Transformations

6th W k 20116th Week, 2011

Line Preserving TransformationsLine-Preserving Transformations

■ Two classes of transformations of importance■ Two classes of transformations of importance to CG that preserves lines

AffineAffine and projectiveprojective transformationstransformations■■ AffineAffine and projectiveprojective transformationstransformations

■■ Homogeneous coordinatesHomogeneous coordinatesV i■ Vectors: (x, y, z, 0), points: (x, y, z, w)=(x/w, y/w, z/w, 1)

■ 4x4 matrices: modeling, viewing, and projection

■ OpenGL pipelineModel-View Projection

Vertices Vertices

■ Model-view: to position objects relative to camera■ Projection: to specify clipping volume and map

vertices to a normalized coordinate system

OpenGL TransformationsOpenGL Transformations

■ Translation■ Translation

R t ti

void glTranslate{fd}(type dx, type dy, type dz);void glTranslate{fd}(type dx, type dy, type dz);

■ Rotationvoid glRotate{fd}(type angle, type ax, type ay, type az);void glRotate{fd}(type angle, type ax, type ay, type az);

■ Scalingvoid glScale{fd}(type sx, type sy, type sz);void glScale{fd}(type sx, type sy, type sz);

■ ConcatenationglMatrixMode(GL_MODELVIEW);glLoadIdentity();glTranslatef(xf, yf, zf);glRotatef(angle, ax, ay, az);lS l f( )glScalef(sx, sy, sz);glTranslate(-xf, -yf, -zf);

GLU Quadric ObjectsGLU Quadric Objects

■ Cylinders■ Cylinders■ Disks or partial disks■ Spheres

GLUquadricObj* gluNewQuadric( void );GLUquadricObj* gluNewQuadric( void );

void gluDeleteQuadric( GLUquadricObj *qobj );void gluDeleteQuadric( GLUquadricObj *qobj );

void gluCylinder(GLUquadricObj *qobj, GLdouble baseRadius, GLdouble topRadius,GLdouble height, GLint slices, GLint stacks);

void gluCylinder(GLUquadricObj *qobj, GLdouble baseRadius, GLdouble topRadius,GLdouble height, GLint slices, GLint stacks);

void gluDisk(GLUquadricObj *qobj, GLdouble innerRadius, GLdouble outerRadius,void gluDisk(GLUquadricObj *qobj, GLdouble innerRadius, GLdouble outerRadius,GLint slices, GLint loops);GLint slices, GLint loops);

void gluPartialDisk(GLUquadricObj *qobj, GLdouble innerRadius, GLdouble outerRadius,GLint slices, GLint loops, GLdouble startAngle, GLdouble sweepAngle);

void gluPartialDisk(GLUquadricObj *qobj, GLdouble innerRadius, GLdouble outerRadius,GLint slices, GLint loops, GLdouble startAngle, GLdouble sweepAngle);

void gluSphere(GLUquadricObj *qobj, GLdouble radius, GLint slices, GLint stacks);void gluSphere(GLUquadricObj *qobj, GLdouble radius, GLint slices, GLint stacks);

GLUT Library (1)GLUT Library (1)

GLUT Library (2)GLUT Library (2)

■■ glut hglut h ( /Microsoft SDKs/Windows/v6 0A/Include/gl)■■ glut.hglut.h ( /Microsoft SDKs/Windows/v6.0A/Include/gl)

■■ glut32.libglut32.lib ( /Microsoft SDKs/Windows/v6.0A/Lib)

■■ glut32.dllglut32.dll ( Windows/system32)void glutWireSphere(GLdouble radius, GLint slices, Glint stacks);void glutSoildSphere(GLdouble radius, GLint slices, Glint stacks);void glutWireSphere(GLdouble radius, GLint slices, Glint stacks);void glutSoildSphere(GLdouble radius, GLint slices, Glint stacks);g p ( , , );g p ( , , );

void glutWireCone(GLdouble base, GLdouble height, GLint slices, Glint stacks);void glutSoildCone(GLdouble base, GLdouble height, GLint slices, Glint stacks);void glutWireCone(GLdouble base, GLdouble height, GLint slices, Glint stacks);void glutSoildCone(GLdouble base, GLdouble height, GLint slices, Glint stacks);

void glutWireCube(GLdouble size);void glutWireCube(GLdouble size);

void glutWireTorus(GLdouble inner, GLdouble outer, GLint sides, Glint slices);void glutSoildTorus(GLdouble inner, GLdouble outer, GLint sides, Glint slices);void glutWireTorus(GLdouble inner, GLdouble outer, GLint sides, Glint slices);void glutSoildTorus(GLdouble inner, GLdouble outer, GLint sides, Glint slices);

void glutWireTetrahedron();void glutWireTetrahedron();void glutWireCube(GLdouble size);void glutSoildCube(GLdouble size);void glutWireCube(GLdouble size);void glutSoildCube(GLdouble size);

void glutWireTeapot(GLdouble size);void glutSoildTeapot(GLdouble size);void glutWireTeapot(GLdouble size);void glutSoildTeapot(GLdouble size);

void glutWireTetrahedron();void glutSoildTetrahedron();void glutWireOctahedron();void glutWireOctahedron();void glutWireDodecahedron();

void glutWireTetrahedron();void glutSoildTetrahedron();void glutWireOctahedron();void glutWireOctahedron();void glutWireDodecahedron();void glutSoildTeapot(GLdouble size);void glutSoildTeapot(GLdouble size); void glutWireDodecahedron();void glutSoildDodecahedron();void glutWireIcosahedron();void glutWireIcosahedron();

void glutWireDodecahedron();void glutSoildDodecahedron();void glutWireIcosahedron();void glutWireIcosahedron();

