Cross-section polygons are made by strict geometric methods.
The principle based on is simple and easy to master:
(1) Two points determine a straight line.
(2) Only two straight lines on the same plane will intersect, and the intersection point is the actual intersection point.
(3) If it is known that two non-overlapping planes have a common point, the intersection of the two planes must pass through the common point.
The best way to understand it is to illustrate it with examples. Here's a more complicated example.
Example question:
As shown above, it is known that the three points P, Q and R on the cuboid are located at the left, back and bottom of the cuboid respectively.
It is required to make a plane PQR and a section of a cuboid.
Analysis: Because P, Q and R are distributed on different surfaces, it is impossible to directly connect the intersection of two points with the ridge line to make the intersection.
You need to use the corner points on the cuboid to assist in drawing.
Because there is a common corner point A on the left side and the back side, the section generated by surface APQ can be made first.
Exercise:
(1) connecting AP and AQ intersect BC (extension line) and BD at E and F respectively.
Principle: Two straight lines that are not parallel to the same plane must intersect.
At this time, there are: PQEF*** faces, and EF is at the bottom.
(2) Connect PQ and EF intersecting at G point, and then get the intersection point Q of PQ and bottom surface.
So PQR surface and PGR surface are the same surface, and G and R are on the bottom.
(3) The ridge line connecting GR and the bottom surface intersects at H and K, and at this time, the two key intersections of the profile have been determined.
This part is changed to PQHK, and the remaining steps are simple.
(3) Connect the main HQ and AB at point L to get the third point.
Connect LP to get the fourth point m, connect HK to get the fifth point n,
Connect MN to get the sixth point S.
So the final section polygon is: HLMSK.