new Exception("超出索引");
- }
- }
- /// <summary>
- /// 得到一个同等大小的单位矩阵
- /// </summary>
- /// <returns > 返回一个同等大小的单位矩阵</returns>
- public Matrix EMatrix()
- {
- if (rows == cols)
- {
- double[,] res = new double[rows, cols];
- for (int i = 0; i <rows; i++)
- {
- for (int j = 0; j < cols; j++)
- {
- if (i == j)
- res[i, j] = 1;
- else
- res[i, j] = 0;
- }
- }
- return new Matrix(res);
- }
- else
- throw new Exception("不是方阵, 无法得到单位矩阵");
- }
- #endregion
- /// <summary>
- /// 深拷贝, 仅仅将值拷贝给一个新的对象
- /// </summary>
- /// <returns > 返回深拷贝后的新对象</returns>
- public Matrix DeepCopy()
- {
- double[,] ele = new double[rows, cols];
- for (int i = 0; i < rows; i++)
- {
- for (int j = 0; j < cols; j++)
- {
- ele[i, j] = this[i, j];
- }
- }
- return new Matrix(ele);
- }
- public override string ToString()
- {
- string str = "";
- for (int i = 0; i < Rows; i++)
- {
- for (int j = 0; j < Cols; j++)
- {
- str += this[i, j].ToString();
- if (j != Cols - 1)
- str += " ";
- else if (i != Rows - 1)
- str += Environment.NewLine;
- }
- }
- return str;
- }
- }
- }
截图
来源: https://www.cnblogs.com/T-ARF/p/12045857.html