Category:LSL Rotation - Revision history

Frionil Fang: slight rephrasing: rot div is quat div, only if the rotation is normalized already

2023-10-28T21:30:15Z

slight rephrasing: rot div is quat div, only if the rotation is normalized already

← Older revision		Revision as of 14:30, 28 October 2023
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	rotation r5 = r2*r1; // <0.5, -0.5, 0.5, 0.5>		rotation r5 = r2*r1; // <0.5, -0.5, 0.5, 0.5>
	</syntaxhighlight>		</syntaxhighlight>
	* Rotation multiplication is true [[quaternion]] multiplication, but division is multiplication by the {{wikipedia\|Quaternion#Conjugation,_the_norm,_and_reciprocal\|conjugate}} instead.<ref name="division">I.e. rotation division is <code>q/p = qp̅</code>. To get true quaternion division, <code>q/p = qp̅/‖p‖²</code>, ~~you must divide~~ the result by the squared magnitude of the divisor <code>m = ‖p‖² = p.xp.x+p.yp.y+p.zp.z+p.sp.s</code>. Since LSL doesn't support multiplying/dividing a rotation by a float, the scaling must be done componentwise, e.g. <code>p = <p.x/m, p.y/m, p.z/m, p.s/m></code> or by multiplying by a scalar rotation <code>p = p*<0, 0, 0, 1.0/m></code>.</ref>		* Rotation multiplication is always true [[quaternion]] multiplication, but division is multiplication by the {{wikipedia\|Quaternion#Conjugation,_the_norm,_and_reciprocal\|conjugate}} instead. This will not produce true quaternion results unless the rotation is normalized.<ref name="division">I.e. rotation division is <code>q/p = qp̅</code>. To get true quaternion division <code>q/p = qp̅/‖p‖²</code> even for non-normalized rotations, the result must be divided by the squared magnitude of the divisor <code>m = ‖p‖² = p.xp.x+p.yp.y+p.zp.z+p.sp.s</code>. Since LSL doesn't support multiplying/dividing a rotation by a float, the scaling must be done componentwise, e.g. <code>p = <p.x/m, p.y/m, p.z/m, p.s/m></code> or by multiplying by a scalar rotation <code>p = p*<0, 0, 0, 1.0/m></code>.</ref>

	==== Vector Rotation, Operators "*" and "/" ====		==== Vector Rotation, Operators "*" and "/" ====

Frionil Fang: also a note that rotations can double as complex numbers in a pinch

2023-10-28T11:52:27Z

also a note that rotations can double as complex numbers in a pinch

← Older revision		Revision as of 04:52, 28 October 2023
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	rotation r5 = r2*r1; // <0.5, -0.5, 0.5, 0.5>		rotation r5 = r2*r1; // <0.5, -0.5, 0.5, 0.5>
	</syntaxhighlight>		</syntaxhighlight>
	* Rotation multiplication is true [[quaternion]] multiplication, but division is multiplication by the {{wikipedia\|Quaternion#Conjugation,_the_norm,_and_reciprocal\|conjugate}} instead.<ref>I.e. rotation division is <code>q/p = qp̅</code>. To get true quaternion division, <code>q/p = qp̅/‖p‖²</code>, you must divide the result by the squared magnitude of the divisor <code>m = ‖p‖² = p.xp.x+p.yp.y+p.zp.z+p.sp.s</code>. Since LSL doesn't support multiplying/dividing a rotation by a float, the scaling must be done componentwise, e.g. <code>p = <p.x/m, p.y/m, p.z/m, p.s/m></code> or by multiplying by a scalar rotation <code>p = p*<0, 0, 0, 1.0/m></code>.</ref>		* Rotation multiplication is true [[quaternion]] multiplication, but division is multiplication by the {{wikipedia\|Quaternion#Conjugation,_the_norm,_and_reciprocal\|conjugate}} instead.<ref name="division">I.e. rotation division is <code>q/p = qp̅</code>. To get true quaternion division, <code>q/p = qp̅/‖p‖²</code>, you must divide the result by the squared magnitude of the divisor <code>m = ‖p‖² = p.xp.x+p.yp.y+p.zp.z+p.sp.s</code>. Since LSL doesn't support multiplying/dividing a rotation by a float, the scaling must be done componentwise, e.g. <code>p = <p.x/m, p.y/m, p.z/m, p.s/m></code> or by multiplying by a scalar rotation <code>p = p*<0, 0, 0, 1.0/m></code>.</ref>

