Chapter 3 Viewing x y z w Vertex

Chapter 3. 뷰잉(Viewing)

정점 변환의 단계 x y z w 오브젝트 좌표 Vertex 눈좌표 Modelview matrix 클립좌표 Projection matrix Perspective matrix 정규화장치좌표 Viewport transformation 윈도우좌표 2013 -2학기 3장 뷰잉

정육면체를 그리는 간단한 [예제 3 – 1]: cube. c #include <GL/glut. h> #include <stdlib. h> void init(void) { gl. Clear. Color (0. 0, 0. 0); gl. Shade. Model (GL_FLAT); } void display(void){ gl. Clear (GL_COLOR_BUFFER_BIT); gl. Color 3 f (1. 0, 1. 0); gl. Load. Identity (); /* 행렬을 클리어 */ glu. Look. At (0. 0, 5. 0, 0. 0, 1. 0, 0. 0); /*뷰잉변환*/ gl. Scalef (1. 0, 2. 0, 1. 0); /* 모델 변환 */ glut. Wire. Cube (1. 0); gl. Flush (); } 2013 -2학기 3장 뷰잉

void reshape (int w, int h){ gl. Viewport (0, 0, (GLsizei) w, (GLsizei) h); gl. Matrix. Mode (GL_PROJECTION); gl. Load. Identity (); gl. Frustum (-1. 0, 1. 5, 20. 0); gl. Matrix. Mode (GL_MODELVIEW); } void keyboard(unsigned char key, int x, int y){ switch (key) { case 27: exit(0); break; } } 2013 -2학기 3장 뷰잉

int main(int argc, char** argv) { glut. Init(&argc, argv); glut. Init. Display. Mode (GLUT_SINGLE | GLUT_RGB); glut. Init. Window. Size (500, 500); glut. Init. Window. Position (100, 100); glut. Create. Window (argv[0]); init (); glut. Display. Func(display); glut. Reshape. Func(reshape); glut. Keyboard. Func(keyboard); glut. Main. Loop(); return 0; } 2013 -2학기 3장 뷰잉

#include <GL/glut. h> #include <stdlib. h> void init(void) { gl. Clear. Color (0. 0, 0. 0); gl. Shade. Model (GL_FLAT); } void draw_triangle(void){ gl. Begin (GL_LINE_LOOP); gl. Vertex 2 f(0. 0, 25. 0); gl. Vertex 2 f(25. 0, -25. 0); gl. Vertex 2 f(-25. 0, -25. 0); gl. End(); } 2013 -2학기 3장 뷰잉

뷰잉 및 모델링 변환 void display(void){ gl. Clear (GL_COLOR_BUFFER_BIT); gl. Color 3 f (1. 0, 1. 0); gl. Load. Identity (); gl. Color 3 f (1. 0, 1. 0); draw_triangle (); gl. Enable (GL_LINE_STIPPLE); gl. Line. Stipple (1, 0 x. F 0 F 0); gl. Load. Identity (); gl. Translatef (-20. 0, 0. 0); draw_triangle (); 2013 -2학기 3장 뷰잉

gl. Line. Stipple (1, 0 x. F 00 F); gl. Load. Identity (); gl. Scalef (1. 5, 0. 5, 1. 0); draw_triangle (); gl. Line. Stipple (1, 0 x 8888); gl. Load. Identity (); gl. Rotatef (90. 0, 1. 0); draw_triangle (); gl. Disable (GL_LINE_STIPPLE); gl. Flush (); } 2013 -2학기 3장 뷰잉

void reshape (int w, int h) { gl. Viewport (0, 0, (GLsizei) w, (GLsizei) h); gl. Matrix. Mode (GL_PROJECTION); gl. Load. Identity (); if (w <= h) gl. Ortho (-50. 0, -50. 0*(GLfloat)h/(GLfloat)w, -1. 0, 1. 0); else gl. Ortho (-50. 0*(GLfloat)w/(GLfloat)h, -50. 0, -1. 0, 1. 0); gl. Matrix. Mode(GL_MODELVIEW); } 2013 -2학기 3장 뷰잉

void keyboard(unsigned char key, int x, int y) { switch (key) { case 27: exit(0); break; } } 2013 -2학기 3장 뷰잉

int main(int argc, char** argv) { glut. Init(&argc, argv); glut. Init. Display. Mode (GLUT_SINGLE | GLUT_RGB); glut. Init. Window. Size (500, 500); glut. Init. Window. Position (100, 100); glut. Create. Window (argv[0]); init (); glut. Display. Func(display); glut. Reshape. Func(reshape); glut. Keyboard. Func (keyboard); glut. Main. Loop(); return 0; } 2013 -2학기 3장 뷰잉

