回転には，X軸を中心に回転，Y軸を中心に回転，Z軸を中心に回転，などがあり，それぞれ次の変換行列で表わされます。
X軸を中心に回転
Y軸を中心に回転
Z軸を中心に回転
Nのような文字を，左下奥を原点に合わせて描き，右上前の点をPとします。この点Pの座標(1.0, 2.0, 2.0)は文字Nの大きさになっています。そして，X軸，Y軸，Z軸は，それぞれ，赤，緑，青で表現されています。
| characterN pointP xyzAxes compoundObject |
characterN := JunOpenGL3dObject characterN.
characterN paint: ColorValue magenta.
characterN := characterN translatedBy: characterN boundingBox corner.
pointP := JunOpenGL3dObject cube.
pointP := pointP scaledBy: 0.1.
pointP := pointP translatedBy: characterN boundingBox corner.
xyzAxes := JunOpenGL3dObject axes.
xyzAxes := xyzAxes scaledBy: 3.5.
compoundObject := JunOpenGL3dCompoundObject new.
compoundObject add: characterN.
compoundObject add: xyzAxes.
compoundObject add: pointP.
compoundObject show.
Transcript cr; show: pointP boundingBox center printString
この文字NをX軸を中心に30度回転してみましょう。点Pの座標は(1.0, 0.732, 2.732)になります。rotateX:のメッセージを使って，Jun3dTransformationのインスタンスを作成し，文字Nに作用させます。すなわち，文字Nにtransform:のメッセージを送ります。同様に点Pも回転しておきます。
| characterN pointP aTransformation xyzAxes compoundObject |
characterN := JunOpenGL3dObject characterN.
characterN paint: ColorValue magenta.
characterN := characterN translatedBy: characterN boundingBox corner.
pointP := JunOpenGL3dObject cube.
pointP := pointP scaledBy: 0.1.
pointP := pointP translatedBy: characterN boundingBox corner.
aTransformation := Jun3dTransformation rotateX: (JunAngle fromDeg: 30).
characterN := characterN transform: aTransformation.
pointP := pointP transform: aTransformation.
xyzAxes := JunOpenGL3dObject axes.
xyzAxes := xyzAxes scaledBy: 3.5.
compoundObject := JunOpenGL3dCompoundObject new.
compoundObject add: characterN.
compoundObject add: xyzAxes.
compoundObject add: pointP.
compoundObject show.
Transcript cr; show: pointP boundingBox center printString
元の文字NをY軸を中心に30度回転してみましょう。rotateY:のメッセージを使います。点Pの座標は(1.866, 2.0, 1.232)になります。
| characterN pointP aTransformation xyzAxes compoundObject |
characterN := JunOpenGL3dObject characterN.
characterN paint: ColorValue magenta.
characterN := characterN translatedBy: characterN boundingBox corner.
pointP := JunOpenGL3dObject cube.
pointP := pointP scaledBy: 0.1.
pointP := pointP translatedBy: characterN boundingBox corner.
aTransformation := Jun3dTransformation rotateY: (JunAngle fromDeg: 30).
characterN := characterN transform: aTransformation.
pointP := pointP transform: aTransformation.
xyzAxes := JunOpenGL3dObject axes.
xyzAxes := xyzAxes scaledBy: 3.5.
compoundObject := JunOpenGL3dCompoundObject new.
compoundObject add: characterN.
compoundObject add: xyzAxes.
compoundObject add: pointP.
compoundObject show.
Transcript cr; show: pointP boundingBox center printString
元の文字NをZ軸を中心に30度回転してみましょう。rotateZ:のメッセージを使います。点Pの座標は(-0.134, 2.232, 2.0)になります。
| characterN pointP aTransformation xyzAxes compoundObject |
characterN := JunOpenGL3dObject characterN.
characterN paint: ColorValue magenta.
characterN := characterN translatedBy: characterN boundingBox corner.
pointP := JunOpenGL3dObject cube.
pointP := pointP scaledBy: 0.1.
pointP := pointP translatedBy: characterN boundingBox corner.
aTransformation := Jun3dTransformation rotateZ: (JunAngle fromDeg: 30).
characterN := characterN transform: aTransformation.
pointP := pointP transform: aTransformation.
xyzAxes := JunOpenGL3dObject axes.
xyzAxes := xyzAxes scaledBy: 3.5.
compoundObject := JunOpenGL3dCompoundObject new.
compoundObject add: characterN.
compoundObject add: xyzAxes.
compoundObject add: pointP.
compoundObject show.
