Angle - Revision history

Xander: Add HAU

2026-09-14T00:05:21Z

Add HAU

← Older revision		Revision as of 00:05, 14 September 2026
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	==Angular Unit==		==Angular Unit==
	An '''angular unit''' or '''angle unit''' is a unit of measurement that describes an angle, specifically yaw, pitch, and roll. An angular unit in Super Mario 64 is equal to 1/65536 of a circle. This translates to about .0055 degrees per unit, or about 182 units per degree. ~~Since~~ the game's trigonometry look-up table ~~is only 1/16 as precise~~, two different angles ~~may~~ be considered the same if they ~~both~~ are ~~rounded~~ to the same ~~value~~. Since ~~16 angular units~~ is less than .1 degrees, this is never noticeable in regular gameplay but can ~~come in to play~~ in with large speed values (e.g. for [[Parallel Universe\|PU]] movement).		An '''angular unit''' or '''angle unit''' is a unit of measurement that describes an angle, specifically yaw, pitch, and roll. An angular unit in Super Mario 64 is equal to 1/65536 of a circle. This translates to about .0055 degrees per unit, or about 182 units per degree.

			==Hexadecimal Angle Unit (HAU)==
			One '''hexadecimal angle unit (HAU)''' is equivalent to 16 angle units. It can be useful to discuss angles in terms of HAU because the game's trigonometry calculations drop the 4 least significant bits of an angle before using the look-up table, so two different angles will be considered the same if they are truncated to the same HAU. Since 1 HAU is less than .1 degrees, this is never noticeable in regular gameplay, but it can be an important factor in micro optimizations or with large speed values (e.g. for [[Parallel Universe\|PU]] movement).

			To compute an angle to HAU precision, either right bitshift the angle by 4 with (angle >> 4) or truncate it to the nearest multiple of 16 with (angle - (angle mod 16)).

	[[Category:Mechanics]]		[[Category:Mechanics]]

SuperHamster: Bolding title in lead

2021-05-08T03:34:52Z

Bolding title in lead

← Older revision		Revision as of 03:34, 8 May 2021
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	Angles are a measurement of a separation between two rays. Using trigonometry, angles give substantial information relating to the position and velocity of an object.		'''Angles''' are a measurement of a separation between two rays. Using trigonometry, angles give substantial information relating to the position and velocity of an object.

	==Yaw, Pitch and Roll==		==Yaw, Pitch and Roll==

	Yaw, Pitch, and Roll are the three turning directions that can be used to represent any angle in 3D space. Yaw is the angle along the X-Z axes. This angle is taken relative to the positive Z-axis, meaning that directly facing the positive Z-direction corresponds to an angle of 0, while facing directly away corresponds to 180 degrees. Pitch is the angle along the Y-Z axes. Roll is taken along the Y-X axes.		Yaw, Pitch, and Roll are the three turning directions that can be used to represent any angle in 3D space. Yaw is the angle along the X-Z axes. This angle is taken relative to the positive Z-axis, meaning that directly facing the positive Z-direction corresponds to an angle of 0, while facing directly away corresponds to 180 degrees. Pitch is the angle along the Y-Z axes. Roll is taken along the Y-X axes.

	==Trigonometry==		==Trigonometry==
	Instead of calculating them in real time, the game uses a look-up table for values of the trigonometric functions Sine and Cosine.		Instead of calculating them in real time, the game uses a look-up table for values of the trigonometric functions Sine and Cosine.