GLUT Library (3)GLUT Library (3)

GLUT Library (4)GLUT Library (4)

GLUT Library (5)GLUT Library (5)

Drawing a Wire CubeDrawing a Wire Cube

실행 결과 A Wire Cube실행 결과 – A Wire Cube

Hierarchical Models (1)Hierarchical Models (1)

■ Parts of a model depend on one another■ Parts of a model depend on one another■ If one part moves, it cause other parts to move

A Simple Robot Arm Hierarchical Representation

Hierarchical Models (2)Hierarchical Models (2)

■ A figure can be constructed from GLU spheres■ A figure can be constructed from GLU spheres and cylinders

Hierarchical representation

Hierarchical Models (3)Hierarchical Models (3)

■ Ex) simple robot arm■ Ex) simple robot arm

gluCylinder( GLUqadricObj *q,gluCylinder( GLUqadricObj *q,g y ( q j q,GLdouble base_radius,GLdouble top_radius,GLdouble height,

g y ( q j q,GLdouble base_radius,GLdouble top_radius,GLdouble height,

BaseGLdouble height,GLint slices, Glint stacks );

GLdouble height,GLint slices, Glint stacks );

l tS lidC b ( GLd bl i )l tS lidC b ( GLd bl i )glutSolidCube( GLdouble size );glutWireCube( GLdouble size );glutSolidCube( GLdouble size );glutWireCube( GLdouble size );

Lower arm Upper arm

Hierarchical Models (4)Hierarchical Models (4)

Hierarchical Models (5)Hierarchical Models (5)

Hierarchical Models (6)Hierarchical Models (6)

Hierarchical Models (7)Hierarchical Models (7)

실행 결과 Hierarchical Models실행 결과 – Hierarchical Models

연습 문제 (1)연습 문제 (1)

■ Cylinder를 회전시켜 옆면이 보이도록 만드시오■ Cylinder를 회전시켜 옆면이 보이도록 만드시오.

Base ArmBase Arm

glPushMatrix( ) and glPopMatrix( )glPushMatrix( ) and glPopMatrix( )

■ Performing a transformation and then■ Performing a transformation and then returning to the same state as before its executionexecution

■ Ex) instance transformationglPushMatrix();glPushMatrix();

glTranslatef(.....);g ( )glRotatef(.....);glScalef(.....);

/* draw object here */

glPopMatrix();glPopMatrix();glPopMatrix();glPopMatrix();

실행 결과 Base Arm실행 결과 – Base Arm

연습 문제 (2)연습 문제 (2)

■ Box를 평행이동 시켜 밑면 중심이 원점에 위치■ Box를 평행이동 시켜 밑면 중심이 원점에 위치시키시오.

Lower ArmLower Arm

실행 결과 Lower Arm실행 결과 – Lower Arm

Upper Arm (1)Upper Arm (1)

실행 결과 Upper Arm (1)실행 결과 – Upper Arm (1)

연습 문제 (3)연습 문제 (3)

■ Upper arm의 밑면 중심이 원점에 놓이도록 평행■ Upper arm의 밑면 중심이 원점에 놓이도록 평행이동 시키시오.

Upper Arm (2)Upper Arm (2)

실행 결과 Upper Arm (2)실행 결과 – Upper Arm (2)

연습 문제 (4)연습 문제 (4)

■ Base arm lower arm upper arm의 순서로 겹치■ Base arm, lower arm, upper arm의 순서로 겹치지 않게 배치하시오.

Viewing 파라미터를 변경하여 화면에 보이는 공간을■ Viewing 파라미터를 변경하여, 화면에 보이는 공간을넓히시오. (모든 오브젝트가 보이도록 만드시오.)

Simple Robot Arm (1)Simple Robot Arm (1)

Simple Robot Arm (2)Simple Robot Arm (2)

실행 결과 Simple Robot Arm (1)실행 결과 – Simple Robot Arm (1)

연습 문제 (5)연습 문제 (5)

■ Simple Robot Arm이 화면의 중앙에 놓이도록■ Simple Robot Arm이 화면의 중앙에 놓이도록Object 전체를 평행이동 시키시오.

Simple Robot Arm (3)Simple Robot Arm (3)

실행 결과 Simple Robot Arm (2)실행 결과 – Simple Robot Arm (2)

Transformation of Hierarchical Models

■ Ex) simple robot arm■ Ex) simple robot arm

Lower ArmBase Upper Arm

Base Arm Rotation (1)Base Arm Rotation (1)

Base Arm Rotation (2)Base Arm Rotation (2)

GetAsyncKeyState( )GetAsyncKeyState( )

Base Arm Rotation (3)Base Arm Rotation (3)

실행 결과 Base Arm Rotation실행 결과 – Base Arm Rotation

연습 문제 (6)연습 문제 (6)

■ Lower arm과 upper arm도 회전이 되도록 프로■ Lower arm과 upper arm도 회전이 되도록 프로그램을 수정하시오.

↑와 ↓ 화살표키 lower arm의 회전■ ↑와 ↓ 화살표키 – lower arm의 회전■ PageUp 과 PageDown 키 – upper arm의 회전

■ Base arm이 평행이동 하도록 수정하시오.■ ‘A’와 ‘D’ – x축 방향으로 좌우 이동■ ‘W’와 ‘S’ – z축 방향으로 전후 이동

Rotation of a Simple Robot ArmRotation of a Simple Robot Arm