Transformations Opengl 11 12 eBook

8/13/2019 Transformations Opengl 11 12 eBook

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Transformations in OpenGL

Lecturer: Carol OSullivanProfessor of Visual Computing

[email protected]

Course www: http://isg.cs.tcd.ie/cosulliv/


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o e ng rans orma ons

transformations are: glTranslate*(),lRotate* and lScale*

These routines transform an object (or

stretching, shrinking, or reflecting it.

producing an appropriate translation, rotation,

or scalin matrix, and then callinglMultMatrix*() with that matrix as the

argument.


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o e ng rans orma ons

glLoadIdentity()

creates an id e nt ity m a trix(used for clearingall trans ormatons

glLoadMatrixf(matrixptr)

loads a use r sp e c if ie d tra nsfo rm a t io n m a trix

where mat r i xpt r is defined as GLf l oat

mat r i xpt r [ 16] ;


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ransa e , ,

translates by d isp la c em en t vec to r(dx, dy, dz)

moves (translates) an object by the given x-, y-,

-

system by the same amounts).

. , . , .means it has no effect on an object or its local

coordinate s stem.


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o a e lRotatef an le vx v vz

rotates about axis (vx, vy, vz) by angl e (specified

in degrees)

rotates an object (or the local coordinates stem) in a counterclockwise direction about

the ray from the origin through the point (x,y,z).The angle parameter specifies the angle of

.The effect of glRotatef(45.0, 0.0, 0.0, 1.0)

is a rotation of 45 de rees about the z-axis. If angle = 0.0 the command has no effect.


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ca e

apply scaling of sx in x direction, sy in y direction

and sz in zdirection (note that these values specifyt e d i agonao a requ re matrx

Multiplies the current matrix by a matrix that, ,

axes. Each x-, y-, and z-coordinate of every point inthe object is multiplied by the correspondingargumen x,y, or z.

With the local coordinate system approach, the, ,

reflected by the x-, y-, and z-factors, and theassociated object is transformed with them.


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rans orma ons n pen OpenGL defines 3 matrices for manipulation of 3D scenes:

GL_MODELVIEW: manipulates the view and models simultaneouslyGL_PROJECTION: per orms pro ec on or sp ay

GL_TEXTURE: for manipulating textures prior to mapping on objects

altered.

_ ,

vertices are created with the specified transformation.

Matrix transformation o erations a l to the currentlselected system matrix:

use glMatrixMode(GL_MODELVIEW) to select modeling

matrix


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tages o ertex rans ormaton

x

Vertex Geometry Pipeline

MODELVIEW

matrix

PROJECTION

matrix

perspective

division

viewport

transformation

z

y

win

win

y

x

eye

eye

y

x

dev

dev

y

x

projxoriginal

vertex /final window

eye

eye

w

z 1 projwobject

coordinates

2d projection normalised devicevertex n t e

eye coordinate

space

of vertex onto

viewing plane /

clip coordinates

(foreshortened)


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matr ixand therefore has12 d e g re e s o f fre e d om:

tcba

y

tih

tfed

1000z

The MODELVI EWmatrix is used for both the model andthe camera transformation

camera in the opposite direction OpenGL usesthe same transformation matrix

this sometimes causes confusion!


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the currentMODELVIEWmatrix C is altered:

= =

glTranslatef(1.5, 0.0, 0.0);

glRotatef(45.0, 0.0, 0.0, 1.0);

CTRvv =


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xamp e

glMatrixMode(GL_MODELVIEW);

lLoadIdentit ();

glMultMatrix(N);glMultMatrix(M);

glMultMatrix(L);

glBegin(GL_POINTS);

glEnd();


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Transformations are applied in the o rd e r sp e c if ie d(with


glTranslatef(1.5, 0.0, 0.0);

glRotatef(45.0, 0.0, 0.0, 1.0);

glVertex3f(1.0, 0.0, 0.0);

original rotate translate


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transformations are specified

using a single matrix we musttransformations on the coo rd i na tef ramesof the camera and

.

Assume we wish to orbi tan objectat a f ixe d o rie nta t io n:

transate o ect away romcamera

rotate around X to look at top ofo ect

then pivot around objects Y inorder to orbit properly.


