Pseudoangles - Revision history

Vegard: add new code variant

2020-02-25T18:19:01Z

add new code variant

← Older revision		Revision as of 18:19, 25 February 2020
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	I personally prefer this last version as there are no performance disadvantages to using it anyway.		I personally prefer this last version as there are no performance disadvantages to using it anyway.

			In languages with a <tt>sign()</tt> (or <tt>copysign()</tt>) function you can use that to further simplify it:

			<source lang="GLSL">
			float pseudoangle(float y, float x)
			{
			return sign(y) * (1. - x / (abs(x) + abs(y)));
			}
			</source>

	=== See also ===		=== See also ===

Vegard: add illustrations

2020-02-25T12:37:04Z

add illustrations

← Older revision		Revision as of 12:37, 25 February 2020
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			[[File:atan.png\|420px\|thumb\|Field lines for regular atan.]]
			[[File:pseudoangles.png\|420px\|thumb\|Field lines for pseudoangles. Note that the sectors near the cardinal directions are slightly narrower compared to regular atan.]]

	Pseudoangles allow you to compare the angles of two vectors without actually computing the angle itself (which could be costly). By extension, it also allows you to sort a list of vectors by angle without calling <tt>atan()</tt> or <tt>atan2()</tt>.		Pseudoangles allow you to compare the angles of two vectors without actually computing the angle itself (which could be costly). By extension, it also allows you to sort a list of vectors by angle without calling <tt>atan()</tt> or <tt>atan2()</tt>.

Vegard: add link

2019-12-18T05:42:09Z

add link

← Older revision		Revision as of 05:42, 18 December 2019
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	I personally prefer this last version as there are no performance disadvantages to using it anyway.		I personally prefer this last version as there are no performance disadvantages to using it anyway.

			=== See also ===

			* https://stackoverflow.com/questions/16542042/fastest-way-to-sort-vectors-by-angle-without-actually-computing-that-angle

	[[Category:Programming]]		[[Category:Programming]]

Vegard: added category

2019-12-17T20:34:45Z

added category

← Older revision		Revision as of 20:34, 17 December 2019
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	[[Category:Programming]]		[[Category:Programming]]
	[[Category:Geometry]]		[[Category:Geometry]]
			[[Category:Trigonometry]]

Vegard: Vegard moved page Psuedoangles to Pseudoangles without leaving a redirect: typo

2019-12-17T19:36:16Z

Vegard moved page Psuedoangles to Pseudoangles without leaving a redirect: typo

← Older revision		Revision as of 19:36, 17 December 2019
(No difference)

Vegard: more typos

2019-12-17T19:35:42Z

more typos

← Older revision		Revision as of 19:35, 17 December 2019
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	<source lang="Python">		<source lang="Python">
	def ~~psuedoangle~~(y, x):		def pseudoangle(y, x):
	r = x / (abs(x) + abs(y))		r = x / (abs(x) + abs(y))
	if y < 0:		if y < 0:
Line 27:		Line 27:

	<source lang="Python">		<source lang="Python">
	def ~~psuedoangle~~(y, x):		def pseudoangle(y, x):
	r = x / (abs(x) + abs(y))		r = x / (abs(x) + abs(y))
	if y < 0:		if y < 0:

Vegard: typo

2019-12-17T19:35:07Z

typo

← Older revision		Revision as of 19:35, 17 December 2019
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	</source>		</source>

	This function returns a value between 1 and 5. When ~~using~~ as a sort key, this yields the same behaviour as the key <tt>mod(atan2(y, x) + 1.5 * pi, 2. * pi)</tt>. It is therefore not a direct replacement for <tt>atan2()</tt> if you care about which angles are considered the smallest/larges, however it does sort in the correct "direction".		This function returns a value between 1 and 5. When used as a sort key, this yields the same behaviour as the key <tt>mod(atan2(y, x) + 1.5 * pi, 2. * pi)</tt>. It is therefore not a direct replacement for <tt>atan2()</tt> if you care about which angles are considered the smallest/larges, however it does sort in the correct "direction".

	If you want to preserve the exact sorting order as if you had used <tt>atan2()</tt> (with the return value in range 0-4), you can use:		If you want to preserve the exact sorting order as if you had used <tt>atan2()</tt> (with the return value in range 0-4), you can use:

Vegard: typo

2019-12-17T19:34:54Z

typo

← Older revision		Revision as of 19:34, 17 December 2019
Line 12:		Line 12:
	</source>		</source>

	This function returns a value ~~between 1 and 5~~ between 1 and 5. When using as a sort key, this yields the same behaviour as the key <tt>mod(atan2(y, x) + 1.5 * pi, 2. * pi)</tt>. It is therefore not a direct replacement for <tt>atan2()</tt> if you care about which angles are considered the smallest/larges, however it does sort in the correct "direction".		This function returns a value between 1 and 5. When using as a sort key, this yields the same behaviour as the key <tt>mod(atan2(y, x) + 1.5 * pi, 2. * pi)</tt>. It is therefore not a direct replacement for <tt>atan2()</tt> if you care about which angles are considered the smallest/larges, however it does sort in the correct "direction".

	If you want to preserve the exact sorting order as if you had used <tt>atan2()</tt> (with the return value in range 0-4), you can use:		If you want to preserve the exact sorting order as if you had used <tt>atan2()</tt> (with the return value in range 0-4), you can use:

Vegard: new page

2019-12-17T17:58:22Z

new page

New page

Pseudoangles allow you to compare the angles of two vectors without actually computing the angle itself (which could be costly). By extension, it also allows you to sort a list of vectors by angle without calling <tt>atan()</tt> or <tt>atan2()</tt>.

The version you'll typically find on Google [https://community.khronos.org/t/pseudo-angles/59520][https://forums.ogre3d.org/viewtopic.php?f=2&t=53495] is basically:

<source lang="Python">
def pseudoangle(y, x):
r = y / (abs(x) + abs(y))
if x < 0:
return 2. - r
else:
return 4. + r
</source>

This function returns a value between 1 and 5 between 1 and 5. When using as a sort key, this yields the same behaviour as the key <tt>mod(atan2(y, x) + 1.5 * pi, 2. * pi)</tt>. It is therefore not a direct replacement for <tt>atan2()</tt> if you care about which angles are considered the smallest/larges, however it does sort in the correct "direction".

If you want to preserve the exact sorting order as if you had used <tt>atan2()</tt> (with the return value in range 0-4), you can use:

<source lang="Python">
def psuedoangle(y, x):
r = x / (abs(x) + abs(y))
if y < 0:
return 1. + r
return 3. - r
</source>

If you also want the sign of the return value to be the same as for <tt>atan2()</tt>, i.e. return value in range (-2 to 2), you can use:

<source lang="Python">
def psuedoangle(y, x):
r = x / (abs(x) + abs(y))
if y < 0:
return r - 1.
return 1. - r
</source>

I personally prefer this last version as there are no performance disadvantages to using it anyway.

[[Category:Programming]]
[[Category:Geometry]]