三维空间中的线性变换与行列式可视化

GeoGebra 命令及参数

1. Point(xAxis) → C
2. Intersect(xAxis, zAxis) → Origin
3. Polygon(Origin, C, 4, xOyPlane) → unitBase, h, i, j, k, D, L
4. Vector(Origin, I) → ihat
5. Vector(Origin, J) → jhat
6. Vector(Origin, K) → khat
7. Line(I, jhat) → f
8. Line(J, ihat) → g
9. Intersect(f, g) → E
10. Prism(Origin, I, E, J, K) → parallelepiped, F, edgeAB, edgeBE, edgeCE, edgeAC, edgeAD, edgeBF, edgeEG, edgeCH, edgeDF, edgeFG, G, edgeGH, edgeDH, H, faceABEC, faceABFD, faceBEGF, faceCEGH, faceACHD, faceDFGH
11. Volume(parallelepiped) → volume
12. Point(parallelepiped) → Pointa
13. Determinant(TransformationMatrix) → determinant
14. Vector(Origin, VectorEndpoint) → u
15. Prism(unitBase, HiddenHeight) → unitCube, A, edge2, edge3, edge4, edge5, edge6, edge7, edge8, B, N, face1, face2, face3, face4, face5, edge1
16. Line(Origin, I) → l
17. Line(Origin, J) → m
18. Line(Origin, K) → n
19. Plane(Origin, L, C) → xOy
20. Plane(I, J, Origin) → xOyTransformed
21. Pyramid(V_1, V_2, V_3, V_4) → origPyramid, face6, edge14, face7, face9, face8, edge9, edge12, edge10, edge11, edge13
22. Vector(V_1) → v_1
23. Vector(V_2) → v_2
24. Vector(V_3) → v_3
25. Vector(V_4) → v_4
26. Point((0, 0, 0), newv_1) → newV_1
27. Point((0, 0, 0), newv_2) → newV_2
28. Point((0, 0, 0), newv_3) → newV_3
29. Point((0, 0, 0), newv_4) → newV_4
30. Pyramid(newV_1, newV_2, newV_3, newV_4) → newPyramid, face10, edge20, face11, face13, face12, edge15, edge18, edge16, edge17, edge19