The document discusses intersections between different geometric solids such as planes, cylinders, cones, and spheres. It provides examples of intersections between different combinations of these objects. It also describes some special cases of intersections that result in lines, circles, or ellipses. Methods for approximating intersections are discussed as well as examples of combining multiple solids with different types of intersections.

1. Plane & plane Rotatory & rotatoryPlane & rotatory
Mutual characteristicsMutual characteristics ：：
planeplane 、、 spacialspacial 、、 commoncommon 、、 closeclose
Problem 3Problem 3
intersections of solids ?intersections of solids ?

2. Visibility?
Plane & rotatory

3. Rotatory & rotatory
Mutual characteristicsMutual characteristics ：：
planeplane 、、 spacialspacial 、、 commoncommon 、、
closeclose 、、 smoothsmooth

4. Example 1 cylinder & cylinder?cylinder & cylinder?

5. Example 1 cylindercylinder && cylinder?cylinder?

6. The hole edge is same as intersections
Hole?

7. 作作
者者
：：
贾贾
皓皓
丽丽
•top ： 1
•bottom ： 2
•front ： 3
•rear ： 4
•arbitrary ： 5 、
6
•top ： 1
•bottom ： 2
•front ： 3
•rear ： 4
•arbitrary ： 5 、
6
Cylinder & cone

8. Step1 special points
Step2 arbitrary points
Step3 visibility?
Step4 join the points smoothly
horizontal cylinder & vertical cone

9. Example 2Example 2 cylinder & cone?cylinder & cone?
Q
H
PV
Method : auxiliary planeMethod : auxiliary plane

10. SV
Example 2Example 2 cylinder & cone?cylinder & cone?
Method : auxiliary planeMethod : auxiliary plane

11. Example 2Example 2 cylinder & cone?cylinder & cone?
Method : auxiliary planeMethod : auxiliary plane

12. Q
H
Example 3Example 3 cone & sphere?cone & sphere?
Method : auxiliary planeMethod : auxiliary plane
Vertical
plane

13. Example 3Example 3 cone & sphere?cone & sphere?
Method : auxiliary planeMethod : auxiliary plane
Vertical
plane

14. Example 3Example 3 cone & sphere?cone & sphere?
Method : auxiliary planeMethod : auxiliary plane
horizontal
plane

15. Example 3Example 3 cone & sphere?cone & sphere?
Method : auxiliary planeMethod : auxiliary plane

16. Exterior figure
Relative place
Causes to intersection shape

17. Equal
diameter
Plane curvesize
Causes to intersection shape

20. Approximate drawing methodApproximate drawing method
R
R

21. Some special instancesSome special instances
1. Intersections are beelines
Axeses are parallelSame vertex

22. 2 .intersections are circles
Some special instancesSome special instances
Same axes

23. 3 .intersections are ellipses
Some special instancesSome special instances

24. Multiple intersections
several solids combined
several kinds of intersections

25. Example 4 3 cylinders combined
analyse

26. Example 4 3 cylinders combined

27. Pv
Sv
Example 5 cylinder 、 cone and sphere combined