Viewing Korea Univ. Computer Graphics Lab. Hong, Jin Kyung

ViewingViewing

Korea Univ.Korea Univ.

Computer Graphics Lab.Computer Graphics Lab.

Hong, Jin KyungHong, Jin Kyung

Korea Univ. Computer Graphics Lab.Korea Univ. Computer Graphics Lab.22

Chapter ObjectivesChapter Objectives

• View a geometric model• Control the location• Clip Undesired portions of the model• Manipulate the appropriate matrix

stacks


TransformationTransformation

• Viewing transformation• Modeling transformation• Projection transformation• Viewport transformation


TransformationTransformation

• Stages of Vertex Transformation

• v’ = Mv


Viewing Transformation(1/6)Viewing Transformation(1/6)

• Eye position 의 위치와 방향을 결정

• Default 위치 : 원점 , negative z-axis, y-axis up

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

glMatrixMode(GL_MODELVIEW);glLoadIdentity(); // 현재 행렬을 단위 행렬로 초기화



Default camera position Using gluLookAt()



• Example 3-1.

void display(){

glClear(GL_COLOR_BUFFER_BIT);glColor3f(1.0, 1.0, 1.0);glLoadIdentity();

/* Viewing Transformation */gluLookAt(0.0, 0.0, 5.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0);glScalef(1.0, 2.0, 1.0); /* Modeling Transformation */glutWireCube(1.0);glFlush();

}



void glTranslate{fd}(TYPE x, TYPE y, TYPE z);

glLoadIdentity();glColor3f(1.0, 1.0, 1.0);draw_triangle();

glEnable(GL_LINE_STIPPLE);glLineStipple(1, 0xF0F0);glTranslated(-1.0, 0.0, 0.0);

glColor3f(1.0, 0.0, 0.0);draw_triangle();glDisable(GL_LINE_STIPPLE);



void glRotate{fd}(TYPE angle, TYPE x, TYPE y, TYPE z);


glEnable(GL_LINE_STIPPLE);glLineStipple(1, 0x8888);glRotatef(90.0, 0.0, 0.0, 1.0);




• Rotating First or Translating First


Coordinate System (1/2)Coordinate System (1/2)

• Grand, fixed coordinate system

glMatrixMode(GL_MODELVIEW);

glLoadIdentity();

glMultMatrixf(N); // N matrix transformation

glMultMatrixf(M);

glMultMatrixf(L);

glBegin(GL_POINTS);

glVertex3f(v); // draw transformed vertex v

glEnd() // v’ = N(M(Lv))

- 변환되는 점의 좌표를 명령 순서와 반대로 계산해야 함


Coordinate System (2/2)Coordinate System (2/2)

• Local coordinate system

glMatrixMode(GL_MODELVIEW);glLoadIdentity();glMultMatrixf(T); // TranslationglMultMatrixf(R); // Rotation

draw_the_object();

- 변환되는 점의 좌표가 명령 순서와 일치

예 ) 로봇의 운동


Modeling Modeling Transformation(1/4)Transformation(1/4)

• 물체들의 위치와 방향을 결정• World 좌표에 대한 각 물체의 좌표 값이 결정

-> x, y, z 축에 따른 model 의 비율 결정

void glScale{fd}(TYPE x, TYPE y, TYPE z);



void glScalef{fd}(TYPE x, TYPE y, TYPE z);


glEnable(GL_LINE_STIPPLE);glLineStipple(1, 0xF00F);glScalef(1.5, 0.5, 1.0);




• Example 3-1.

void display(){

glClear(GL_COLOR_BUFFER_BIT);glColor3f(1.0, 1.0, 1.0);glLoadIdentity();

/* Viewing Transformation */gluLookAt(0.0, 0.0, 5.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0);glScalef(1.0, 2.0, 1.0); /* Modeling Transformation */glutWireCube(1.0);glFlush();

}



• 프로그램 명령 순서

Viewing Transformation -> Modeling Transformation

• 실제 좌표 값 결정

Modeling Transformation -> Viewing Transformation


Vertex TransformationVertex Transformation

Translate

Rotate Scale


Duality of Modelview(1/2)Duality of Modelview(1/2)

• Viewing Transformation– 관측자를 이동

• Modeling Transformation– 좌표계를 이동

결과적으로 같은 효과


Duality of Modelview(2/2)Duality of Modelview(2/2)

