3D Viewing Transformation

Tong-Yee Lee

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Setup Camera parameters to view 3D scenes

https://www.youtube.com/watch?v=2K4ntXceeqg

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Viewing and viewport Transformation

viewport transformation:

open a window on the monitor screen to

display an image display

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Case A): rotating objects, the camera does not move

Case B): rotating camera, the object does not move

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World space and

eye space coordinate

: visible objects are on

negative Z direction

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World

Coordinate

Local Coordinate

View coordinate

Project plane

OpenGL Graphics

Pipeline

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使用glViewport

指定 Viewport 變換

使用GL_PROJECTION 指定投影變換，OpenGL 支持透視投影和正側投影（一般用於工程製圖）-1<=x,y,z<=1

• 使用GL_MODELVIEW 來同時指定viewing matrix 和modeling matrix.

• OpenGL matrix transform

http://www.songho.ca/opengl/gl_transform.html

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Front and Back Clipping Planes

• Frustum
• Volume of space between front and back clipping planes
• What camera can see – what drawn on screen

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• Near and far clipping planes defined by distance along Look Vector

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• Objects appearing outside of view volume don't get drawn

• Objects intersecting view volume get clipped

OpenGL: Field of View, gluPerspective�Yet another way to set viewing

• Can always use:

glFrustum(left, right, bottom, top, near, far)

• This is certainly sufficient
• But may be inconvenient in some applications
• Can be difficult to get desired view

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• May want to use:

gluPerspective(fovy, aspect, near, far)

• specifies field of view along y axis
• angle θ made by the sides of frustum
• aspect ratio of viewport
• just (width / height)

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World coordinate v.s. eye corrdinate

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Eye-coordinate to Clip coordinate

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Viewing Specification

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Back-face culling

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Back-face culling (trivial rejection)

Viewing direction

Back-face culling (trivial rejection)

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One method of implementing back-face culling is by discarding all triangles where the dot productOne method of implementing back-face culling is by discarding all triangles where the dot product of their surface normal and the camera-to-triangle vector is greater than or equal to zero

where P is the view point, V₀ is the first vertex of a triangle and N is its normal, defined as a cross product of two vectors representing sides of the triangle adjacent to V₀

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V0

V1

V2

P

N

Reject condition

P

N

V₀

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Viewing frustum and backface culling: The mesh is coarsened outside of the viewing frustum. Triangles oriented away from the viewer are coarsened as well. 

View dependent LOD (Level of Details)

https://www.youtube.com/watch?v=wI5kcNhyoSU&ab_channel=HuguesHoppe

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Intuitive Camera Specification

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X axis vector

Y axis vector

Z axis vector

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Intuitive Camera Specification

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Not easy for user to pick up

exact up vector!!

So, we compute v automatically

from up vector.

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Note that matrix storage order is column major

in OpenGL

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Treat yourself (viewer) as an airplane heading to –Zc

Note that: as a viewer is moving, the object is moving in

opposite direction on the viewing plane!!

u (i.e., x) axis

n (i.e.,z) axis

v (i.e., y) axis

俯仰

翻滾

偏航

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Pitch (x), Roll (z) and Yaw (y) rotation

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This is z-like rotation

How about slide()

• Sliding a camera means to move it along one of its own axes-that is in the u,v,n direction-without rotating it.
• Along n means forward or backward
• Along u is left and right
• Along v is up and down
• Assume slide(delU, delV, delN)

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延camera座標軸 walking

i.e., needs to transfer its change to word coordinate on eye position

And eye u, v, w directions are not changed!

Flythrough �a Scene!!!

‘P’-64

=ctrl+‘P’

Homework

#3 (optional) Add

this camera control!!

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Camera Frame

Light v.s. Eye coordinate

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Animate camera along paths

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http://graphics.csie.ncku.edu.tw/Motion_Overview/

Motion Overview of Human Actions

Same v.s. Different camera paths for different motions

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Cinemachine Tutorials | How to make Unity the path animation?

Camera editing Using Unity

https://www.programmersought.com/article/69213097748/

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Cinemachine Tutorials | How to make Unity the path animation?

https://www.programmersought.com/article/69213097748/

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Zoom-in/Zoom-out

Camera moving

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Sliding a camera to create panorama images

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