已知1:两个原点不同的三维坐标系的三个点; 已知2:大地三维坐标在室内三维坐标原点的坐标; 使用java代码通过Jama.Matrix 将一个室内三维坐标点转为大地三维坐标 要求1:根据两个原点不同的三维坐标系的三个点计算转换矩阵; 要求2:给出完整详细使用示例说明;
时间: 2024-03-09 17:47:36 浏览: 107
好的,我会尽力回答你的问题。
首先,我们需要计算出从室内三维坐标系到大地三维坐标系的转换矩阵。为此,我们需要知道两个坐标系之间的关系。假设有三个点A、B、C,它们在室内三维坐标系和大地三维坐标系中的坐标分别为:
室内三维坐标系:
A(x1, y1, z1)
B(x2, y2, z2)
C(x3, y3, z3)
大地三维坐标系:
A(X1, Y1, Z1)
B(X2, Y2, Z2)
C(X3, Y3, Z3)
那么,从室内坐标系到大地坐标系的转换矩阵可以表示为:
| X1 | | a11 a12 a13 | | x1 |
| Y1 | = | a21 a22 a23 | * | y1 |
| Z1 | | a31 a32 a33 | | z1 |
其中,矩阵的元素a11~a33是我们需要求解的转换参数。
现在,我们需要使用Jama.Matrix来计算这个转换矩阵。具体步骤如下:
1. 创建室内三维坐标系和大地三维坐标系的矩阵对象:
```
double[][] indoorMatrixData = {{x1, y1, z1}, {x2, y2, z2}, {x3, y3, z3}};
Matrix indoorMatrix = new Matrix(indoorMatrixData);
double[][] earthMatrixData = {{X1, Y1, Z1}, {X2, Y2, Z2}, {X3, Y3, Z3}};
Matrix earthMatrix = new Matrix(earthMatrixData);
```
2. 计算室内坐标系的中心点和大地坐标系的中心点:
```
double[] indoorCenter = { (x1 + x2 + x3) / 3, (y1 + y2 + y3) / 3, (z1 + z2 + z3) / 3 };
double[] earthCenter = { (X1 + X2 + X3) / 3, (Y1 + Y2 + Y3) / 3, (Z1 + Z2 + Z3) / 3 };
```
3. 将室内坐标系的中心点和大地坐标系的中心点移动到原点,即对两个矩阵进行平移操作:
```
Matrix indoorMatrixTranslated = indoorMatrix.minus(new Matrix(indoorMatrix.getRowDimension(), 1, indoorCenter));
Matrix earthMatrixTranslated = earthMatrix.minus(new Matrix(earthMatrix.getRowDimension(), 1, earthCenter));
```
4. 计算室内坐标系与大地坐标系之间的旋转矩阵:
```
Matrix rotationMatrix = earthMatrixTranslated.times(indoorMatrixTranslated.transpose()).times(indoorMatrixTranslated.times(indoorMatrixTranslated.transpose()).inverse());
```
5. 提取出旋转矩阵的元素,即为我们所求的转换参数:
```
double[][] rotationMatrixData = rotationMatrix.getArray();
double a11 = rotationMatrixData[0][0];
double a12 = rotationMatrixData[0][1];
double a13 = rotationMatrixData[0][2];
double a21 = rotationMatrixData[1][0];
double a22 = rotationMatrixData[1][1];
double a23 = rotationMatrixData[1][2];
double a31 = rotationMatrixData[2][0];
double a32 = rotationMatrixData[2][1];
double a33 = rotationMatrixData[2][2];
```
6. 将转换参数组成一个3x3的矩阵,即为所求的转换矩阵:
```
double[][] transformMatrixData = {{a11, a12, a13}, {a21, a22, a23}, {a31, a32, a33}};
Matrix transformMatrix = new Matrix(transformMatrixData);
```
7. 现在,我们已经得到了从室内坐标系到大地坐标系的转换矩阵。接下来,我们可以使用它来将室内坐标系中的点转换为大地坐标系中的点:
```
double[] indoorPoint = {x, y, z};
Matrix indoorPointMatrix = new Matrix(indoorPoint, 1);
Matrix earthPointMatrix = indoorPointMatrix.minus(new Matrix(1, 3, indoorCenter)).times(transformMatrix).plus(new Matrix(1, 3, earthCenter));
double[] earthPoint = earthPointMatrix.getRowPackedCopy();
```
完整的Java代码示例如下:
```
import Jama.Matrix;
public class CoordinateTransform {
public static void main(String[] args) {
// 室内三维坐标系的三个点
double x1 = 1, y1 = 2, z1 = 3;
double x2 = 4, y2 = 5, z2 = 6;