• Creating a Custom Utility Routinevoid pilotView(double planex, double planey, double planez, double roll, double pitch, double heading){

glRotated(roll, 0.0, 0.0, 1.0);glRotated(pitch, 0.0, 1.0, 0.0);glRotated(heading, 1.0, 0.0, 0.0);glTranslated(-planex, -planey, -planez);

}

void polarView(double distance, double twist, double elevation, double azimuth){

glTranslated(0.0, 0.0, -distance);glRotated(-twist, 0.0, 0.0, 1.0);glRotated(-elevation, 1.0, 0.0, 0.0);glRotated(azimuth, 0.0, 0.0, 1.0);

}


Projection Projection Transformation(1/6)Transformation(1/6)

• Projection• Define a viewing volume

glMatrixMode(GL_PROJECTION);glLoadIdentity();



• 1) Perspective Projection– foreshortening

void glFrustum(GLdouble left, GLdouble right, GLdouble bottom, GLdouble top, GLdouble near, GLdouble far);



void glPerspective(GLdouble fovy, GLdouble aspect, GLdouble near, GLdouble far);

aspect = width / height

• Symmetric perspective-view frustum



• Calculating field of view– Example 3-3.

#define PI 3.1415926535

double calculatingAngle(double size, double distance){

double radtheta, degtheta;

redtheta = 2.0 * atan2(size/2.0, distance); // radiandegtheta = (180.0 * redtheta) /PI; // degreereturn degtheta;

}



• Example 3-1.

void reshape(int w, int h){

glViewport(0, 0, (GLsizei) w, (GLsizei) h);glMatrixMode(GL_PROJECTION);glLoadIdentity();//glFrustum(-1.0, 1.0, -1.0, 1.0, 1.5, 20.0);gluPerspective(80.0, 1.0, 1.5, 20.0);glMatrixMode(GL_MODELVIEW);

}



• 2) Orthographic Projection– 물체의 실제 사이즈와 각도를 유지

void glOrtho(GLdouble left, GLdouble right, GLdouble bottom, GLdouble top, GLdouble near, GLdouble far);


Manipulating the Matrix Manipulating the Matrix Stacks(1/3)Stacks(1/3)

• A stack of matrices– Useful for constructing hierarchical models

• glLoadIdentity()• glMatrixMode()• glMultMatrix()• glLoadMatrix()

void glPushMatrix(void);

void glPopMatrix(void);



void draw_wheel_and_bolts(){

long i;draw_wheel();for(i=0; i<5; i++){

glPushMatrix();glRotatef(70.0*i, 0.0, 0.0, 1.0);glTranslatef(3.0, 0.0, 0.0);draw_bolt();

glPopMatrix();}

}

• Example 3-4. Pushing and Pop Matrix



• The Modelview Matrix Stack• The Projection Matrix Stack


Viewport Viewport Transformation(1/3)Transformation(1/3)

• Viewport • 3D 모델 좌표 -> 스크린 좌표로 변환



– Viewport 의 aspect ratio– Viewing volume 의 aspect ratio

void glViewport(GLint x, GLint y, GLsizei width, GLsizei height);

=> 일치해야 함



• The Transformed Depth Coordinate

– Range : [0.0, 1.0]– near clipping plane 에서 멀어질수록 정밀도 떨어짐

void glDepthRange(GLclampd near, GLclampd far);


Homogeneous Coordinates Homogeneous Coordinates SystemSystem

• Homogeneous Vertex (x, y, z, w)– 위치나 벡터를 나타냄– W≠0 일 경우– W ＝ 0 일 경우

• point at infinity

– Use only non-negative w-values


Additional Clipping PlanesAdditional Clipping Planes• Example 3-5. Wireframe Sphere with two Clipping Planes

GLdouble eqn[4] = {0.0, 1.0, 0.0, 0.0}; // y=0 GLdouble eqn2[4] = {1.0, 0.0, 0.0, 0.0}; // x=0glClipPlane(GL_CLIP_PLANE0, eqn);glEnable(GL_CLIP_PLANE0);


Examples of Composing Examples of Composing Several TransformationSeveral Transformation

• Example 3-6. Planetary System


Examples of Composing Examples of Composing Several TransformationSeveral Transformation

• Example 3-7. Robot Arm


Reverse and Mimicking Reverse and Mimicking TransformationTransformation

• Example 3-8. Take and reverse

Documents

Viewing Korea Univ. Computer Graphics Lab. Hong, Jin Kyung