1. Viewing System
한신대학교
류승택

2. 3D Transformation 3D Transformation Modeling Coordinates (Xm, Ym, Zm)
World
Coordinates
(Xw, Yw, Zw)
Viewing
Transformation
Viewing
Coordinates
(Xv, Yv, Zv)
Projection
Transformation
Projection
Coordinates
(Xp, Yp)
Device
Coordinates
(Xd, Yd)
Workstation
Transformation

3. Viewing Transformation (1/5)
Pview = R T
Translation (T)
Rotation (R)

4. Scalar Product Scalar Product (= dot product) (내적)
The sum of the products of their corresponding components
Using the law of cosine, the angle between two vectors a and b satisfies the equation
Scalar Product Properties
If a is perpendicular to b, then a b
Scalar ??
A quantity that is completely specified by its magnitude and has no direction.

5. Scalar Product Scalar Product
Use the dot product to project a vector onto another vector
V  unit vector
The dot product of V and W  the length the projection of W onto V
A property of dot product used in CG
Sign W
V (unit vector) X

6. Vector Product Vector Product (= Cross Product) 외적
c = a x b  c is perpendicular to both a and b
 direction: right-hand property
Perpendicular to the pane defined by a and b c b a

7. Viewing Transformation (2/5)
N vector
V vector
Up vector
U vector V -N Up

8. Viewing Transformation (3/5)
Another Way
대문자 V  Up 벡터를 말함

9. Viewing Transformation (4/5)
Projection
Parallel Projection
Parallel
Perspective

10. Viewing Transformation (5/5)
Perspective Projection

11. Conclusion (1/2) 3D Viewing Transformation Parallel Projection
(Xp, Yp, 0, 1)
(Xw, Yw, Zw, 1)
(Xv, Yv, Zv, 1)

12. Conclusion (2/2) 3D Viewing Transformation Perspective Projection
(Xp, Yp, Zp, 1)
(Xw, Yw, Zw, 1)
(Xv, Yv, Zv, 1)

13. 3D Viewing Process (1/2) 3D Viewing Process Modeling Coordinates
(Xm, Ym, Zm)
Modeling
Transformation
World
Coordinates
(Xw, Yw, Zw)
Viewing
Transformation
Viewing
Coordinates
(Xv, Yv, Zv)
Projection
Transformation
Projection
Coordinates
(Xp, Yp)
Device
Coordinates
(Xd, Yd)
Workstation
Transformation

14. 3D Viewing Process (2/2) 3D Viewing Process Modeling Coordinates
(Xm, Ym, Zm)
Modeling
Transformation
World
Coordinates
(Xw, Yw, Zw)
Viewing
Transformation
Viewing
Coordinates
(Xv, Yv, Zv)
Normalizing
Transformation
Normalizing
Coordinates
(Xn, Yn, Zn)
Clipping
Clipping
Coordinates
(Xc, Yc, Zc)
Projection
Transformation
Projection
Coordinates
(Xp, Yp)
Workstation
Transformation
Device
Coordinates
(Xd, Yd)