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WPF 画一个3D矩形并旋转

IP云
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09/10
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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(, , ), 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 / * (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 / * (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 / * (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[] = new Point3D(rect.Width / , rect.Height / , -(ModeZWidth/));
Group[] = new Point3D( - (rect.Width / ), rect.Height / , -(ModeZWidth / ));
Group[] = new Point3D( - (rect.Width / ), - (rect.Height / ), -(ModeZWidth / ));
Group[] = new Point3D((rect.Width / ), - (rect.Height / ), -(ModeZWidth / ));
Group[] = new Point3D(rect.Width / , rect.Height / , (ModeZWidth / ));
Group[] = new Point3D( - (rect.Width / ), rect.Height / , (ModeZWidth / ));
Group[] = new Point3D( - (rect.Width / ), - (rect.Height / ), (ModeZWidth / ));
Group[] = new Point3D((rect.Width / ), - (rect.Height / ), (ModeZWidth / )); for (var i = ; i < ; 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(, , ui,Colors.Black);
Set(, , ui,Colors.Blue);
Set(, , ui, Colors.Red);
Set(, , ui, Colors.Fuchsia);
Set(, , ui, Colors.DarkSlateBlue);
Set(, , ui, Colors.Red);
Set(, , ui, Colors.Red);
Set(, , ui, Colors.Red);
Set(, , ui, Colors.Red);
Set(, , ui, Colors.Red);
Set(, , ui, Colors.Red);
Set(, , 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[, ];
D[, ] = MP.X;
D[, ] = MP.Y;
D[, ] = MP.Z;
D[, ] = ;
return new Matrix(D);
}
private static Point3D ReturnP3D(Matrix MP) => new Point3D(MP[, ], MP[, ], MP[, ]); 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[];
private static Point[] PP = new Point[];
private static Matrix Y轴转置矩阵(double DegX, double DegY, double DegZ)
{
var A = new double[, ];
A[, ] = ;
A[, ] = ;
A[, ] = ;
A[, ] = ;
A[, ] = Math.Cos(X);
A[, ] = Math.Sin(X);
A[, ] = ;
A[, ] = - Math.Sin(X);
A[, ] = Math.Cos(X);
A[, ] = ;
A[, ] = ;
A[, ] = ;
A[, ] = ;
A[, ] = ;
A[, ] = ;
A[, ] = ;
var B = new double[, ];
B[, ] = Math.Cos(Y);
B[, ] = ;
B[, ] = -Math.Sin(Y);
B[, ] = ;
B[, ] = ;
B[, ] = ;
B[, ] = Math.Sin(Y);
B[, ] = ;
B[, ] = Math.Cos(Y);
B[, ] = ;
B[, ] = ;
B[, ] = ;
B[, ] = ;
B[, ] = ;
B[, ] = ;
B[, ] = ;
var C = new double[, ];
C[, ] = Math.Cos(Z);
C[, ] = Math.Sin(Z);
C[, ] = ;
C[, ] = - Math.Sin(Z);
C[, ] = Math.Cos(Z);
C[, ] = ;
C[, ] = ;
C[, ] = ;
C[, ] = ;
C[, ] = ;
C[, ] = ;
C[, ] = ;
B[, ] = ;
B[, ] = ;
B[, ] = ;
C[, ] = ;
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

<Window 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="" Width="">
<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="">
<!--X轴旋转-->
<Slider Minimum="" Maximum="" x:Name="s1"/>
<!--Y轴旋转-->
<Slider Minimum="" Maximum="" x:Name="s2"/>
<!--Z轴旋转-->
<Slider Minimum="" Maximum="" x:Name="s3"/>
<!--视野远近-->
<Slider Minimum="" Maximum="" x:Name="s4" />
</StackPanel>
</Grid>
</Window>

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 = ;
private int cols = ;
/// <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();
this.cols = m.GetLength();
int count = ;
this.element = new double[Rows * Cols];
for (int i = ; i < rows; i++)
{
for (int j = ; j < cols; j++)
{
element[count++] = m[i][j];
}
}
}
public Matrix(double[,] m)
{
this.rows = m.GetLength();
this.cols = m.GetLength();
this.element = new double[this.rows * this.cols];
int count = ;
for (int i = ; i < rows; i++)
{
for (int j = ; j < cols; j++)
{
element[count++] = m[i, j];
}
}
}
public Matrix(List<List<double>> m)
{
this.rows = m.Count;
this.cols = m[].Count;
this.element = new double[Rows * Cols];
for (int i = ; i < rows; i++)
{
for (int j = ; 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 = ; i < a.Rows; i++)
{
for (int j = ; 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 = ; i < a.Rows; i++)
{
for (int j = ; 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 = ; i < a.Rows; i++)
{
for (int j = ; 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 = ; i < a.rows; i++)
{
for (int j = ; 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 = ; i < a.rows; i++)
{
for (int j = ; j < b.cols; j++)
{
for (int k = ; 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 = ; i < a.rows; i++)
{
for (int j = ; 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 = ; i < cols; i++)
{
for (int j = ; 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() != )
{
//初始化一个同等大小的单位阵
Matrix res = _thisCopy.EMatrix();
for (int i = ; 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, -, r);
res.Exchange(i, -, r);
//消元
for (int j = ; 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 = ; i < a.Rows; i++)
{
for (int j = ; 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 = ; i < a.Rows; i++)
{
for (int j = ; 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 = ; i < a.Rows; i++)
{
for (int j = ; 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 = ; i < a.Rows; i++)
{
for (int j = ; 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 = ; i < a.Rows; i++)
{
for (int j = ; 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 = ; i < a.Rows; i++)
{
for (int j = ; 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 = ;
for (int i = ; 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 *= -;
}
//消元
for (int j = i + ; 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 = ; 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) >= && Math.Max(r1, r2) < rows)
{
for (int j = ; 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) >= && Math.Max(r1, r2) < rows)
{
for (int j = ; j < cols; j++)
{
this[r2, j] += this[r1, j] * num;
}
return this;
}
else if (r2 < )
{
for (int j = ; 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 = ; i < rows; i++)
{
for (int j = ; j < cols; j++)
{
if (i == j)
res[i, j] = ;
else
res[i, j] = ;
}
}
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 = ; i < rows; i++)
{
for (int j = ; j < cols; j++)
{
ele[i, j] = this[i, j];
}
}
return new Matrix(ele);
} public override string ToString()
{
string str = "";
for (int i = ; i < Rows; i++)
{
for (int j = ; j < Cols; j++)
{
str += this[i, j].ToString();
if (j != Cols - )
str += " ";
else if (i != Rows - )
str += Environment.NewLine;
}
}
return str;
}
}
}

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