Intersections of rotatory solids
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Plane & plane Rotatory & rotatoryPlane & rotatory
Mutual characteristicsMutual characteristics : :
planeplane 、 、 spacialspacial 、 、 commoncommon 、、 closeclose
Problem 3Problem 3 intersections of solids ?intersections of solids ?
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Visibility?
Plane & rotatory
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Rotatory & rotatory
Mutual characteristicsMutual characteristics : :
planeplane 、 、 spacialspacial 、 、 commoncommon 、、 closeclose 、、 smoothsmooth
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Example 1 cylinder & cylinder & cylinder?cylinder?Example 1 cylinder & cylinder & cylinder?cylinder?
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Example 1 cylinder cylinder && cylinder?cylinder?Example 1 cylinder cylinder && cylinder?cylinder?
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The hole edge is same as intersections
Hole?
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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
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Step1 special pointsStep2 arbitrary pointsStep3 visibility?Step4 join the points smoothly
horizontal cylinder & vertical cone
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Example 2Example 2 cylinder & cone?cylinder & cone?Example 2Example 2 cylinder & cone?cylinder & cone?
QH
PV
Method : auxiliary planeMethod : auxiliary plane
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SV
Example 2Example 2 cylinder & cone?cylinder & cone?Example 2Example 2 cylinder & cone?cylinder & cone?
Method : auxiliary planeMethod : auxiliary plane
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Example 2Example 2 cylinder & cone?cylinder & cone?Example 2Example 2 cylinder & cone?cylinder & cone?
Method : auxiliary planeMethod : auxiliary plane
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QH
Example 3Example 3 cone & sphere?cone & sphere?Example 3Example 3 cone & sphere?cone & sphere?
Method : auxiliary planeMethod : auxiliary plane
Vertical plane
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Example 3Example 3 cone & sphere?cone & sphere?Example 3Example 3 cone & sphere?cone & sphere?
Method : auxiliary planeMethod : auxiliary plane
Vertical plane
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Example 3Example 3 cone & sphere?cone & sphere?Example 3Example 3 cone & sphere?cone & sphere?
Method : auxiliary planeMethod : auxiliary plane
horizontal plane
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Example 3Example 3 cone & sphere?cone & sphere?Example 3Example 3 cone & sphere?cone & sphere?
Method : auxiliary planeMethod : auxiliary plane
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Exterior figure
Relative place
Causes to intersection shape
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Equal diameter
Plane curvesize
Causes to intersection shape
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Approximate drawing methodApproximate drawing method
R
R
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Some special instancesSome special instances
1. Intersections are beelines
Axeses are parallelSame vertex
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2 .intersections are circles
Some special instancesSome special instances
Same axes
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3 .intersections are ellipses
Some special instancesSome special instances
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Multiple intersections
several solids combinedseveral kinds of intersections
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Example 4 3 cylinders combined
Example 4 3 cylinders combined
analyse
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Example 4 3 cylinders combined
Example 4 3 cylinders combined
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Pv
Sv
Example 5 cylinder 、 cone and sphere combinedExample 5 cylinder 、 cone and sphere combined