Transcript cr; show: pointP boundingBox center printString
複数軸を中心に回転させる場合には，座標変換の順序すなわち変換行列の結合順序が重要になります。X軸，Y軸，Z軸と回転させるのと，Z軸，Y軸，X軸と回転させるのでは，結果が丸っ切り異なります。
| characterN pointP aTransformation xyzAxes compoundObject |
characterN := JunOpenGL3dObject characterN.
characterN paint: ColorValue magenta.
characterN := characterN translatedBy: characterN boundingBox corner.
pointP := JunOpenGL3dObject cube.
pointP := pointP scaledBy: 0.1.
pointP := pointP translatedBy: characterN boundingBox corner.
aTransformation := ((Jun3dTransformation rotateX: (JunAngle fromDeg: 30))
product: (Jun3dTransformation rotateY: (JunAngle fromDeg: 30)))
product: (Jun3dTransformation rotateZ: (JunAngle fromDeg: 30)).
characterN := characterN transform: aTransformation.
pointP := pointP transform: aTransformation.
xyzAxes := JunOpenGL3dObject axes.
xyzAxes := xyzAxes scaledBy: 3.5.
compoundObject := JunOpenGL3dCompoundObject new.
compoundObject add: characterN.
compoundObject add: xyzAxes.
compoundObject add: pointP.
compoundObject show.
Transcript cr; show: pointP boundingBox center printString
| characterN pointP aTransformation xyzAxes compoundObject |
characterN := JunOpenGL3dObject characterN.
characterN paint: ColorValue magenta.
characterN := characterN translatedBy: characterN boundingBox corner.
pointP := JunOpenGL3dObject cube.
pointP := pointP scaledBy: 0.1.
pointP := pointP translatedBy: characterN boundingBox corner.
aTransformation := ((Jun3dTransformation rotateZ: (JunAngle fromDeg: 30))
product: (Jun3dTransformation rotateY: (JunAngle fromDeg: 30)))
product: (Jun3dTransformation rotateX: (JunAngle fromDeg: 30)).
characterN := characterN transform: aTransformation.
pointP := pointP transform: aTransformation.
xyzAxes := JunOpenGL3dObject axes.
xyzAxes := xyzAxes scaledBy: 3.5.
compoundObject := JunOpenGL3dCompoundObject new.
compoundObject add: characterN.
compoundObject add: xyzAxes.
compoundObject add: pointP.
compoundObject show.
Transcript cr; show: pointP boundingBox center printString
ある直線すなわち任意の軸に回転するには，rotate:around:のメッセージを使うと便利です。文字Nを直線((0,0,0),(1,2,2))を中心にして30度回転させてみましょう。文字Nを対角線を中心に回転させていることになりますから，点Pの座標(1.0, 2.0, 2.0)に変化はありません。
| characterN pointP aLine aTransformation xyzAxes aPolyline compoundObject |
characterN := JunOpenGL3dObject characterN.
characterN paint: ColorValue magenta.
characterN := characterN translatedBy: characterN boundingBox corner.
pointP := JunOpenGL3dObject cube.
pointP := pointP scaledBy: 0.1.
pointP := pointP translatedBy: characterN boundingBox corner.
aLine := Jun3dLine from: 0 , 0 , 0 to: characterN boundingBox corner.
aTransformation := Jun3dTransformation rotate: (JunAngle fromDeg: 30)
around: aLine.
characterN := characterN transform: aTransformation.
pointP := pointP transform: aTransformation.
xyzAxes := JunOpenGL3dObject axes.
xyzAxes := xyzAxes scaledBy: 3.5.
aPolyline := JunOpenGL3dPolyline vertexes: (Array with: (aLine atT: -2)
with: (aLine atT: 2)).
aPolyline paint: ColorValue cyan.
compoundObject := JunOpenGL3dCompoundObject new.
compoundObject add: characterN.
compoundObject add: xyzAxes.
compoundObject add: pointP.
compoundObject add: aPolyline.
compoundObject show.
Transcript cr; show: pointP boundingBox center printString