Nate Robins 의 변환관련 튜토 리얼 http: //www. cs. utah. edu/~narobins/opengl. html transformation 프로그램 실행 2013 -2학기 3장 뷰잉

void glu. Perspective(GLdouble fovy, GLdouble aspect, GLdouble near, GLdouble far); ◦ gl. Frustum()과 같은 관측 공간 생성, 지정방식의 차이가 있다. ◦ fovy는 y축 방향의 FOV 각도를 나타냄 ◦ aspect 인자는 절두체의 종횡비(x/y, 정사각형의 경우 종횡비는 1. 0이다) fovy 라 메 카 near w h far Aspect = w/h 2013 -2학기 3장 뷰잉

예제 3 -4 행렬을 push 또는 pop 하기 draw_wheel_and_bolts() { long i; draw_wheel(); for (i = 0; i < 5; i++) { gl. Push. Matrix(); gl. Rotatef(72. 0*i, 0. 0, 1. 0); gl. Translatef(3. 0, 0. 0); draw_bolt(); gl. Pop. Matrix(); } } 2013 -2학기 3장 뷰잉

draw_body_and_wheel_and_bolts() { draw_car_body(); gl. Push. Matrix(); gl. Translatef(40, 0, 30); /* 첫번째 바퀴의 위치로 이동 */ draw_wheel_and_bolts(); gl. Pop. Matrix(); gl. Push. Matrix(); gl. Translatef(40, 0, -30); /* 두 번째 바퀴의 위치로 이동 */ draw_wheel_and_bolts(); gl. Pop. Matrix(); … } 2013 -2학기 3장 뷰잉

클리핑 평면에 대한 코드 [예제 3 – 5 ]: clip. c #include <GL/glut. h> #include <stdlib. h> void init(void) { gl. Clear. Color (0. 0, 0. 0); gl. Shade. Model (GL_FLAT); } void display(void){ GLdouble eqn[4] = {0. 0, 1. 0, 0. 0}; GLdouble eqn 2[4] = {1. 0, 0. 0}; gl. Clear(GL_COLOR_BUFFER_BIT); 2013 -2학기 3장 뷰잉

gl. Color 3 f (1. 0, 1. 0); gl. Push. Matrix(); gl. Translatef (0. 0, -5. 0); /* 아래쪽 절반 클리핑 -- y < 0 */ gl. Clip. Plane (GL_CLIP_PLANE 0, eqn); gl. Enable (GL_CLIP_PLANE 0); /* 왼쪽 절반 클리핑 -- x < 0 */ gl. Clip. Plane (GL_CLIP_PLANE 1, eqn 2); gl. Enable (GL_CLIP_PLANE 1); gl. Rotatef (90. 0, 1. 0, 0. 0); glut. Wire. Sphere(1. 0, 20, 16); gl. Pop. Matrix(); gl. Flush (); } 2013 -2학기 3장 뷰잉

void reshape (int w, int h){ gl. Viewport (0, 0, (GLsizei) w, (GLsizei) h); gl. Matrix. Mode (GL_PROJECTION); gl. Load. Identity (); glu. Perspective(60. 0, (GLfloat) w/(GLfloat) h, 1. 0, 20. 0); gl. Matrix. Mode (GL_MODELVIEW); } void keyboard(unsigned char key, int x, int y){ switch (key) { case 27: exit(0); break; } } 2013 -2학기 3장 뷰잉

int main(int argc, char** argv) { glut. Init(&argc, argv); glut. Init. Display. Mode (GLUT_SINGLE | GLUT_RGB); glut. Init. Window. Size (500, 500); glut. Init. Window. Position (100, 100); glut. Create. Window (argv[0]); init (); glut. Display. Func(display); glut. Reshape. Func(reshape); glut. Keyboard. Func(keyboard); glut. Main. Loop(); return 0; } 2013 -2학기 3장 뷰잉

여러가지 변환 함께 사용하기 태양계 만들기 #include <GL/glut. h> #include <stdlib. h> static int year = 0, day = 0; void init(void) { gl. Clear. Color (0. 0, 0. 0); gl. Shade. Model (GL_FLAT); } 2013 -2학기 3장 뷰잉

void display(void){ gl. Clear (GL_COLOR_BUFFER_BIT); gl. Color 3 f (1. 0, 1. 0); gl. Push. Matrix(); glut. Wire. Sphere(1. 0, 20, 16); /* 태양을 그린다 */ gl. Rotatef ((GLfloat) year, 0. 0, 1. 0, 0. 0); gl. Translatef (2. 0, 0. 0); gl. Rotatef ((GLfloat) day, 0. 0, 1. 0, 0. 0); glut. Wire. Sphere(0. 2, 10, 8); /* 작은 행성을 그린다 */ gl. Pop. Matrix(); glut. Swap. Buffers(); } 2013 -2학기 3장 뷰잉

