1. THREE-DIMENSIONAL VIEWING I12
고려대학교 컴퓨터 학과
김 창 헌

2. Contents Classification of Planar Projections Parallel Projection
Isometric Projection
Oblique Projection
Perspective projection
Vanishing Point
Special techniques

3. In 3D viewing system...
void mouse(int button, int state, int x, int y) {...}
void myReshape(int w, int h) {
glMatrixMode(GL_PROJECTION);
glLoadIdentity();
// gluPerspective(45.0, (GLfloat)h/ (GLfloat)w, 0.1, );
glOrtho(-10.0,10.0,-10.0,10.0,10.0,200.0);
glMatrixMode(GL_MODELVIEW);
glViewport(0,0,w,h); }
void main()
glutInitWindowSize(500, 500);
glutInitDisplayMode(GLUT_RGB | GLUT_DEPTH | GLUT_DOUBLE);
glutCreateWindow(”Cylinder mapping program");
LoadTexture();
PencilObj = gluNewQuadric();
gluQuadricTexture(PencilObj, GL_TRUE);
glutReshapeFunc(myReshape);
glutDisplayFunc(display);
glutMouseFunc(mouse);
glutMotionFunc(motion);
glutMainLoop();
#include < Header files...>
#define CONSTANTS...
// declare global variables..
void display (void) {
glEnable(GL_TEXTURE_2D);
glTexEnvi(GL_TEXTURE_ENV,
GL_TEXTURE_ENV_MODE, GL_DECAL);
glClearColor(1.0,1.0,1.0,1.0);
glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);
glPushMatrix();
glRotatef(90.0,-1.0,0.0,0.0);
glRotatef(angle1, 0.0, 1.0, 0.0);
glRotatef(angle2, 1.0, 0.0, 0.0);
gluQuadricNormals(PencilObj, GLU_FLAT);
gluQuadricDrawStyle(PencilObj, GLU_FILL);
glCallList(Texture);
gluCylinder(PencilObj, 8.0, 8.0, 10.0, 20, 1);
glPopMatrix();
glFlush();
glutSwapBuffers(); }

4. Classification of Planar Projections
Parallel
Perspective
Oblique
Orthographic
1-pt
2-pt
3-pt
Multiview
Orthographic
Cavalier
Cabinet
Axonometric
Isometric
Dimetric
Trimetric

5. Projections
Parallel Projection
Perspective Projection

6. Parallel Projection Orthographic parallel projection
the projection is perpendicular to the view plane
Oblique parallel projection
The projectors are inclined with respect to the view plane

7. Orthographic Projection
Multiview orthographic
Singlview orthographic - Axonometric projection
- The planes of the object remain
parallel to the principle planes
of projection
- Orthographic projections that display
more than one face of an object
- The planes of the object are
inclined with respect to the
projection plane

8. Orthographic coordinates

9. Isometric Projection Definition
- The most commonly used axonometric projection
- Aligning the projection plane so that it intersects each coordinate axis in which the object is defined at the same distance from the origin
- The angles between the principal axis are all equal to 120º
Isometric axis
Isometric
Axonometric

10. Isometric Projection(con’t)

11. Isometric Projection(con’t)
The projections of the unit vectors are found as follows:
The projected length of each unit vector is
So, the condition for the isometric projection is,
(1)
(2)

12. Isometric Projection(con’t)A
and,
Foreshortening ratio F :

13. Oblique projection

14. Oblique projection(con’t)

15. Oblique projection(con’t)
Cavalier projection ( )
Cabinet projection ( )

16. Perspective Projection

17. Perspective Projection (con’t)

18. Perspective Projection(con’t)
Orthographic
projection
Perspective
transformation
Center of Projection
on the x axis
Center of Projection
on the y axis

19. Perspective Projection(con’t)
2-point perspectives
3-point perspectives

20. Vanishing point
- When using perspective transformation equations, any set of parallel
lines in the object that are not parallel to the plane are projected into
converging lines.
- The point at which a set of projected parallel lines appears to converge
is called a vanishing point.
- A scene can have any number of vanishing points, depending on how
many sets of parallel lines there are in the scene

21. Principal vanishing point
The vanishing point for any set of lines that are parallel to one of
the principal axis of an object
One-point perspective projection
Two-point perspective projection
Three-point perspective projection

22. Vanishing point a’ a Vanishing line View plane Vanishing Point
Projection
Center a’ a

23. Vanishing point(con’t)
View plane
If lines are parallel to the projection plane,
then no vanishing point.

24. Special techniques Two point Perspective One point Perspective
Three point
Perspective