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If the GL MODELVIEWmatrix is an identit matrix then the_

camera frame and the model frame are the same.

i.e. they are specified using the same co-ordinate system If we issue command glTranslatef(0.0,0.0,-10.0);

and then create the model: , , , , -

the camera frame i.e. we have moved the object away from the camera

This may be viewed conceptually in 2 ways:

we have positioned the object with respect to thewor rame we have moved the world-frame with respect to the

camera frame


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coordinate system approach) is:

lMatrixMode GL MODELVIEWmove away from

read transformations

in reverse order_

glLoadIdentity();glTranslatef(0.0, 0.0, -10.0);

rotate around world X. , . , . , .

glRotatef(Pivot_Angle, 0.0, 1.0, 0.0);(tilt towards camera)

_

glEnd();

draw required object


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view) is:

glMatrixMode(GL_MODELVIEW);clear previous transformations

glTranslatef(0.0, 0.0, -10.0);glRotatef(30.0, 1.0, 0.0, 0.0);

rotate object into view

g o a e vo _ ng e, . , . , . ;

glBegin(GL_POLYGON);

pivot around objects Y axis

glEnd();draw required object


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objects new Y

rotate

translate


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naturally to the specification of h ie ra rc h ic a l m o d e l

f rames.

This allows creation ofjo in te d a ssem b lie s

articulated figures (animals, robots etc.)

In the hierarchical model, each sub-component hasits own lo c a l fra m e.

Changes made to the p a re n t fra m eare propagated

down to the c h ild fra m e s(thus all models in a branchare g o a y con ro e y e paren .

This simplifies the specification of an ima t ion.


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It is often expensive to compute or create a model for.

We would prefer not to have to recalculate it each time for

each new animation frame.

Disp la y listsallow the creation of an object in memory,where it resides until destroyed.

Objects are drawn by issuing a request to the server to displaya given display list. number of list IDs to create

list = glGenLists(1);

glNewList(list, GL_COMPILE);

create_model();

GLui nt of first

list ID

begin specification of the list

glEndList();

glCallList(list);

used later to display the list

glDeleteLists(list, 1);delete when finished

(specifying number of lists)


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o e rans orma ons

created with respect to a changing transformation.

orCTM .

The CTMbehaves like a 3D ointe selectin new

positions and orientations for the creation ofgeometries.

The only complication with this view is that each newCTMis derived from a previousCTM, i.e. all CTM sarespec e re a ve o prev ous versons.

A sc a ling tra nsfo rm a tio ncan cause some confusion.


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Scalin Transformation and the CTM


glLoadIdentity();

lTranslatef 3 0 0

glTranslatef(1, 0, 0);

lMatrixMode GL MODELVIEW_

glLoadIdentity();

glTranslatef(3, 0, 0);

. , . , .. , . , .glTranslatef(1, 0, 0);

g uCy n er ;


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erarc ca rans orma ons

For geometries with an

implicit hie ra rc hy we wish toassociate local frames withsub-objects in the assembly.

Pa re nt-c h ild fra m e sarerelated via a transformation.

rans orma on n age sdescribed by a tree:

ac no e as s own o c ac o -o rd ina te system.


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R

RT

over sub-parts of an assembly


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translate base rotatej oi nt 1

rotate j oi nt 2 complex hierarchical transformation


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glLoadIdentity();

glTranslatef(bx, by, bz);

create base_

glTranslatef(0, j1y, 0);

glRotatef(joint1_orientation);

_

glTranslatef(0, uay, 0);create_upperarm();

,

glRotatef(joint2_orientation);

create_joint2();g Trans ate , ay, ;

create_lowerarm();

glTranslatef(0, py, 0);

glRotatef(pointer_orientation);

create_pointer();


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- -parent-child linkages.

In eneral there ma be man c h ild fra m e sderived from a single parent frame.

We need some mechanism to remember the

parent frame and return to it when creating newchildren.

pen prov e a ma rx s ac or us spurpose:

glPopMatrix() returns to the last saved CTM


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Each finger is a child of the parent (wrist)

independent control over the orientationof the fingers relative to the wrist


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lLoadIdentit

glTranslatef(bx, by, bz);create_base();

glTranslatef(0, jy, 0);

lRotatef oint1 orientation_

create_joint1();

glTranslatef(0, ay, 0);

create_upperarm();

lTranslatef 0 w

glRotatef(wrist_orientation);

create_wrist();

glPushMatrixglPushMatrix();(); // save frame

lTranslatef -xf f 0 0

glRotatef(lowerfinger1_orientation);

glTranslatef(0, fy1, 0);

create_lowerfinger1();

lTranslatef(0 f 2 0);

glRotatef(upperfinger1_orientation);

create_fingerjoint1();

glTranslatef(0, fy3, 0);

create u erfin er1();_glPopMatrixglPopMatrix();(); // restore frame

glPushMatrixglPushMatrix();();

// do finger 2...

lPo MatrixlPo Matrix();();Finger1

glPushMatrixglPushMatrix();();

// do finger 3...glPopMatrixglPopMatrix();();

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