簡單的說，通過這些具體的變換，首先告訴系統觀察者在那裏看，其次看到的物體擺在那裏，再次這個三維物體如何投影得到二維圖形，最後把這個圖形在窗口上用像素呈現出來。每個變換實際上是一個矩陣，所有變換疊加的結果，用矩陣表現出來就是這些矩陣照順序相乘起來，並得到最終的變換矩陣。
以下對每種變換分別作一個解釋：
Viewing Transformations
By default, the point of observation in a perspective projection is at the origin (0,0,0) looking down the negative z-axis (“into” the monitor screen).
The viewing transformation allows you to place the point of observation anywhere you want and look in any direction. Determining the viewing transformation is like placing
and pointing a camera at the scene.
這個變換是移動觀察者的位置，默認的觀察位置是(0,0,0)，觀察方向指向屏幕內部。觀察變換使你可以在任意位置或任意方向上進行觀察。
Modeling Transformations
These transformations move objects into place, rotate them, and scale them.
模型變換包括平移，旋轉和縮放。
Modelview Duality
The viewing and modeling transformations are, in fact, the same in terms of their internal effects as well as their effects on the final appearance of the scene. The distinction between the two is made purely as a convenience for the programmer. There is no real difference visually between moving an object backward and moving the reference system forward;
觀察變換和模型變換式是等效的，只是爲了使用者的方便而設，因爲運動的相對性，你既可以一個方向上移動觀察着，也可以在反方向上移動物體。
Projection Transformations
This projection actually defines the viewing volume and establishes clipping planes.
The clipping planes are plane equations in 3D space that OpenGL uses to determine whether geometry can be seen by the viewer. More specifically, the projection transformation specifies how a finished scene (after all the modeling is done) is projected to the final image on the screen.
Two types of projections—orthographic and perspective.
投影變換確定了視覺空間和剪裁平面。剪裁平面確定了3D物體投影后得到的2D投影圖形。OpenGL中存在兩種投影方式，正投影和透視投影。
插入一點英文詞彙解釋，引自：http://www.dictall.com/indu54/63/54638430CA4.htm
1) clipping planes剪裁平面2) flat cutting平面裁剪1.This article analysis and compare the characteristic, cutting process between solid cutting and flat cutting, explained two methods from its own system, each has its strong points also cannot substitute.本文從分析比較立體裁剪與平面裁剪兩種服裝結構設計方法的特點及裁剪過程入手,說明兩種方法自成體系,各有所長且不能被取代。3) OpenGL clip planeOpenGL裁剪平面4) surface trimming曲面裁剪1.Scan line algorithm for NURBS surface trimming;用於非均勻有理B樣條曲面裁剪的掃描線算法2.This paper discusses the algorithm and implementation of the advanced surface design functions in BSURF-GI (an interactive 3D surface modelling system), presents a method which can do surface trimming along with the suface / surface intersection curves and filleting surface boundaries, and also points out the system further research direction and the way of integration with solid modelling system.提出了一種能沿曲面與曲面交線和過渡曲面邊界線進行曲面裁剪的算法,指出了該系統今後進一步研究的方向及與實體造型系統集成的途徑。3.In CAD/CAM engineering,surface trimming is one of the most important and complex problems and quadrangular meshes are widely employed.曲面裁剪運算是CAD/CAM領域最重要、最複雜的問題之一,四邊形網格在工程CAD/CAM的實際應用中較爲廣泛。5) trimmed surface裁剪曲面1.Algorithm of trimmed surface triangulation of prepositive disposal in predicting RCS of aircraft;飛行器RCS計算前置處理中裁剪曲面剖分算法2.Here the tool surface is represented by the analytical surface,the trimmed surface is approximated with the triangular patches, and the problem of interfer-ence avoidance is solved by transforming them to the test of relations between tool surface andtriangular patches.在分析國內外三座標數控加工刀具軌跡干涉檢查和消除算法的基礎上,提出了一種適合於球頭刀、平底刀和圓角刀的刀具軌跡干涉檢查和消除的算法,該算法將刀具看成解析曲面,裁剪曲面由三角片逼近表示,將刀具軌跡干涉檢查與消除的問題轉化爲刀具曲面與三角片的相關性測試。3.That is referred to how a model represented by many trimmed surfaces is transferred to a watertight model.曲面縫合是曲面造型過程中常用到的處理技術,即把由多張裁剪曲面表示的模型轉換成一個"不漏水"的模型。6) trimmed surfaces裁剪曲面1.An algorithm for triangulating multi trimmed surfaces is introduced in this paper.提出一種新的多裁剪曲面三角劃分的方法。
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