06 cg transformation 01

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Course:Computer Graphics 2010

Lecture 6:

geometric transformationsPart 1

Vernica [email protected]

www.dcc.fc.up.pt/~veronica.orvalho
mailto:[email protected]:[email protected]


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agenda

. brief introduction to transformations

. OpenGL: geometric transformation

. examples


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introduction

rigid bodytransformations non-rigid bodytransformations

Images by Ron Fedkiw Stanford Universityhttp://physbam.stanford.edu/~fedkiw/


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introduction

rigid body transformations

orient and place the objects on a scene

rotation translation


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introduction

non-rigid body transformations

distance between points on objects

DO NOT remain constant


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introduction

what can you do with transformations?


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introduction

what can you do with transformations?

rotatetranslate

stretchshrinkwrapetc.

project 3D coordinates onto a 2D screen

(move around)


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transform:operation that takes an attribute:points, vectors or colors

converts them in some way

http://www.ltutech.comhttp://www.lohmueller.business.t-online.de/pov_tut/trans/scale1t.jpg

transform


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examples

Textures >

http://www.youtube.com/watch?v=QNJMz5xqEuE&feature=related

3D Object >

http://www.youtube.com/watch?v=de7tOeiMcLc


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OpenGL transformations

view

modeling

modelview

projection

viewport

specifies the location of theviewer or camera

moves objects around scene

describes the duality of viewingand modeling transformations

clips and sizes the viewing

volume

scales final output to thewindow


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OpenGL transformations

view

modeling

modelview

projection

viewport

specifies the location of theviewer or camera

moves objects around scene

describes the duality of viewingand modeling transformations

clips and sizes the viewing

volume

scales final output to thewindow


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OpenGL transformations pipeline


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xyzw

0

0

0

0

originalvertexdata

in homogeneouscoordinates


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xyzw

0

0

0

0

modelviewmatrix

originalvertexdata



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xyzw

0

0

0

0

modelviewmatrix

xyzw

e

e

e

e

originalvertexdata

transformedeye

coordinates



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xyzw

0

0

0

0

modelviewmatrix

xyzw

e

e

e

e

projectionmatrix

originalvertexdata

transformedeye

coordinates



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xyzw

0

0

0

0

modelviewmatrix

xyzw

e

e

e

e

projectionmatrix

xyzw

c

c

c

c

originalvertexdata

transformedeye

coordinates

clipcoordinates



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xyzw

0

0

0

0

modelviewmatrix

xyzw

e

e

e

e

projectionmatrix

xyzw

c

c

c

c

perspectivematrix

originalvertexdata

transformedeye

coordinates

clipcoordinates



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xyzw

0

0

0

0

modelviewmatrix

xyzw

e

e

e

e

projectionmatrix

xyzw

c

c

c

c

perspectivematrix

x /wy /wz /w

c

c

c

c

c

c

originalvertexdata

transformedeye

coordinates

clipcoordinates

normalized

coordinatesin homogeneouscoordinates


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xyzw

0

0

0

0

modelviewmatrix

xyzw

e

e

e

e

projectionmatrix

xyzw

c

c

c

c

perspectivematrix

x /wy /wz /w

cc

c

viewporttrasform(also amatrix)

cc

c

originalvertexdata

transformedeye

coordinates

clipcoordinates

normalized



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xyzw

0

0

0

0

modelviewmatrix

xyzw

e

e

e

e

projectionmatrix

xyzw

c

c

c

c

perspectivematrix

x /wy /wz /w

cc

c

viewporttrasform(also amatrix)

cc

c

windowcoordinates

originalvertexdata

transformedeye

coordinates

clipcoordinates

normalized



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glTranslatef (float x, float y, float z)

glRotatef (float angle, float x, float y, float z)

glScalef( float x, float y, float z)

translate, rotate and scale in OpenGL


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glTranslatef (float x, float y, float z)

glTranslatef (0, 2, 0)


x

y

x

y

you can translate in any direction

(1,0,0)


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glRotatef (float angle, float x, float y, float z)

glRotatef (45, 1, 1, 1)

around an arbitrary axis specified by (1,1,1)


x

y

x

y

the angle of rotation is in counterclockwise

(1,1,1)


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glScalef (float x, float y, float z)

glScalef (2, 1, 1)


multiplies the X, Y, Z values by the scalingfactor

2x


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glLoadIdentity ()

very useful to reset the ModelView Matrix!

the identity matrix in OpenGL


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example

// set current matrix to Modelview and restglMatrixMode( GL_MODELVIEW);glLoadIdentity ();

glTranslatef(0, 2, 0); //go 2 units up the y-axisdrawObject_1();

glLoadIdentity(); //reset modelview matrix againglTranslatef(2, 0, 0); //go 2 units out the x-axisdrawObject_2();

the identity matrix in OpenGL


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Example Transformations OpenGL

glMatrixMode(GL_MODELVIEW);glMatrixMode(GL_MODELVIEW);glLoadIdentity();glLoadIdentity();glTranslatef(...);glTranslatef(...);

glRotatef(...);glRotatef(...);glScalef(...);glScalef(...);glutSolidCylinder(...)glutSolidCylinder(...)


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matrix stack OpenGL

glPushMatrix() glPopMatrix()

matrix stack

Example:http://www.gamedev.net/reference/articles/article1267.asp

k


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matrix stack OpenGL

When to use Push and Pop ?

if parts of a model depend on one another.Moving one part, causes other parts to move

Models MUST be arranged as a tree datastructure e.g. a simple robot arm

Example:

http://www.gamedev.net/reference/articles/article1267.asp

i k O GL


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matrix stack OpenGL

i k O GL


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matrix stack OpenGLglLoadIdentity();glColor3f(1.0, 0.0, 0.0);

glRotatef(theta[0], 0.0, 1.0, 0.0);torso();

glPushMatrix(); //save current model-view matrix glTranslatef(0.0, TORSO_HEIGHT+0.5*HEAD_HEIGHT, 0.0);

glRotatef(theta[1], 1.0, 0.0, 0.0);glRotatef(theta[2], 0.0, 1.0, 0.0);

glTranslatef(0.0, -0.5*HEAD_HEIGHT, 0.0);head();glPopMatrix(); //we have drawn the head so go back up to torso

glPushMatrix(); //but now want to draw left arm so save the torso matrix againglTranslatef(-(TORSO_RADIUS+UPPER_ARM_RADIUS), 0.9*TORSO_HEIGHT,

0.0);glRotatef(theta[3], 1.0, 0.0, 0.0);

left_upper_arm();glTranslatef(0.0, UPPER_ARM_HEIGHT, 0.0);glRotatef(theta[4], 1.0, 0.0, 0.0);left_lower_arm();

glPopMatrix(); //we have drawn the left_arm so go back up to torso

d t i i l ti O GL


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advance matrix manipulation OpenGLglFloat m[] = { 1, 0, 0, 0,

0, 1, 0, 0,

0, 0, 1, 0,0, 0, 0, 1};

glMatrixMode(GL_MODELVIEW)glLoadMatrixf(m);

//Define a translation Matrix

glFloat m_t[] = { 1, 0, 0, 10 ,0, 1, 0, 0,0, 0, 1, 0,0, 0, 0, 1};

// multiply the translation matrix by the current modelview matrix.// the new matrix becomes the modelview matrix

glMatrixMode(GL_MODELVIEW)glLoadMatrixf(m_t);


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questions

06 cg transformation 01

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