大三-05計(jì)算機(jī)圖形學(xué)-51classical

ObjectivesIntroduce

the

classical

views介紹經(jīng)典視圖Compare

and

contrast

image

formationbycomputer

with

how

images

have

been

formedby

architects,artists,and

engineers比較由計(jì)算機(jī)形成的圖像與建筑師、畫家和工程師繪制的圖像Learn

the

benefits

and

drawbacks

of

each

typeof

view學(xué)習(xí)每種視圖的優(yōu)勢(shì)與不足Outline5.1

Classical

Viewing

and

Computer

Viewing5.1.1

Classical

Viewing經(jīng)典視圖5.1.2

Orthographic

Projection正交投影5.1.3

Axonometric

Projections軸測(cè)投影5.1.4

Oblique

Projection傾斜投影5.1.5

Projection

投影5.1

ClassicalViewing

andComputerViewing(為什么需要經(jīng)典視圖？)傳統(tǒng)由手工操作的制圖工作現(xiàn)在可以用計(jì)算機(jī)模擬中的動(dòng)畫，建筑圖紙，機(jī)器零件圖紙-這些領(lǐng)域中需要不同的經(jīng)典視圖等角投影（等軸測(cè)圖）（isometrics)，正視圖(elevation)，經(jīng)典視圖與計(jì)算機(jī)視圖之間的對(duì)比關(guān)系表明了在大多數(shù)API中所采用方法的長(zhǎng)處，當(dāng)然也具有一些不足和-

經(jīng)典照相機(jī)與 照相機(jī)5.1

ClassicalViewing

andComputerViewing(Classical

Viewing經(jīng)典視圖-1)Viewingrequiresthreebasicelements視圖中需要三個(gè)基本要素One

ormoreobjects一個(gè)或多個(gè)對(duì)象A

viewer

with

a

projection

plane

觀察者，帶有一個(gè)投影面Projectors

that

go

from

the

object(s)to

theprojection

plane從對(duì)象到投影平面的投影變換5.1

ClassicalViewing

andComputerViewing(Classical

Viewing經(jīng)典視圖-2)Classical

views

are

based

on

the

relationshipamongtheseelements經(jīng)典視圖就是基于這些要素之間的關(guān)系的The

viewer

picks

up

the

object

and

orients

it

howd

like

toseeit觀察者撿取一個(gè)對(duì)象并進(jìn)行定向，確定希望看到的結(jié)果Each

object

is

assumed

to

constructed

from

flatprincipalfaces每個(gè)對(duì)象都假定是用平面的基本多邊形構(gòu)造出來的Buildings,

polyhedra,manufactured

objects如：建筑物、多面體、鍛造物5.1

ClassicalViewing

andComputerViewing(Planar

Geometric

Projections平面幾何投影)Standard

projections

project

onto

a

plane即投影到平面上的標(biāo)準(zhǔn)投影Projectors

are

lines

thateither投影線為直線，這些直線converge enter

of

projection匯聚于投影中心，或者are

parallel彼此平行Such

projectionspreservelines這種投影保持線性but

not

necessaril

les但不一定保角Nonplanar

projections

are

needed

for

applications

such

asmap

construction在諸如地圖繪制等應(yīng)用中需要非平面投影5.1.1

Classical

Viewing(Classical

Projections經(jīng)典投影)等軸測(cè)圖單點(diǎn)Figure

5.3

Classical

Viewing三點(diǎn)正面圖、前視圖立面斜視圖斜平面圖5.1.1

Classical

Viewing(基準(zhǔn)面、主面principal

faces)在諸如建筑業(yè)等實(shí)際應(yīng)用中，所觀察的對(duì)象通常由許多平坦面構(gòu)成。這些面中任一個(gè)都可以認(rèn)為是一個(gè)基準(zhǔn)面(Principalfaces)，從而進(jìn)行定位對(duì)于規(guī)則物體，例如房屋，按照通常的方式可以定義前、后、左、右、頂、底等面許多對(duì)象上都有幾個(gè)面相交于直角，從而可以得到三個(gè)正交的方向，稱為基準(zhǔn)方向建模坐標(biāo)系統(tǒng)5.1.1

