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Viewing System

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

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Viewing System

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  1. Viewing System 한신대학교 류승택

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

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

  4. a b 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 Scalar ?? A quantity that is completely specified by its magnitude and has no direction.

  5. V (unit vector) W X 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

  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 Perspective Parallel

  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) World Coordinates (Xw, Yw, Zw) Viewing Coordinates (Xv, Yv, Zv) Modeling Transformation Viewing Transformation Device Coordinates (Xd, Yd) Projection Coordinates (Xp, Yp) Projection Transformation Workstation Transformation

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

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