我正在编写一个小图表编写程序作为个人项目。
每个点都应该在wpf画布上绘制，但是我无法将图形坐标系中的点转换为例如：x = -8 to 4 y=-4 to 4到画布的坐标系示例： x = 600 to 0 y = 400 to 0。
我正在使用概述here的方法来预先计算变换方程式。
但是我遇到乘法v=M^-1*u的结果有问题。
我的预期结果是：
[0.2 ]
[0.0 ]
[-8.0]
[4.0 ]
但我得到的结果是：
[4.0 ]
[-4.0 ]
[0.01 ]
[-0.006]
我已经确认我的转换矩阵是正确的，当我手动计算时，我得到了预期的结果。
计算变换方程的方法：
private void CalculateTransformationFunctions()
{
// Define the transformation matrix
var transformationMatrix = new Matrix4x4
{
M11 = _destArea.XMin,
M12 = _destArea.YMin,
M13 = 1,
M14 = 0,
M21 = -_destArea.YMin,
M22 = _destArea.XMin,
M23 = 0,
M24 = 1,
M31 = _destArea.XMax,
M32 = _destArea.YMax,
M33 = 1,
M34 = 0,
M41 = -_destArea.YMax,
M42 = _destArea.XMax,
M43 = 0,
M44 = 1
};
// Define the source vector
var srcVector = new Vector4
{
X = _srcArea.XMin,
Y = _srcArea.YMax,
Z = _srcArea.XMax,
W = _srcArea.YMin
};
// Invert the transformationmatrix before the multiplication
Matrix4x4 invertedTransformationMatrix;
if(!Matrix4x4.Invert(transformationMatrix,out invertedTransformationMatrix))
throw new Exception();
// Returns the wrong value
var transformResult = Vector4.Transform(srcVector, invertedTransformationMatrix);
float a = transformResult.X,
b = transformResult.Y,
c = transformResult.Z,
d = transformResult.W;
_xTransformationFunction = (x, y) => (a*x + b*y - b*d - a*c)/(a*a + b*b);
_yTransformationFunction = (x, y) => (b*x - a*y - b*c + a*d)/(a*a + b*b);
}
在其父类的构造函数中调用它。
我的问题：
我误解了Vector4.Transform()在这里的作用吗？还是我完全失明并且遗失了一些非常明显的东西？
全班同学：
using System;
using System.Numerics;
using System.Windows;
using System.Windows.Media;
using Grapher.Control.Grapher;
namespace Grapher.GraphingMath
{
public class Translator
{
private GraphingArea _srcArea;
private GraphingArea _destArea;
public GraphingArea SourceArea
{
get
{
return _srcArea;
}
set
{
_srcArea = value;
CalculateTransformationFunctions();
}
}
public GraphingArea DestinationArea
{
get { return _destArea; }
set
{
_destArea = value;
CalculateTransformationFunctions();
}
}
private Func<double, double, double> _xTransformationFunction;
private Func<double, double, double> _yTransformationFunction;
public Translator(GraphingArea sourceArea, GraphingArea destArea)
{
_destArea = destArea;
_srcArea = sourceArea;
CalculateTransformationFunctions();
}
public Point TranslatePoint(Point point)
{
var x = point.X;
var y = point.Y;
return new Point
{
X = _xTransformationFunction(x, y),
Y = _yTransformationFunction(x, y)
};
}
/*
x1 y1 1 0
-y1 x1 0 1
M= x2 y2 1 0
-y2 x2 0 1
x1,y1 = dest_min
x2,y2 = dest_max
*/
private void CalculateTransformationFunctions()
{
// Define the transformation matrix
var transformationMatrix = new Matrix4x4
{
M11 = _destArea.XMin,
M12 = _destArea.YMin,
M13 = 1,
M14 = 0,
M21 = -_destArea.YMin,
M22 = _destArea.XMin,
M23 = 0,
M24 = 1,
M31 = _destArea.XMax,
M32 = _destArea.YMax,
M33 = 1,
M34 = 0,
M41 = -_destArea.YMax,
M42 = _destArea.XMax,
M43 = 0,
M44 = 1
};
// Define the source vector
var srcVector = new Vector4
{
X = _srcArea.XMin,
Y = _srcArea.YMax,
Z = _srcArea.XMax,
W = _srcArea.YMin
};
// Invert the transformationmatrix before the multiplication
