画法几何-平面的投影

Two intersecting
lines
Planar shape
2、各种位置的平面 Positions of Planes (1) 平面对一个投影面的投影特性
Projection characteristics of planes to a single projection plane
平行
Parallel
V 正垂面 V-perp. plane
V
H 铅垂面 H-perp. plane
W 侧垂面 W-perp. plane
b
a c
Z
A
a
X
C O c
B
b
H
a
c
W
b
Y
铅
垂 面 H-perp. plane
Lead
Perpendicular
Plane
plumb line ：a cord from which a metal (lead) weight is suspended pointing directly to the earth's center of gravity; used to determine the vertical from a given point
特殊位置平面
Special position planes
平行于某一投影面， 垂直于另两个投影面
Parallel to a projection plane and perpendicular to the other two
投影面平行面
Planes parallel to projection plane
第四讲 平面的投影 Projection of Plane
• 平面的表示法 Representations of planes • 各种位置的平面 Position of Planes • 平面上的点和直线Points and lines in planes
Z
平面图形投影总是
Y
为平面图形或直线。
X
Perpendicular to a projection plane and inclined to the other two
投影面垂直面
Planes perpendicular to projection plane
正垂面V-perpendicular 侧垂面W-perpendicular 铅垂面H-perpendicular
The projection of a planar
surface always is a line or a
planar surface.
1、平面的表示法 Representations of planes
c
●
c
●
a●
a●
a●
● b
● b
●b
●b
a●
a●
a●
● c
● c
不在同一 直线及线
直线上的 外一点
垂直
perpendicular
投 影特性
★ 平面平行投影面-----投影体现实形
Plane ∥Projection plane
★ 平面垂直投影面-----投影积聚成直线
Plane⊥ Projection plane
★ 平面倾斜(Inclined)投影面-----投影亲似原平面
Plane inclined to Projection plane
g f
g f
a h b
e d c
h a
b
e d
c
a (b) g(h) f(e)
d (c)
(4) 投影面平行面Planes parallel to projection plane
积聚性
collecting
a b c a c b
积聚性
collecting
存真性
a
True
shape
c百度文库
投影特性：
b
水平面
亲似性
Affinity
b
b
亲似性
Affinity
a
积聚性
c c a
collecting
βc
b
γ
a
投影特性：
铅垂面
H-perpendicular plane
在它垂直的投影面上的投影积聚成直线。该直线与投影 轴的夹角反映空间平面与另外两投影面夹角的大小。
It appears as a line in the perpendicular projection plane. The angles between that line and the projection axes represented the angles between the plane and the other two projection planes.
正平面 Frontal plane 侧平面 Profile plane 水平面 Horizontal plane
与三个投影面都倾斜
Inclined to three projection planes
一般位置平面
General position plane
(3) 投影面垂直面
Planes perpendicular to projection plane
倾斜
inclined
存真性
True shape
积聚性
Collecting
亲似性
Similarity
(2) 平面在三投影面体系中的投影特性
平面对于三投影面的位置可分为三类：
Positions relative to three principal projection planes
垂直于某一投影面，倾 斜于另两个投影面
c
●
d a●
●
● b ●b
●c
●d a●
c ● a●
● b ●b
a● ●c
c
●
● b ●b
●c
两相交 平面
两平行
直线
图形
三个点 Three
points not on a straight line
A line and a point not on
the line
直线
Two parallel lines
Horizontal plane
(1)一个投影存真 One projection is true-show type. (2)另外两投影积聚----面平行于投影轴的线
The other two projections are line-collecting type.
(Plane-> line ∥axis)
另外两个投影面上的投影有亲似性。
The other two projections are affinal shapes.
例1. 已知多边形的VH投影，求其W投影。
Complete the W projection of polygon with the given V & H projections.