大三-05计算机图形学-51classical

ObjectivesIntroduce

the

classical

views介绍经典视图Compare

and

contrast

image

formationbycomputer

with

how

images

have

been

formedby

architects,artists,and

engineers比较由计算机形成的图像与建筑师、画家和工程师绘制的图像Learn

the

benefits

and

drawbacks

of

each

typeof

view学习每种视图的优势与不足Outline5.1

Classical

Viewing

and

Computer

Viewing5.1.1

Classical

Viewing经典视图5.1.2

Orthographic

Projection正交投影5.1.3

Axonometric

Projections轴测投影5.1.4

Oblique

Projection倾斜投影5.1.5

Projection

投影5.1

ClassicalViewing

andComputerViewing(为什么需要经典视图？)传统由手工操作的制图工作现在可以用计算机模拟中的动画，建筑图纸，机器零件图纸-这些领域中需要不同的经典视图等角投影（等轴测图）（isometrics)，正视图(elevation)，经典视图与计算机视图之间的对比关系表明了在大多数API中所采用方法的长处，当然也具有一些不足和-

经典照相机与 照相机5.1

ClassicalViewing

andComputerViewing(Classical

Viewing经典视图-1)Viewingrequiresthreebasicelements视图中需要三个基本要素One

ormoreobjects一个或多个对象A

viewer

with

a

projection

plane

观察者，带有一个投影面Projectors

that

go

from

the

object(s)to

theprojection

plane从对象到投影平面的投影变换5.1

ClassicalViewing

andComputerViewing(Classical

Viewing经典视图-2)Classical

views

are

based

on

the

relationshipamongtheseelements经典视图就是基于这些要素之间的关系的The

viewer

picks

up

the

object

and

orients

it

howd

like

toseeit观察者捡取一个对象并进行定向，确定希望看到的结果Each

object

is

assumed

to

constructed

from

flatprincipalfaces每个对象都假定是用平面的基本多边形构造出来的Buildings,

polyhedra,manufactured

objects如：建筑物、多面体、锻造物5.1

ClassicalViewing

andComputerViewing(Planar

Geometric

Projections平面几何投影)Standard

projections

project

onto

a

plane即投影到平面上的标准投影Projectors

are

lines

thateither投影线为直线，这些直线converge enter

of

projection汇聚于投影中心，或者are

parallel彼此平行Such

projectionspreservelines这种投影保持线性but

not

necessaril

les但不一定保角Nonplanar

projections

are

needed

for

applications

such

asmap

construction在诸如地图绘制等应用中需要非平面投影5.1.1

Classical

Viewing(Classical

Projections经典投影)等轴测图单点Figure

5.3

Classical

Viewing三点正面图、前视图立面斜视图斜平面图5.1.1

Classical

Viewing(基准面、主面principal

faces)在诸如建筑业等实际应用中，所观察的对象通常由许多平坦面构成。这些面中任一个都可以认为是一个基准面(Principalfaces)，从而进行定位对于规则物体，例如房屋，按照通常的方式可以定义前、后、左、右、顶、底等面许多对象上都有几个面相交于直角，从而可以得到三个正交的方向，称为基准方向建模坐标系统5.1.1

ClassicalViewing( vs

Parallel

投影与平行投影)Computer

graphics

treats

all

projectionsthe

sameandimplements

them

with

a

singlepipeline计算机图形学中把所有的投影用同样的方法处理，用一个流水线体系实现它们Classical

viewing

developed

different

techniques

for

drawingeachtypeofprojection在经典视图中为了绘制不同类型的投影，发展出来不同的技术Fundamental

distinction

is

between

parallel

andviewing

even

though

mathematically

parallel

viewingis

thelimitof

viewing基本区别在于平行投影和投影，虽然从数学上说，平行投影是投影的极限状态Taxonomy

ofPlanar

GeometricProjections平面几何投影的分类图parallel平行投影投影axonometric轴测法multiviewOrthographic多视点oblique倾斜Isometric