void reshape (int w, int h) { gl. Viewport (0, 0, (GLsizei) w, (GLsizei) h); gl. Matrix. Mode (GL_PROJECTION); gl. Load. Identity (); glu. Perspective(60. 0, (GLfloat) w/(GLfloat) h, 1. 0, 20. 0); gl. Matrix. Mode(GL_MODELVIEW); gl. Load. Identity(); glu. Look. At (0. 0, 5. 0, 0. 0, 1. 0, 0. 0); } 2013 -2학기 3장 뷰잉

void keyboard (unsigned char key, int x, int y) { switch (key) { case 'd': day = (day + 10) % 360; glut. Post. Redisplay(); break; case 'D': day = (day - 10) % 360; glut. Post. Redisplay(); break; 2013 -2학기 3장 뷰잉

case 'y': year = (year + 5) % 360; glut. Post. Redisplay(); break; case 'Y': year = (year - 5) % 360; glut. Post. Redisplay(); break; case 27: exit(0); break; default: break; } } 2013 -2학기 3장 뷰잉

int main(int argc, char** argv) { glut. Init(&argc, argv); glut. Init. Display. Mode (GLUT_DOUBLE | GLUT_RGB); glut. Init. Window. Size (500, 500); glut. Init. Window. Position (100, 100); glut. Create. Window (argv[0]); init (); glut. Display. Func(display); glut. Reshape. Func(reshape); glut. Keyboard. Func(keyboard); glut. Main. Loop(); return 0; } 2013 -2학기 3장 뷰잉

로봇팔 만들기 #include <GL/glut. h> #include <stdlib. h> static int shoulder = 0, elbow = 0; void init(void) { gl. Clear. Color (0. 0, 0. 0); gl. Shade. Model (GL_FLAT); } 2013 -2학기 3장 뷰잉

void display(void) { gl. Clear (GL_COLOR_BUFFER_BIT); gl. Push. Matrix(); gl. Translatef (-1. 0, 0. 0); gl. Rotatef ((GLfloat) shoulder, 0. 0, 1. 0); gl. Translatef (1. 0, 0. 0); gl. Push. Matrix(); gl. Scalef (2. 0, 0. 4, 1. 0); glut. Wire. Cube (1. 0); gl. Pop. Matrix(); 2013 -2학기 3장 뷰잉

gl. Translatef (1. 0, 0. 0); gl. Rotatef ((GLfloat) elbow, 0. 0, 1. 0); gl. Translatef (1. 0, 0. 0); gl. Push. Matrix(); gl. Scalef (2. 0, 0. 4, 1. 0); glut. Wire. Cube (1. 0); gl. Pop. Matrix(); glut. Swap. Buffers(); } 2013 -2학기 3장 뷰잉

void reshape (int w, int h) { gl. Viewport (0, 0, (GLsizei) w, (GLsizei) h); gl. Matrix. Mode (GL_PROJECTION); gl. Load. Identity (); glu. Perspective(65. 0, (GLfloat) w/(GLfloat) h, 1. 0, 20. 0); gl. Matrix. Mode(GL_MODELVIEW); gl. Load. Identity(); gl. Translatef (0. 0, -5. 0); } 2013 -2학기 3장 뷰잉

void keyboard (unsigned char key, int x, int y){ switch (key) { case 's': shoulder = (shoulder + 5) % 360; glut. Post. Redisplay(); break; case 'S': shoulder = (shoulder - 5) % 360; glut. Post. Redisplay(); break; case 'e': elbow = (elbow + 5) % 360; glut. Post. Redisplay(); break; 2013 -2학기 3장 뷰잉

case 'E': elbow = (elbow - 5) % 360; glut. Post. Redisplay(); break; case 27: exit(0); break; default: break; } } 2013 -2학기 3장 뷰잉

int main(int argc, char** argv) { glut. Init(&argc, argv); glut. Init. Display. Mode (GLUT_DOUBLE | GLUT_RGB); glut. Init. Window. Size (500, 500); glut. Init. Window. Position (100, 100); glut. Create. Window (argv[0]); init (); glut. Display. Func(display); glut. Reshape. Func(reshape); glut. Keyboard. Func(keyboard); glut. Main. Loop(); return 0; } 2013 -2학기 3장 뷰잉

int glu. Un. Project(GLdouble winx, GLdouble winy, GLdouble winz, const GLdouble model. Matrix[16], const GLdouble proj. Matrix[16], const GLint viewport[4], GLdouble *objx, GLdouble *objy, GLdouble *objz); ◦ 모델뷰 행렬(model. Matrix)과 투영행렬(proj. Matrix), 뷰포트 (viewport)로 정의된 변환을 사용하여 주어진 윈도우 좌표 (winx, winy, winz)를 오브젝트 좌표(objx, objy, objz)에 매핑한 다. ◦ 함수가 성공적이면 GL_TRUE, 에러가 발생하면 GL_FALSE를 리턴한다. 2013 -2학기 3장 뷰잉