ClassicalViewing( vs

Parallel

投影與平行投影)Computer

graphics

treats

all

projectionsthe

sameandimplements

them

with

a

singlepipeline計(jì)算機(jī)圖形學(xué)中把所有的投影用同樣的方法處理，用一個(gè)流水線體系實(shí)現(xiàn)它們Classical

viewing

developed

different

techniques

for

drawingeachtypeofprojection在經(jīng)典視圖中為了繪制不同類型的投影，發(fā)展出來不同的技術(shù)Fundamental

distinction

is

between

parallel

andviewing

even

though

mathematically

parallel

viewingis

thelimitof

viewing基本區(qū)別在于平行投影和投影，雖然從數(shù)學(xué)上說，平行投影是投影的極限狀態(tài)Taxonomy

ofPlanar

GeometricProjections平面幾何投影的分類圖parallel平行投影投影axonometric軸測(cè)法multiviewOrthographic多視點(diǎn)oblique傾斜Isometric

dimetric等角(等軸測(cè))四邊(正二測(cè))Trimetric三度(正三測(cè))2

point兩點(diǎn)1

point單點(diǎn)3

point三點(diǎn)planar

geometric

projections平面幾何投影5.1.1

Classical

ViewingProjection

投影)(投影線對(duì)象投影平面投影中心Figure

5.1

Viewing觀察5.1.1

Classical

Viewing(Parallel

Projection平行投影)對(duì)象投影線投影方向投影平面Figure

5.2

Movementof

the

COP

toinfinity5.1.2

Orthographic

Projection正交投影Projectors

are

orthogonal

to

projectionsurface投影線垂直于投影平面Figure

5.4

Orthographic

Projection5.1.2

Orthographic

Projection正交投影

(MultiviewOrthographic

Projection多視點(diǎn)正交投影)Projection

plane

parallel

to

principalface投影面平行于基準(zhǔn)面Usually

form

front,

top,side

views通常從前面、頂部和側(cè)面進(jìn)行投影isometric

(not

multivieworthographic

view)等角投影圖（不是多視點(diǎn)正交視圖中的一部分）Front前面Side側(cè)面Top頂部in

CAD

and

architecture,we

often

display

threemultiviews

plusisometric在CAD和建筑行業(yè)中，通常顯示出來三個(gè)視點(diǎn)圖以及等角投影圖5.1.2

Orthographic

Projection正交投影

(機(jī)器零件的多視點(diǎn)視圖)5.1.2

Orthographic

Projection正交投影

(Advantages

and

Disadvantages優(yōu)勢(shì)與不足)Preserves

both

distances

andangles保持了距離與角度Sh sp

保持形狀Can

be

used

for

measurements可以用來測(cè)量Building

plans建筑規(guī)劃Manuals手冊(cè)Cannot

see

what

object

really

looks

like

becausemanysurfaceshidden

fromview不能看到對(duì)象真正的全局形狀，因?yàn)樵S多面在視點(diǎn)中不可見Often

we

add

the

isometric有時(shí)加上等角圖5.1.3Axonometric

Projections軸測(cè)投影Allow

projectionplane

to

move

relative

to

object投影面相對(duì)于對(duì)象基準(zhǔn)面有一定的夾角classify

by

how

man lesofa

corner

of

a

projected

cube

arethe

same根據(jù)對(duì)立方體進(jìn)行投影時(shí)一個(gè)角點(diǎn)處有多少個(gè)角相等進(jìn)行分類none沒有:trimetric三度(正三測(cè))two兩個(gè):dimetric四邊(正二測(cè))three三個(gè):isometric等角(等軸測(cè))：

1

2

35.1.3Axonometric

Projections軸測(cè)投影

(Types

ofAxonometricProjections軸測(cè)投影的示例)四邊(正二測(cè))三度(正三測(cè))等角(等軸測(cè))5.1.3Axonometric

Projections軸測(cè)投影

(Advantages

and

Disadvantages優(yōu)勢(shì)與不足)Lines

arescaled(foreshortened縮短)but

can

find

scalingfactors直線段長(zhǎng)度被縮短，但可以求出收縮因子Lines

p but

angles

arenot保持直線但不保角Projectionof

a

circlein

a

plane

not

parallel

to

theprojection

plane

is

an

ellipse

圓所在平面如果不平行于投影面，它的投影為橢圓Can

see

three

principalfaces

of

a

box-likeobject可以見到盒子類對(duì)象的三個(gè)基準(zhǔn)面Some

opticalillusions

possible會(huì)導(dǎo)致某些觀察錯(cuò)覺Parallel

lines

appear

to

diverge

平行線角度不同Does

not

look

realbecausefar

objects

are

scaledthe

sameas

near

objects不是很真實(shí)，因?yàn)檫h(yuǎn)的對(duì)象與近的對(duì)象具有同樣的收縮因子Used

in

CADapplications

在CAD應(yīng)用中經(jīng)常用到5.1.4

Oblique

Projection傾斜投影Arbitrary

relationship

between

projectors

andprojectionplane投影線與投影面之間的關(guān)系任意投影面投影面 投影面Figure

5.8

Oblique

Projection

(a)Constrution

(b)Topview

(c)

