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RealTime??!! It’s amazing!!!!

More Transforms 三月 11, 2008

Filed under: 3D Graph — kevinlin @ 5:29 下午

一位美國的詩人Robert Penn Warren曾寫:
“What if angry vectors veer
Round your sleeping head, and form.
There’s never need to fear
Violence of the poor world’s abstract storm."
很符合Transforms要表達的意涵…

Transform在圖學中幫助我們定位(position)、變形(reshape)、移動物件燈光攝影機(animate objects、lights、cameras)

Real-Time Rendering書中將Transforms分成5個小節: Basic Transforms、Special Matrix Transforms and Operations、Quaternions、Vertex Blending、Projections.

上一篇是屬於Basic Transforms。稍微解說一下
1.Linear Transformations 是說 F(a)是線性的
F(a+b) = F(a) + F(b) and F(ka) = kF(a)

2.Affine Transformations 是指linear transformations後面多一個translation.所以可以這樣說,所有的linear transformations都是affine transformations. 但是反過來就不事了.
大概是這樣 v’ = vM + b. 

3.Invertible Transformations是指轉換可逆.就是可以Undo它。
假如F(a)是invertible就是表示會有一個F-1使得F-1(F(a)) = a

4.Angle-preserving Transformations很簡單,就是夾角在經過transform後是不變的。

5.Orthogonal Transformations ,會被稱為Orthogonal Transformations的就只有Translation、Rotation跟Reflection。

6.Rigid Body Transformations,顧名思義,這東西就只是改變位置跟方向而已,其他都是不變的。Reflection不能算是Rigid Body Transformations.

Special Matrix Transforms and Operations包含了Euler(尤拉) Transform跟Rotation about an Arbitrary Axis(任意軸旋轉)

 

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