	==== Vector Rotation, Operators "*" and "/" ====		==== Vector Rotation, Operators "*" and "/" ====
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	==Uses==		==Uses==
	Functions in this category fall into two categories: rotations in the purely mathematical sense and rotations as in prim / object rotation.		Functions in this category fall into two categories: rotations in the purely mathematical sense and rotations as in prim / object rotation. The [[rotation]] page has detailed information about how to work with rotations. [[Quaternion]] is an alias for variables of rotation type, and the article explains some further mathematical details behind them.
			* Rotations are also the most memory-efficient way of storing non-rotation related bundles of 4 [[float]] values, especially inside [[list]]s.
	The [[rotation]] page ~~is where you can find~~ detailed information about how to work with rotations. [[Quaternion]] is ~~also~~ an ~~acceptable~~ alias for variables of rotation type, and the article explains some further mathematical details behind them.		* Rotations can substitute for {{wikipedia\|Complex number\|complex numbers}}: by choosing one of the x/y/z components to represent the complex imaginary part, the s component to represent the real part and leaving the others at 0, the rotation operations behave like their complex equivalents, other than division that requires adjustment<ref name="division"/>.

	Rotations are also the most memory-efficient way of storing non-rotation related bundles of 4 [[float]] values, especially inside [[list]]s.

	==Useful Snippets==		==Useful Snippets==

Frionil Fang: reordered since addition/subtraction are not very useful; added footnote about what rot div actually means mathematically

2023-10-28T11:40:34Z

reordered since addition/subtraction are not very useful; added footnote about what rot div actually means mathematically

@@ Line 22: / Line 22: @@
 ===Operators===
 Rotations support the following operations:
 ==== Composition, Operators "*" and "/" ====
-Composition combines two rotations into a new rotation representing the combined action of both, unlike addition/subtraction. "/" rotates in the opposite direction to "*".
+Composition combines two rotations into a new rotation representing the combined action of both, unlike addition/subtraction. "/" rotates in the opposite direction to "*". Composition is not commutative, i.e. the order of the operands matters.
 <syntaxhighlight lang="lsl2">
 // 90 degree rotation around x-axis
@@ Line 49: / Line 36: @@
 rotation r5 = r2*r1; // <0.5, -0.5, 0.5, 0.5>
 </syntaxhighlight>
 ==== Vector Rotation, Operators "*" and "/" ====
@@ Line 62: / Line 50: @@
 vector vr4 = v*r4; // <0, -1, 2> - rotated 90 degrees around x, then -90 degrees around z
 vector vr4 = v*r5; // <-2, 0, 1> - rotated 90 degrees around z, then 90 degrees around x
 </syntaxhighlight>
@@ Line 74: / Line 69: @@
 To reverse a rotation (say something is facing north and you want it to face south, e.g. 180 degrees difference), add pi to the z value of the euler vector:
 <syntaxhighlight lang="lsl2">llEuler2Rot(<0.0, 0.0, PI>) * llGetRot()</syntaxhighlight>

Frionil Fang: made more in-depth like the other data type category pages

2023-10-18T15:08:03Z

made more in-depth like the other data type category pages

@@ Line 1: / Line 1: @@
 {{LSL Header|ml=*}}{{LSLC|}}{{LSLC|Types}}
-The [[rotation]] page is where you can find detailed information about how to work with rotations.
+A rotation is a data {{LSLGC|Types|type}} that contains a set of four {{LSLGC|Float|float}} values.
-Functions in this category fall into two categories: Rotations in the purely mathematical sense and Rotations as in prim / object rotation.
+===Components===
-Quick Tip! To reverse a rotation (say something is facing north and you want it to face south, e.g. 180 degrees difference), add pi to the z value of the euler vector:
+<syntaxhighlight lang="lsl2">
-<source lang="lsl2">llEuler2Rot(<0.0, 0.0, PI>) * llGetRot()</source>
+Note that components can be only accessed with rotation variables. Attempting to access the components of a rotation literal or a return value from a function is illegal.

