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컴퓨터 그래픽스를 위한 기하학적 기초 (Line Geometry for Computer Graphics)

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Presentation on theme: "컴퓨터 그래픽스를 위한 기하학적 기초 (Line Geometry for Computer Graphics)"— Presentation transcript:

1 컴퓨터 그래픽스를 위한 기하학적 기초 (Line Geometry for Computer Graphics)
서울대학교 컴퓨터공학부 김명수

2 View Volume

3 3D Culling and Clipping

4 Viewing Transformation

5 Do you remember?

6 Line Equation in 2D

7 Line in Plane

8 Line in Homogeneous Coords

9 Line from Two Points in Plane

10 Using Homogeneous Coord

11 Example

12 Intersecting Two Lines

13 Example

14 Plane in Space

15 Plane by Three Points

16 Plane by Three Points

17 Wedge Product

18 Point by Three Planes

19 Perspective Projection in 2D

20 Its Matrix Form

21 Parallel Projection in 2D

22 Its Matrix Form

23 Projection in 3D

24 Projection in 3D

25 Projection in 3D

26 Projection in 3D

27 Perspective Projection in 3D

28 Parallel Projection in 3D

29 Transformation to X-axis

30 Its Geometric Meaning

31 Transformation to XY-Plane

32 Conclusions (Line Geometry in Computer Graphics)
Duality Between Points and Lines in 2D Duality Between Points and Planes in 3D Intersecting Two Lines (or Three Planes) using Cross Products (or Wedge Products) Simple Viewing Transformation Matrix Perspective and Parallel Projection in the Same Way


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