Viewing

ViewingViewingKorea 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


Viewing Transformation(2/6)Viewing Transformation(2/6)

Default camera position Using gluLookAt()


Viewing Transformation(3/6)Viewing Transformation(3/6)• 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();

}


Viewing Transformation(4/6)Viewing Transformation(4/6)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);


Viewing Transformation(5/6)Viewing Transformation(5/6)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);



Viewing Transformation(6/6)Viewing Transformation(6/6)• 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 결정void 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

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