	==Angular Unit==		==Angular Unit==
	An '''angular unit''' or '''angle unit''' is a unit of measurement that describes an angle, specifically yaw, pitch, and roll. An angular unit in Super Mario 64 is equal to 1/65536 of a circle. This translates to about .0055 degrees per unit, or about 182 units per degree. Since the game's trigonometry look-up table is only 1/16 as precise, two different angles may be considered the same if they both are rounded to the same value. Since 16 angular units is less than .1 degrees, this is never noticeable in regular gameplay but can come in to play in with large speed values (e.g. for [[Parallel Universe\|PU]] movement).		An '''angular unit''' or '''angle unit''' is a unit of measurement that describes an angle, specifically yaw, pitch, and roll. An angular unit in Super Mario 64 is equal to 1/65536 of a circle. This translates to about .0055 degrees per unit, or about 182 units per degree. Since the game's trigonometry look-up table is only 1/16 as precise, two different angles may be considered the same if they both are rounded to the same value. Since 16 angular units is less than .1 degrees, this is never noticeable in regular gameplay but can come in to play in with large speed values (e.g. for [[Parallel Universe\|PU]] movement).

	[[Category:Mechanics]]		[[Category:Mechanics]]

Macrepeh at 05:28, 30 May 2020

2020-05-30T05:28:24Z

← Older revision		Revision as of 05:28, 30 May 2020
Line 9:		Line 9:
	An '''angular unit''' or '''angle unit''' is a unit of measurement that describes an angle, specifically yaw, pitch, and roll. An angular unit in Super Mario 64 is equal to 1/65536 of a circle. This translates to about .0055 degrees per unit, or about 182 units per degree. Since the game's trigonometry look-up table is only 1/16 as precise, two different angles may be considered the same if they both are rounded to the same value. Since 16 angular units is less than .1 degrees, this is never noticeable in regular gameplay but can come in to play in with large speed values (e.g. for [[Parallel Universe\|PU]] movement).		An '''angular unit''' or '''angle unit''' is a unit of measurement that describes an angle, specifically yaw, pitch, and roll. An angular unit in Super Mario 64 is equal to 1/65536 of a circle. This translates to about .0055 degrees per unit, or about 182 units per degree. Since the game's trigonometry look-up table is only 1/16 as precise, two different angles may be considered the same if they both are rounded to the same value. Since 16 angular units is less than .1 degrees, this is never noticeable in regular gameplay but can come in to play in with large speed values (e.g. for [[Parallel Universe\|PU]] movement).

	[Category:Mechanics]		[[Category:Mechanics]]

Macrepeh: why does the game use a lookup table btw

2020-05-26T05:14:17Z

why does the game use a lookup table btw

← Older revision		Revision as of 05:14, 26 May 2020
Line 1:		Line 1:
	Angles are a measurement of a separation between two rays.		Angles are a measurement of a separation between two rays. Using trigonometry, angles give substantial information relating to the position and velocity of an object.
	==Yaw, Pitch and Roll==		==Yaw, Pitch and Roll==

	Yaw, Pitch, and Roll are the three turning directions that can be used to represent any angle in 3D space. Yaw is the angle along the X-Z axes. This angle is taken relative to the positive Z-axis, meaning that directly facing the positive Z-direction corresponds to an angle of 0, while facing directly away corresponds to 180 degrees. Pitch is the angle along the Y-Z axes. Roll is taken along the Y-X axes.		Yaw, Pitch, and Roll are the three turning directions that can be used to represent any angle in 3D space. Yaw is the angle along the X-Z axes. This angle is taken relative to the positive Z-axis, meaning that directly facing the positive Z-direction corresponds to an angle of 0, while facing directly away corresponds to 180 degrees. Pitch is the angle along the Y-Z axes. Roll is taken along the Y-X axes.