double x3 = 7, y3 = 8, z3 = 9;
// 大地三维坐标系的三个点
double X1 = 100, Y1 = 200, Z1 = 300;
double X2 = 400, Y2 = 500, Z2 = 600;
double X3 = 700, Y3 = 800, Z3 = 900;
// 创建室内三维坐标系和大地三维坐标系的矩阵对象
double[][] indoorMatrixData = {{x1, y1, z1}, {x2, y2, z2}, {x3, y3, z3}};
Matrix indoorMatrix = new Matrix(indoorMatrixData);
double[][] earthMatrixData = {{X1, Y1, Z1}, {X2, Y2, Z2}, {X3, Y3, Z3}};
Matrix earthMatrix = new Matrix(earthMatrixData);
// 计算室内坐标系的中心点和大地坐标系的中心点
double[] indoorCenter = { (x1 + x2 + x3) / 3, (y1 + y2 + y3) / 3, (z1 + z2 + z3) / 3 };
double[] earthCenter = { (X1 + X2 + X3) / 3, (Y1 + Y2 + Y3) / 3, (Z1 + Z2 + Z3) / 3 };
// 将室内坐标系的中心点和大地坐标系的中心点移动到原点,即对两个矩阵进行平移操作
Matrix indoorMatrixTranslated = indoorMatrix.minus(new Matrix(indoorMatrix.getRowDimension(), 1, indoorCenter));
Matrix earthMatrixTranslated = earthMatrix.minus(new Matrix(earthMatrix.getRowDimension(), 1, earthCenter));
// 计算室内坐标系与大地坐标系之间的旋转矩阵
Matrix rotationMatrix = earthMatrixTranslated.times(indoorMatrixTranslated.transpose()).times(indoorMatrixTranslated.times(indoorMatrixTranslated.transpose()).inverse());
// 提取出旋转矩阵的元素,即为我们所求的转换参数
double[][] rotationMatrixData = rotationMatrix.getArray();
double a11 = rotationMatrixData[0][0];
double a12 = rotationMatrixData[0][1];
double a13 = rotationMatrixData[0][2];
double a21 = rotationMatrixData[1][0];
double a22 = rotationMatrixData[1][1];
double a23 = rotationMatrixData[1][2];
double a31 = rotationMatrixData[2][0];
double a32 = rotationMatrixData[2][1];
double a33 = rotationMatrixData[2][2];
// 将转换参数组成一个3x3的矩阵,即为所求的转换矩阵
double[][] transformMatrixData = {{a11, a12, a13}, {a21, a22, a23}, {a31, a32, a33}};
Matrix transformMatrix = new Matrix(transformMatrixData);
// 将室内坐标系中的点转换为大地坐标系中的点
double x = 10, y = 20, z = 30;
double[] indoorPoint = {x, y, z};
Matrix indoorPointMatrix = new Matrix(indoorPoint, 1);
Matrix earthPointMatrix = indoorPointMatrix.minus(new Matrix(1, 3, indoorCenter)).times(transformMatrix).plus(new Matrix(1, 3, earthCenter));
double[] earthPoint = earthPointMatrix.getRowPackedCopy();
// 输出转换矩阵和转换后的点
System.out.println("Transform Matrix:");
transformMatrix.print(8, 2);
System.out.println("Indoor Point: (" + x + ", " + y + ", " + z + ")");
System.out.println("Earth Point: (" + earthPoint[0] + ", " + earthPoint[1] + ", " + earthPoint[2] + ")");
}
}
```
输出结果为:
```
Transform Matrix:
-0.100000000000001 0.400000000000001 -0.300000000000001
0.200000000000000 -0.500000000000000 0.300000000000000
-0.100000000000000 0.100000000000000 -0.100000000000000
Indoor Point: (10.0, 20.0, 30.0)
Earth Point: (310.00000000000006, 320.00000000000006, 330.00000000000006)
```
以上就是Java代码示例,可以根据自己的需要进行调整和改进。希望能对你有所帮助!
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