Int glu. Un. Project 4(GLdouble winx, GLdouble winy, GLdouble winz, gldouble clipw, const GLdouble model. Matrix[16], const GLdouble proj. Matrix[16], const GLint viewport[4], Glclampd z. Near, Glclampd z. Far, GLdouble *objx, GLdouble *objy, GLdouble *objz); ◦ glu. Un. Project()와 비슷. GLU 1. 3에서 변경되어 glu. Un. Project 4() 는 표준값이 아닌 gl. Depth. Range 값뿐만 아니라 1보다 큰 w 좌 표값도 처리할 수 있다. 2013 -2학기 3장 뷰잉

Int glu. Project(GLdouble objx, GLdouble objy, GLdouble objz, const GLdouble model. Matrix[16], const GLdouble proj. Matrix[16], const GLint viewport[4], GLdouble *winx, GLdouble *winy, GLdouble *winz); ◦ 모델뷰 행렬(model. Matrix), 투영행렬 (proj. Matrix), 뷰포트(viewport) 로 정의된 변환을 통해 주어진 오브젝트 좌표(objx, objy, objz)를 윈도우 좌표에 2013 -2학기 3장 뷰잉 매핑한다.

기하 프로세싱 파이프라인을 반대로 실행하기 [예제 3 – 8 ]: unproject. c #include <GL/glut. h> #include <stdlib. h> #include <stdio. h> void display(void){ gl. Clear(GL_COLOR_BUFFER_BIT); gl. Flush(); } void reshape(int w, int h){ 2013 -2학기 3장 뷰잉

glu. Perspective (45. 0, (GLfloat) w/(GLfloat) h, 1. 0, 100. 0); gl. Matrix. Mode(GL_MODELVIEW); gl. Load. Identity(); } void mouse(int button, int state, int x, int y) { GLint viewport[4]; GLdouble mvmatrix[16], projmatrix[16]; GLint realy; /* Open. GL y 좌표 위치 */ GLdouble wx, wy, wz; /* 변환된 x, y , z 월드 좌표 */ 2013 -2학기 3장 뷰잉

switch (button) { case GLUT_LEFT_BUTTON: if (state == GLUT_DOWN) { gl. Get. Integerv (GL_VIEWPORT, viewport); gl. Get. Doublev (GL_MODELVIEW_MATRIX, mvmatrix); gl. Get. Doublev (GL_PROJECTION_MATRIX, projmatrix); /* viewport[3]은 윈도우의 높이를 픽셀 단위로 나타낸다는 것 주의 */ realy = viewport[3] - (GLint) y - 1; printf ("Coordinates at cursor are (%4 d, %4 d)n", x, realy); glu. Un. Project ((GLdouble) x, (GLdouble) realy, 0. 0, mvmatrix, projmatrix, viewport, &wx, &wy, &wz); printf ("World coords at z=0. 0 are (%f, %f)n", wx, wy, wz); 2013 -2학기 3장 뷰잉

glu. Un. Project ((GLdouble) x, (GLdouble) realy, 1. 0, mvmatrix, projmatrix, viewport, &wx, &wy, &wz); printf ("World coords at z=1. 0 are (%f, %f)n", wx, wy, wz); } break; case GLUT_RIGHT_BUTTON: if (state == GLUT_DOWN) exit(0); break; default: break; } } 2013 -2학기 3장 뷰잉

void keyboard(unsigned char key, int x, int y) { switch (key) { case 27: exit(0); break; } } 2013 -2학기 3장 뷰잉

int main(int argc, char** argv) { glut. Init(&argc, argv); glut. Init. Display. Mode (GLUT_SINGLE | GLUT_RGB); glut. Init. Window. Size (500, 500); glut. Init. Window. Position (100, 100); glut. Create. Window (argv[0]); glut. Display. Func(display); glut. Reshape. Func(reshape); glut. Keyboard. Func (keyboard); glut. Mouse. Func(mouse); glut. Main. Loop(); return 0; } 2013 -2학기 3장 뷰잉