viewing and transformation

CGGM Lab. Tan-Chi Ho 2001

Viewing and Transformation


The Camera Analogy1/2

Set up tripod and pointing the camera at the scene (viewing transformation).

Arrange the scene to be photographed into the desired composition (modeling transformation).


The Camera Analogy2/2

Choose a camera lens or adjust the zoom (projection transformation).

Determine how large you want the final photograph to be (viewport transformation).


Overview

ModelviewMatrix

ModelviewMatrix

ViewTransformation

ViewTransformation

ModelviewMatrix

ModelviewMatrix

PerspectiveDivision

eye coordinat

es

clip coordinat

es

normalized device

coordinates

window coordinat

es

XYZW

Object coordinat

es

VertexVertex


Transformations1/12

The Viewing Transformation To positioning and aiming the camera. Use gluLookAt() to indicate where the ca

mera is placed and aimed. If gluLookAt() was not called, the camera

has a default position at the origin, points down the negative Z-axis, and an up-vector of (0, 1, 0).


Transformations2/12

gluLookAt(GLdouble eyex, GLdouble eyey, GLdouble eyez, GLdouble centerx, GLdouble centery, GLdouble centerz, GLdouble upx, GLdouble upy, GLdoubpe upz);

eyex, eyey, eyez is where the camera is positioned.

centerx, centery, centerz is where the camera look at.

Upx, upy, upz is the up-vector of the camera.


Transformations3/12

The Modeling Transformation To position and orient the models.

Rotate, translate, scale and some combination of these operations.

In OpenGL, modeling and viewing transformation are combined into the modelview matrix before the transformation are applied.


Transformations4/12

glTranslate{fd}(TYPE x,TYPE y,TYPE z); Multiplies current matrix by a matrix that mo

ves an object by x,y,z glRotate{fd}(TYPR angle,TYPE x,TYPR y,

TYPE z); Multiplies current matrix by a matrix that rot

ates an object in a counterclockwise direction about the ray from origin to (x,y,z) with angle as the degrees.


Transformations5/12

glScale{fd}(TYPE x,TYPE y,TYPE z); Multiplies current matrix by a matrix that scal

es an object along axes.


Transformations6/12

The Projection Transformation Determine what the field of view(or

viewing volume) is and how objects are projected onto the screen.

Two types of projections are provided: Perspective projection Orthographic projection


Transformations7/12

Perspective Projection glFrustum(GLdouble left, GLdouble rig

ht, GLdouble bottom, GLdouble top, GLdouble near, GLdouble far);


Transformations8/12

gluPerspective(GLdouble fovy, GLdouble aspect, GLdouble near, GLdouble far);


Transformations9/12

Orthographic Projection glOrtho(Gldouble left, Gldouble right,

Gldouble bottom, Gldouble top, Gldouble near, Gldouble far);

gluOrtho2D(Gldouble left, Gldouble right, Gldouble bottom, Gldouble top);

For 2D projection matrix The Z coordinates for objects are assumed to

lie between –1.0 and 1.0.


Transformations10/12



The Viewport Transformation Transform the final image into some regi

on of the window. The viewport is measured in window coo

rdinates. glViewport(GLint x, GLint y, GLsizei wi

dth, GLsizei height); Initial values are (0, 0, winWidth, winHeight).



Switch between matrix modes glMatrixMode(GLenum mode);

Switch between modelview, projection, tecture matrix mode.(GL_MODELVIEW, GL_PROJECTION, GL_TEXTURE)

Current matrix mode is a state variable. glLoadIdentity();

Set current matrix to the 4x4 identity matrix. Always call this after change matrix mode.


The Matrix Manipulation glLoadIdentity(); glLoadMatrix{f,d}( const TYPE* m ); glMultMatrix{f,d}( const TYPE* m ); glPushMatrix(); glPopMatrix();

Stack operation of matrix is very useful for constructing a hierarchical structures.

Ex: a car with four wheels.


Transformation Program1/5

#include <GL/glut.h>

static GLfloat year=0.0f, day=0.0f;

void init(){

glClearColor(0.0, 0.0, 0.0, 0.0);}

void GL_display(){

// clear the bufferglClear(GL_COLOR_BUFFER_BIT);

glColor3f(1.0, 1.0, 1.0);glPushMatrix();

glutWireSphere(1.0, 20, 16); // the SunglRotatef(year, 0.0, 1.0, 0.0);



glTranslatef(3.0, 0.0, 0.0);glRotatef(day, 0.0, 1.0, 0.0);glutWireSphere(0.5, 10, 8); // the Planet

glPopMatrix();// swap the front and back buffersglutSwapBuffers();

}void GL_reshape(GLsizei w, GLsizei h){

// viewport transformationglViewport(0, 0, w, h);

// projection transformationglMatrixMode(GL_PROJECTION);glLoadIdentity();gluPerspective(60.0, (GLfloat)w/(GLfloat)h, 1.0, 20.0);



// viewing and modeling transformationglMatrixMode(GL_MODELVIEW);glLoadIdentity();gluLookAt(0.0, 3.0, 5.0, // eye

0.0, 0.0, 0.0, // center 0.0, 1.0, 0.0); // up

}

// GLUT idle functionvoid GL_idle(){

day += 10.0;if(day > 360.0)

day -= 360.0;year += 1.0;if(year > 360.0)

year -= 360.0;// recall GL_display() functionglutPostRedisplay();

}



// GLUT keyboard functionvoid GL_keyboard(unsigned char key, int x, int y){

switch(key){case 'd': day += 10.0;

if(day > 360.0)day -= 360.0;

glutPostRedisplay();break;

case 'y': year += 1.0;if(year > 360.0)

year -= 360.0;glutPostRedisplay();break;

case 'a': // assign idle functionglutIdleFunc(GL_idle);break;

case 'A': glutIdleFunc(NULL);break;

case 27: exit(0);}

}



int main(int argc, char** argv){

glutInit(&argc, argv);glutInitWindowSize(500, 500);glutInitWindowPosition(0, 0);glutInitDisplayMode(GLUT_DOUBLE | GLUT_RGB);glutCreateWindow("Planet");init();glutDisplayFunc(GL_display);glutReshapeFunc(GL_reshape);glutKeyboardFunc(GL_keyboard);glutMainLoop();

}


Any Question?

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viewing and transformation

Documents

gldouble eyey

gldouble farcggm

gldouble eyez

gldouble centery

gldouble upx

gldouble centerz

gldouble centerx

gldouble upy