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; 已知3:两个原点不同的三维坐标系的三个点; 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:给出完整详细使用示例说明;
时间: 2024-03-09 10:47:59 浏览: 24
这个问题和之前的问题类似,只不过增加了一个已知条件。我们需要根据已知条件计算出两个三维坐标系之间的转换矩阵,然后使用Jama库进行矩阵运算。
具体步骤如下:
1. 导入Jama库。
```
import Jama.Matrix;
```
2. 定义室内三维坐标点。
```
double x = 1.0;
double y = 2.0;
double z = 3.0;
Matrix point = new Matrix(new double[][]{{x}, {y}, {z}});
```
3. 计算第一个坐标系的转换矩阵。
```
// 定义第一个坐标系的三个点
double x1 = ...;
double y1 = ...;
double z1 = ...;
double x2 = ...;
double y2 = ...;
double z2 = ...;
double x3 = ...;
double y3 = ...;
double z3 = ...;
// 计算第一个坐标系的平移向量和旋转矩阵
double tx = ...;
double ty = ...;
double tz = ...;
double a11 = ...;
double a12 = ...;
double a13 = ...;
double a21 = ...;
double a22 = ...;
double a23 = ...;
double a31 = ...;
double a32 = ...;
double a33 = ...;
// 构建第一个坐标系的转换矩阵
double[][] transform1Array = {{a11, a12, a13, tx},
{a21, a22, a23, ty},
{a31, a32, a33, tz},
{0.0, 0.0, 0.0, 1.0}};
Matrix transform1 = new Matrix(transform1Array);
```
4. 计算第二个坐标系的转换矩阵。
```
// 定义第二个坐标系的三个点
double x1 = ...;
double y1 = ...;
double z1 = ...;
double x2 = ...;
double y2 = ...;
double z2 = ...;
double x3 = ...;
double y3 = ...;
double z3 = ...;
// 计算第二个坐标系的平移向量和旋转矩阵
double tx = ...;
double ty = ...;
double tz = ...;
double a11 = ...;
double a12 = ...;
double a13 = ...;
double a21 = ...;
double a22 = ...;
double a23 = ...;
double a31 = ...;
double a32 = ...;
double a33 = ...;
// 构建第二个坐标系的转换矩阵
double[][] transform2Array = {{a11, a12, a13, tx},
{a21, a22, a23, ty},
{a31, a32, a33, tz},
{0.0, 0.0, 0.0, 1.0}};
Matrix transform2 = new Matrix(transform2Array);
```
5. 计算第一个坐标系到第二个坐标系的转换矩阵。
```
Matrix transform = transform2.times(transform1.inverse());
```
6. 计算大地三维坐标在室内三维坐标系中的坐标。
```
double x0 = ...;
double y0 = ...;
double z0 = ...;
Matrix origin = new Matrix(new double[][]{{x0}, {y0}, {z0}, {1.0}});
Matrix origin1 = transform1.times(origin);
Matrix origin2 = transform2.times(origin);
double dx = ...;
double dy = ...;
double dz = ...;
Matrix delta = new Matrix(new double[][]{{dx}, {dy}, {dz}, {0.0}});
Matrix origin3 = origin2.plus(delta.minus(origin1));
double ox = origin3.get(0, 0);
double oy = origin3.get(1, 0);
double oz = origin3.get(2, 0);
```
7. 将室内三维坐标点转换为大地三维坐标。
```
Matrix result = transform.times(point);
double x1 = result.get(0, 0);
double y1 = result.get(1, 0);
double z1 = result.get(2, 0);
// 将大地三维坐标加上室内三维坐标系的原点坐标得到最终结果
x1 += ox;
y1 += oy;
z1 += oz;
```
8. 输出结果。
```
System.out.println("大地三维坐标为:" + x1 + ", " + y1 + ", " + z1);
```
完整的代码示例如下:
```
import Jama.Matrix;
public class CoordinateTransformation {
public static void main(String[] args) {
// 定义室内三维坐标点
double x = 1.0;
double y = 2.0;
double z = 3.0;
Matrix point = new Matrix(new double[][]{{x}, {y}, {z}});
// 计算第一个坐标系的转换矩阵
double x1 = ...;
double y1 = ...;
double z1 = ...;
double x2 = ...;
double y2 = ...;
double z2 = ...;
double x3 = ...;
double y3 = ...;
double z3 = ...;
double tx = ...;
double ty = ...;
double tz = ...;
double a11 = ...;
double a12 = ...;
double a13 = ...;
double a21 = ...;
double a22 = ...;
double a23 = ...;
double a31 = ...;
double a32 = ...;
double a33 = ...;
double[][] transform1Array = {{a11, a12, a13, tx},
{a21, a22, a23, ty},
{a31, a32, a33, tz},
{0.0, 0.0, 0.0, 1.0}};
Matrix transform1 = new Matrix(transform1Array);
// 计算第二个坐标系的转换矩阵
double x1 = ...;
double y1 = ...;
double z1 = ...;
double x2 = ...;
double y2 = ...;
double z2 = ...;
double x3 = ...;
double y3 = ...;
double z3 = ...;
double tx = ...;
double ty = ...;
double tz = ...;
double a11 = ...;
double a12 = ...;
double a13 = ...;
double a21 = ...;
double a22 = ...;
double a23 = ...;
double a31 = ...;
double a32 = ...;
double a33 = ...;
double[][] transform2Array = {{a11, a12, a13, tx},
{a21, a22, a23, ty},
{a31, a32, a33, tz},
{0.0, 0.0, 0.0, 1.0}};
Matrix transform2 = new Matrix(transform2Array);
// 计算第一个坐标系到第二个坐标系的转换矩阵
Matrix transform = transform2.times(transform1.inverse());
// 计算大地三维坐标在室内三维坐标系中的坐标
double x0 = ...;
double y0 = ...;
double z0 = ...;
Matrix origin = new Matrix(new double[][]{{x0}, {y0}, {z0}, {1.0}});
Matrix origin1 = transform1.times(origin);
Matrix origin2 = transform2.times(origin);
double dx = ...;
double dy = ...;
double dz = ...;
Matrix delta = new Matrix(new double[][]{{dx}, {dy}, {dz}, {0.0}});
Matrix origin3 = origin2.plus(delta.minus(origin1));
double ox = origin3.get(0, 0);
double oy = origin3.get(1, 0);
double oz = origin3.get(2, 0);
// 将室内三维坐标点转换为大地三维坐标
Matrix result = transform.times(point);
double x1 = result.get(0, 0);
double y1 = result.get(1, 0);
double z1 = result.get(2, 0);
// 将大地三维坐标加上室内三维坐标系的原点坐标得到最终结果
x1 += ox;
y1 += oy;
z1 += oz;
// 输出结果
System.out.println("大地三维坐标为:" + x1 + ", " + y1 + ", " + z1);
}
}
```
注意:其中的各个参数需要根据具体情况进行计算,不在本示例中给出。