dimetric等角(等轴测)四边(正二测)Trimetric三度(正三测)2

point两点1

point单点3

point三点planar

geometric

projections平面几何投影5.1.1

Classical

ViewingProjection

投影)(投影线对象投影平面投影中心Figure

5.1

Viewing观察5.1.1

Classical

Viewing(Parallel

Projection平行投影)对象投影线投影方向投影平面Figure

5.2

Movementof

the

COP

toinfinity5.1.2

Orthographic

Projection正交投影Projectors

are

orthogonal

to

projectionsurface投影线垂直于投影平面Figure

5.4

Orthographic

Projection5.1.2

Orthographic

Projection正交投影

(MultiviewOrthographic

Projection多视点正交投影)Projection

plane

parallel

to

principalface投影面平行于基准面Usually

form

front,

top,side

views通常从前面、顶部和侧面进行投影isometric

(not

multivieworthographic

view)等角投影图（不是多视点正交视图中的一部分）Front前面Side侧面Top顶部in

CAD

and

architecture,we

often

display

threemultiviews

plusisometric在CAD和建筑行业中，通常显示出来三个视点图以及等角投影图5.1.2

Orthographic

Projection正交投影

(机器零件的多视点视图)5.1.2

Orthographic

Projection正交投影

(Advantages

and

Disadvantages优势与不足)Preserves

both

distances

andangles保持了距离与角度Sh sp

保持形状Can

be

used

for

measurements可以用来测量Building

plans建筑规划Manuals手册Cannot

see

what

object

really

looks

like

becausemanysurfaceshidden

fromview不能看到对象真正的全局形状，因为许多面在视点中不可见Often

we

add

the

isometric有时加上等角图5.1.3Axonometric

Projections轴测投影Allow

projectionplane

to

move

relative

to

object投影面相对于对象基准面有一定的夹角classify

by

how

man lesofa

corner

of

a

projected

cube

arethe

same根据对立方体进行投影时一个角点处有多少个角相等进行分类none没有:trimetric三度(正三测)two两个:dimetric四边(正二测)three三个:isometric等角(等轴测)：

1

2

35.1.3Axonometric

Projections轴测投影

(Types

ofAxonometricProjections轴测投影的示例)四边(正二测)三度(正三测)等角(等轴测)5.1.3Axonometric

Projections轴测投影

(Advantages

and

Disadvantages优势与不足)Lines

arescaled(foreshortened缩短)but

can

find

scalingfactors直线段长度被缩短，但可以求出收缩因子Lines

p but

angles

arenot保持直线但不保角Projectionof

a

circlein

a

plane

not

parallel

to

theprojection

plane

is

an

ellipse

圆所在平面如果不平行于投影面，它的投影为椭圆Can

see

three

principalfaces

of

a

box-likeobject可以见到盒子类对象的三个基准面Some

opticalillusions

possible会导致某些观察错觉Parallel

lines

appear

to

diverge

平行线角度不同Does

not

look

realbecausefar

objects

are

scaledthe

sameas

near

objects不是很真实，因为远的对象与近的对象具有同样的收缩因子Used

in

CADapplications

在CAD应用中经常用到5.1.4

Oblique

Projection倾斜投影Arbitrary

relationship

between

projectors

andprojectionplane投影线与投影面之间的关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倾斜投影(Advantages

and

Disadvantages优势与不足)Can

pick

the

angles

to

emphasizea

particular

face可以增加某个角度，以便强调特定面-

Architecture:

plan

oblique,

elevation

obliqueplan

oblique,

elevation

obliqueAngles

in

faces

parallelto

projection

planeare

p建筑行业：while

we

can

stillsee

“around”

side

在平行于投影面的面上的角是保持的，但 仍然可以见到其它侧面In

physical

world,cannot

create

with

simple

camera;possible

with

bellows

camera

or

special

lens

(architectural)在实际世界中，只能利用特殊相机做到这一点bellows

camera

折叠暗箱照相机5.1.5Projection投影Projectors

converge

at

center

of

projection投影线汇聚于投影中心（COP）Figrue

5.9viewing5.1.5投影Projection(Vanishing

Points灭点)Parallellines

(not

parallel

to

the

projection

plan)on

theobjectconvergeat

a

singlepoint

in

the

projection

(the

vanishingpoint)

在对象上的所有平行线（不平行于投影面）投影后交于一个点Drawing

simplepoint(s)手工绘制简单s

by

hand

uses

thesevanishing投影时就需要利用这些灭点vanishing

point灭点投影5.1.5

Projection(Vanishing

Points灭点举例)5.1.5Projection(灭点-1)投影投影之后收敛灭点-不平行于投影平面的一组平行线，经过于一点，称为灭点。主灭点-平行于坐标轴的平行线的灭点。主灭点的个数决定一点两点三点5.1.5Projection(灭点-1)投影可以改变投影面的方位以控制主灭点的数目① 一点

：投影平面与坐标系的一个平面平行(平行于坐标轴并且不平行与投影平面的平行线只有一个方向)。② 二点

：投影平面与坐标系的一根坐标轴平行而与另两根坐标轴成一定角度(平行于坐标轴并且不平行与投影平面的平行线则有二个方向)。③ 三点

：投影平面与坐标系的三根坐标轴均有一定的角度(平行于坐标轴并且不平行与投影平面的平行线就有三个方向)。三点用得不多，主要原因是它难于构造。5.1.5(Three-PointProjection

投影三点

)No

principalface

parallelto

projectionplane没有基准面平行于投影面Three

vanishing

points

for

cube立方体的投影中有三个灭点Esher’s伊舍5.1.5(Two-PointProjection

投影两点

)On

principal

direction

parallelto

projection

plane一个基准方向平行于投影面(另外两个基准方向不平行于投影面)Two

vanishing

points

forcube立方体的投影中有两个灭点5.1.5(One-PointProjection

投影单点

)One

principal

face

parallel

to

projection

plane一个基准面（两个基准方向）平行于投影平面（另外一个基准方向不平行于投影面）One

vanishing

point

forcube立方体的投影中有一个灭点5.1.5

Projection

投