Merge pull request mrdoob#10553 from looeee/docs/euler/eulerTypeNote

Added note on intrinsic and extrinsic Euler types
pixnblox · Jan 11, 2017 · 240065e · 240065e
2 parents e7dc951 + 19c9247
commit 240065e
Showing 1 changed file with 21 additions and 6 deletions.
diff --git a/docs/api/math/Euler.html b/docs/api/math/Euler.html
@@ -10,11 +10,12 @@
 	<body>
 		<h1>[name]</h1>
 
-		<div class="desc">A class representing [link:http://en.wikipedia.org/wiki/Euler_angles Euler Angles].<br /><br />
+		<div class="desc">
+			A class representing [link:http://en.wikipedia.org/wiki/Euler_angles Euler Angles].<br /><br />
 
-		Euler angles describe a rotational transformation by rotating an object on its various
-		axes in specified amounts per axis, and a specified axis order.
-	</div>
+			Euler angles describe a rotational transformation by rotating an object on its various
+			axes in specified amounts per axis, and a specified axis order.
+		</div>
 
 		<h2>Example</h2>
 
@@ -51,9 +52,23 @@ <h3>[property:String order]</h3>
 		<div>
 			The order in which to apply rotations. Default is 'XYZ', which means that the object will first be
 			rotated around its X axis, then its Y axis and finally its Z axis. Other possibilities are:
-			'YZX', 'ZXY', 'XZY', 'YXZ' and 'ZYX'. Note that these must be in upper case.<br /><br />
+			'YZX', 'ZXY', 'XZY', 'YXZ' and 'ZYX'. These must be in upper case.<br /><br />
 
-			If this is changed, [page:.onChangeCallback onChangeCallback] will be called.
+			Three.js uses <em>intrinsic</em> (Tait-Bryan) ordering, also known as <em>yaw</em>, <em>pitch</em>
+			and <em>roll</em>. This means that rotations are performed with respect to the <em>local</em>
+			coordinate system. That is, for order 'XYZ', the rotation is first around world-X, then around
+			local-Y (which may now be different from the world Y-axis), then local-Z (which may be different
+			from the world Z-axis).<br /><br />
+
+			Some implementations may use <em>extrinsic</em> (proper) ordering, in which case rotations are performed
+			with respect to the <em>world</em> coordinate system, so that for order 'XYZ', the rotations
+			are around world-X, world-Y, and world-Z.<br /><br />
+
+			Converting between the two types is relatively straightforward, you just need to reverse the order
+			and the rotation, so that an intrinsic (three.js) Euler rotation of angles a, b, c about XYZ
+			will be equivalent to to an extrinsic Euler rotation of angles c, b, a about ZYX.<br /><br />
+
+			If the order is changed, [page:.onChangeCallback onChangeCallback] will be called.
 		</div>
 
 		<h3>[property:Float x]</h3>