Vegard: add general formula for vectors

2020-04-21T12:21:26Z

add general formula for vectors

← Older revision		Revision as of 12:21, 21 April 2020
Line 1:		Line 1:
	~~Shortest~~ angular distance between two ~~angles,~~ in ~~radians~~ ~~(always positive)~~:		In general, the smallest angle (angular distance) between two vectors is given by:

			<math>
			a = \cos^{-1} \frac{A \cdot B}{\left \| A \right \| \cdot \left \| B \right \|}
			</math>

			(if <math>A</math> and <math>B</math> are unit/normalized, then this can be simplified further).

			Given two angles <math>a_0</math> and <math>a_1</math>, you ''could'' substitute <math>A = \left [ \cos a_0, \sin a_0 \right ]</math> and <math>B = \left [ \cos a_1, \sin a_1 \right ]</math> above, or you could use the following code:

	<source lang="C++">		<source lang="C++">
	// https://gamedev.stackexchange.com/a/4472		// https://gamedev.stackexchange.com/a/4472
			// a0 and a1 are in radians (always positive)
	float delta_angle(float a0, float a1)		float delta_angle(float a0, float a1)
	{		{

Vegard: new page

2019-12-26T07:27:54Z

new page

New page

Shortest angular distance between two angles, in radians (always positive):

<source lang="C++">
// https://gamedev.stackexchange.com/a/4472
float delta_angle(float a0, float a1)
{
return M_PI - fabs(fabs(a1 - a0) - M_PI);
}
</source>

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

Angular distance - Revision history

Vegard: add general formula for vectors

Vegard: new page