Plane & plane Rotatory & rotatoryPlane & rotatory

Mutual characteristicsMutual characteristics ： ：

planeplane 、 、 spacialspacial 、 、 commoncommon 、、 closeclose

Problem 3Problem 3 intersections of solids ?intersections of solids ?

Visibility?

Plane & rotatory

Rotatory & rotatory

Mutual characteristicsMutual characteristics ： ：

planeplane 、 、 spacialspacial 、 、 commoncommon 、、 closeclose 、、 smoothsmooth

Example 1 cylinder & cylinder & cylinder?cylinder?Example 1 cylinder & cylinder & cylinder?cylinder?

Example 1 cylinder cylinder && cylinder?cylinder?Example 1 cylinder cylinder && cylinder?cylinder?

The hole edge is same as intersections

Hole?

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 & coneCylinder & cone

Step1 special pointsStep2 arbitrary pointsStep3 visibility?Step4 join the points smoothly

horizontal cylinder & vertical cone

Example 2Example 2 cylinder & cone?cylinder & cone?Example 2Example 2 cylinder & cone?cylinder & cone?

QH

PV

Method : auxiliary planeMethod : auxiliary plane

SV

Example 2Example 2 cylinder & cone?cylinder & cone?Example 2Example 2 cylinder & cone?cylinder & cone?

Method : auxiliary planeMethod : auxiliary plane

Example 2Example 2 cylinder & cone?cylinder & cone?Example 2Example 2 cylinder & cone?cylinder & cone?

Method : auxiliary planeMethod : auxiliary plane

QH

Example 3Example 3 cone & sphere?cone & sphere?Example 3Example 3 cone & sphere?cone & sphere?

Method : auxiliary planeMethod : auxiliary plane

Vertical plane

Example 3Example 3 cone & sphere?cone & sphere?Example 3Example 3 cone & sphere?cone & sphere?

Method : auxiliary planeMethod : auxiliary plane

Vertical plane

Example 3Example 3 cone & sphere?cone & sphere?Example 3Example 3 cone & sphere?cone & sphere?

Method : auxiliary planeMethod : auxiliary plane

horizontal plane

Example 3Example 3 cone & sphere?cone & sphere?Example 3Example 3 cone & sphere?cone & sphere?

Method : auxiliary planeMethod : auxiliary plane

Exterior figure

Relative place

Causes to intersection shape

Equal diameter

Plane curvesize

Causes to intersection shape

Approximate drawing methodApproximate drawing method

R

R

Some special instancesSome special instances

1. Intersections are beelines

Axeses are parallelSame vertex

2 .intersections are circles

Some special instancesSome special instances

Same axes

3 .intersections are ellipses

Some special instancesSome special instances

Multiple intersections

several solids combinedseveral kinds of intersections

Example 4 3 cylinders combined

Example 4 3 cylinders combined

analyse

Example 4 3 cylinders combined

Example 4 3 cylinders combined

Pv

Sv

Example 5 cylinder 、 cone and sphere combinedExample 5 cylinder 、 cone and sphere combined