Side

view5.1.4

Oblique

Projection傾斜投影(Advantages

and

Disadvantages優(yōu)勢(shì)與不足)Can

pick

the

angles

to

emphasizea

particular

face可以增加某個(gè)角度，以便強(qiáng)調(diào)特定面-

Architecture:

plan

oblique,

elevation

obliqueplan

oblique,

elevation

obliqueAngles

in

faces

parallelto

projection

planeare

p建筑行業(yè)：while

we

can

stillsee

“around”

side

在平行于投影面的面上的角是保持的，但 仍然可以見到其它側(cè)面In

physical

world,cannot

create

with

simple

camera;possible

with

bellows

camera

or

special

lens

(architectural)在實(shí)際世界中，只能利用特殊相機(jī)做到這一點(diǎn)bellows

camera

折疊暗箱照相機(jī)5.1.5Projection投影Projectors

converge

at

center

of

projection投影線匯聚于投影中心（COP）Figrue

5.9viewing5.1.5投影Projection(Vanishing

Points滅點(diǎn))Parallellines

(not

parallel

to

the

projection

plan)on

theobjectconvergeat

a

singlepoint

in

the

projection

(the

vanishingpoint)

在對(duì)象上的所有平行線（不平行于投影面）投影后交于一個(gè)點(diǎn)Drawing

simplepoint(s)手工繪制簡(jiǎn)單s

by

hand

uses

thesevanishing投影時(shí)就需要利用這些滅點(diǎn)vanishing

point滅點(diǎn)投影5.1.5

Projection(Vanishing

Points滅點(diǎn)舉例)5.1.5Projection(滅點(diǎn)-1)投影投影之后收斂滅點(diǎn)-不平行于投影平面的一組平行線，經(jīng)過于一點(diǎn)，稱為滅點(diǎn)。主滅點(diǎn)-平行于坐標(biāo)軸的平行線的滅點(diǎn)。主滅點(diǎn)的個(gè)數(shù)決定一點(diǎn)兩點(diǎn)三點(diǎn)5.1.5Projection(滅點(diǎn)-1)投影可以改變投影面的方位以控制主滅點(diǎn)的數(shù)目① 一點(diǎn)

：投影平面與坐標(biāo)系的一個(gè)平面平行(平行于坐標(biāo)軸并且不平行與投影平面的平行線只有一個(gè)方向)。② 二點(diǎn)

：投影平面與坐標(biāo)系的一根坐標(biāo)軸平行而與另兩根坐標(biāo)軸成一定角度(平行于坐標(biāo)軸并且不平行與投影平面的平行線則有二個(gè)方向)。③ 三點(diǎn)

：投影平面與坐標(biāo)系的三根坐標(biāo)軸均有一定的角度(平行于坐標(biāo)軸并且不平行與投影平面的平行線就有三個(gè)方向)。三點(diǎn)用得不多，主要原因是它難于構(gòu)造。5.1.5(Three-PointProjection

投影三點(diǎn)

)No

principalface

parallelto

projectionplane沒有基準(zhǔn)面平行于投影面Three

vanishing

points

for

cube立方體的投影中有三個(gè)滅點(diǎn)Esher’s伊舍5.1.5(Two-PointProjection

投影兩點(diǎn)

)On

principal

direction

parallelto

projection

plane一個(gè)基準(zhǔn)方向平行于投影面(另外兩個(gè)基準(zhǔn)方向不平行于投影面)Two

vanishing

points

forcube立方體的投影中有兩個(gè)滅點(diǎn)5.1.5(One-PointProjection

投影單點(diǎn)

)One

principal

face

parallel

to

projection

plane一個(gè)基準(zhǔn)面（兩個(gè)基準(zhǔn)方向）平行于投影平面（另外一個(gè)基準(zhǔn)方向不平行于投影面）One

vanishing

point

forcube立方體的投影中有一個(gè)滅點(diǎn)5.1.5

Projection

投