Matrix4x4 invertedTransformationMatrix;
if(!Matrix4x4.Invert(transformationMatrix,out invertedTransformationMatrix))
throw new Exception();
// Returns the wrong value
var transformResult = Vector4.Transform(srcVector, invertedTransformationMatrix);
float a = transformResult.X,
b = transformResult.Y,
c = transformResult.Z,
d = transformResult.W;
_xTransformationFunction = (x, y) => (a*x + b*y - b*d - a*c)/(a*a + b*b);
_yTransformationFunction = (x, y) => (b*x - a*y - b*c + a*d)/(a*a + b*b);
}
}
}
对于图形区域struct：
using System;
namespace Grapher.Control.Grapher
{
public struct GraphingArea
{
public float XMin { get; set; }
public float YMin { get; set; }
public float XMax { get; set; }
public float YMax { get; set; }
public float Width => Math.Abs(XMax - XMin);
public float Height => Math.Abs(YMax - YMin);
}
}
在我的main方法中，我像这样调用Translator类：
Point testPoint = new Point {X = 0, Y = 0};
var srcArea = new GraphingArea
{
XMax = 4,
XMin = -8,
YMax = 4,
YMin = -4
};
var destArea = new GraphingArea
{
XMax = 600,
XMin = 0,
YMax = 400,
YMin = 0
};
var translator = new Translator(srcArea, destArea);
var translatedPoint = translator.TranslatePoint(testPoint);
修改
结束了我自己的矩阵乘法方法。我必须误解Vector4.Transform()做什么......
代码在这里，对任何感兴趣的人：
using System.Numerics;
namespace Grapher.GraphingMath.MatrixAndVectorMath
{
public static class Matrix4x4Multiply
{
public static Vector4 Vector4Multiply(Matrix4x4 matrix, Vector4 vector)
{
var mat = new float[4, 4]
{
{matrix.M11, matrix.M12, matrix.M13, matrix.M14},
{matrix.M21, matrix.M22, matrix.M23, matrix.M24},
{matrix.M31, matrix.M32, matrix.M33, matrix.M34},
{matrix.M41, matrix.M42, matrix.M43, matrix.M44}
}; // We'll just wrap the matrix in a float so we can index it.
var vec = new float[4] {vector.X, vector.Y, vector.Z, vector.W}; // And the same with the vector
var result = new float[4] {0, 0, 0, 0};
for (var row = 0; row < mat.GetLength(0); row++)
{
for (var col = 0; col < mat.GetLength(1); col++)
{
result[row] += mat[row, col]*vec[col];
}
}
return new Vector4
{
X = result[0],
Y = result[1],
Z = result[2],
W = result[3]
};
}
}
}
答案 0 :(得分：0)
我不知道这是否会有所帮助，但我在其中一个项目中按照这些方针做了一些事情。我不会使用矩阵，所以它可能不是你想要的。我只是存储图形的坐标范围和容器（画布）的宽度和高度。然后我提供了两个扩展函数：
public static System.Windows.Point ConvertToScreen(this System.Windows.Point point, CartesianExtents2D extents, double containerWidth, double containerHeight)
{
var x = (point.X - extents.XMinimum) * containerWidth / (extents.XMaximum - extents.XMinimum);
var y = (extents.YMaximum - point.Y) * containerHeight / (extents.YMaximum - extents.YMinimum);
return new System.Windows.Point(x, y);
}
public static System.Windows.Point ConvertToReal(this System.Windows.Point point, CartesianExtents2D extents, double containerWidth, double containerHeight, )
{
var x = extents.XMinimum + (point.X * (extents.XMaximum - extents.XMinimum)) / containerWidth;
var y = extents.YMaximum - (point.Y * (extents.YMaximum - extents.YMinimum)) / containerHeight;
return new System.Windows.Point(x, y);
}
致电：
Point p = new Point();
p.ConvertToReal(...);
我希望CartesianExtents2D的内容很明显 - 只需要x和y的最小值和最大值