ObviousAltIsObvious Resident at 21:23, 25 January 2015

2015-01-25T21:23:08Z

← Older revision		Revision as of 14:23, 25 January 2015
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	Quick Tip! To reverse a rotation (say something is facing north and you want it to face south, e.g. 180 degrees difference), add pi to the z value of the euler vector:		Quick Tip! To reverse a rotation (say something is facing north and you want it to face south, e.g. 180 degrees difference), add pi to the z value of the euler vector:

	llEuler2Rot(<0.0, 0.0, PI>) * llGetRot()		<source lang="lsl2">llEuler2Rot(<0.0, 0.0, PI>) * llGetRot()</source>

Strife Onizuka at 21:37, 24 October 2008

2008-10-24T21:37:35Z

← Older revision		Revision as of 14:37, 24 October 2008
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	~~{{Multi-lang}}~~		{{LSL Header\|ml=*}}{{LSLC\|}}{{LSLC\|Types}}
	{{LSL Header}}{{LSLC\|}}{{LSLC\|Types}}
	The [[rotation]] page is where you can find detailed information about how to work with rotations.		The [[rotation]] page is where you can find detailed information about how to work with rotations.

Chaz Longstaff at 18:05, 20 July 2008

2008-07-20T18:05:09Z

← Older revision		Revision as of 11:05, 20 July 2008
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	Functions in this category fall into two categories: Rotations in the purely mathematical sense and Rotations as in prim / object rotation.		Functions in this category fall into two categories: Rotations in the purely mathematical sense and Rotations as in prim / object rotation.

			Quick Tip! To reverse a rotation (say something is facing north and you want it to face south, e.g. 180 degrees difference), add pi to the z value of the euler vector:

			llEuler2Rot(<0.0, 0.0, PI>) * llGetRot()

Strife Onizuka at 23:21, 9 June 2008

2008-06-09T23:21:11Z

← Older revision		Revision as of 16:21, 9 June 2008
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	{{Multi-lang}}		{{Multi-lang}}
	{{LSL Header}}{{LSLC\|}}		{{LSL Header}}{{LSLC\|}}{{LSLC\|Types}}
	The [[rotation]] page is where you can find detailed information about how to work with rotations.		The [[rotation]] page is where you can find detailed information about how to work with rotations.

	Functions in this category fall into two categories: Rotations in the purely mathematical sense and Rotations as in prim / object rotation.		Functions in this category fall into two categories: Rotations in the purely mathematical sense and Rotations as in prim / object rotation.

Gally Young: add multi lang

2008-03-15T10:50:14Z

add multi lang

← Older revision		Revision as of 03:50, 15 March 2008
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			{{Multi-lang}}
	{{LSL Header}}{{LSLC\|}}		{{LSL Header}}{{LSLC\|}}
	The [[rotation]] page is where you can find detailed information about how to work with rotations.		The [[rotation]] page is where you can find detailed information about how to work with rotations.

	Functions in this category fall into two categories: Rotations in the purely mathematical sense and Rotations as in prim / object rotation.		Functions in this category fall into two categories: Rotations in the purely mathematical sense and Rotations as in prim / object rotation.

Strife Onizuka at 22:42, 6 March 2008

2008-03-06T22:42:14Z

← Older revision		Revision as of 15:42, 6 March 2008
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	{{LSL Header}}		{{LSL Header}}{{LSLC\|}}
	The [[rotation]] page is where you can find detailed information about how to work with rotations.		The [[rotation]] page is where you can find detailed information about how to work with rotations.
	~~{{LSLC\|}}~~
			Functions in this category fall into two categories: Rotations in the purely mathematical sense and Rotations as in prim / object rotation.