			==Trigonometry==
			Instead of calculating them in real time, the game uses a look-up table for values of the trigonometric functions Sine and Cosine.
	==Angular Unit==		==Angular Unit==
	An '''angular unit''' or '''angle unit''' is a unit of measurement that describes an angle, specifically yaw, pitch, and roll. An angular unit in Super Mario 64 is equal to 1/65536 of a circle. This translates to about .0055 degrees per unit, or about 182 units per degree. Since the game's trigonometry look-up table is only 1/16 as precise, two different angles may be considered the same if they both are rounded to the same value. Since 16 angular units is less than .1 degrees, this is never noticeable in regular gameplay but can come in to play in with large speed values (e.g. for [[Parallel Universe\|PU]] movement).		An '''angular unit''' or '''angle unit''' is a unit of measurement that describes an angle, specifically yaw, pitch, and roll. An angular unit in Super Mario 64 is equal to 1/65536 of a circle. This translates to about .0055 degrees per unit, or about 182 units per degree. Since the game's trigonometry look-up table is only 1/16 as precise, two different angles may be considered the same if they both are rounded to the same value. Since 16 angular units is less than .1 degrees, this is never noticeable in regular gameplay but can come in to play in with large speed values (e.g. for [[Parallel Universe\|PU]] movement).

			[Category:Mechanics]

Macrepeh: slightly less bad

2020-03-31T16:22:44Z

slightly less bad

← Older revision		Revision as of 16:22, 31 March 2020
Line 1:		Line 1:
	Angles are a measurement of a separation between two rays.		Angles are a measurement of a separation between two rays.


	==Yaw, Pitch and Roll==		==Yaw, Pitch and Roll==

	~~TODO~~		Yaw, Pitch, and Roll are the three turning directions that can be used to represent any angle in 3D space. Yaw is the angle along the X-Z axes. This angle is taken relative to the positive Z-axis, meaning that directly facing the positive Z-direction corresponds to an angle of 0, while facing directly away corresponds to 180 degrees. Pitch is the angle along the Y-Z axes. Roll is taken along the Y-X axes.
	==Angular Unit==		==Angular Unit==
	An '''angular unit''' or '''angle unit''' is a unit of measurement that describes an angle, specifically yaw, pitch, and roll. ~~Similarly~~ to ~~how there are 360 [[wikipedia:degree (angle)\|degrees]] or 2π [[wikipedia:radian\|radians]] in~~ a circle, ~~there are precisely 65536 angular~~ units ~~in a circle~~. ~~The~~ game's trigonometry look-up table~~, however,~~ is only 1/16 as precise, so angles ~~from 0~~ to ~~15 function exactly~~ the same. ~~Other~~ units ~~of measurement used are [[Hexadecimal Angle Unit]]s, revolutions, the aforementioned~~ degrees ~~and radians~~, ~~and~~ [[~~wikipedia:gradian~~\|~~gradians~~]].		An '''angular unit''' or '''angle unit''' is a unit of measurement that describes an angle, specifically yaw, pitch, and roll. An angular unit in Super Mario 64 is equal to 1/65536 of a circle. This translates to about .0055 degrees per unit, or about 182 units per degree. Since the game's trigonometry look-up table is only 1/16 as precise, two different angles may be considered the same if they both are rounded to the same value. Since 16 angular units is less than .1 degrees, this is never noticeable in regular gameplay but can come in to play in with large speed values (e.g. for [[Parallel Universe\|PU]] movement).

	~~==Angles in Super Mario 64==~~

	~~TODO~~

Macrepeh: Made this because the angular unit page said to. I don't know how to delete pages so someone delete the angular unit page.

2020-02-25T08:17:37Z

Made this because the angular unit page said to. I don't know how to delete pages so someone delete the angular unit page.

New page

Angles are a measurement of a separation between two rays.

==Yaw, Pitch and Roll==

TODO
==Angular Unit==
An '''angular unit''' or '''angle unit''' is a unit of measurement that describes an angle, specifically yaw, pitch, and roll. Similarly to how there are 360 [[wikipedia:degree (angle)|degrees]] or 2π [[wikipedia:radian|radians]] in a circle, there are precisely 65536 angular units in a circle. The game's trigonometry look-up table, however, is only 1/16 as precise, so angles from 0 to 15 function exactly the same. Other units of measurement used are [[Hexadecimal Angle Unit]]s, revolutions, the aforementioned degrees and radians, and [[wikipedia:gradian|gradians]].

==Angles in Super Mario 64==

TODO