Angular distance: Difference between revisions
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In general, the smallest angle (angular distance) between two vectors is given by: |
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<math> |
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a = \cos^{-1} \frac{A \cdot B}{\left | A \right | \cdot \left | B \right |} |
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</math> |
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(if <math>A</math> and <math>B</math> are unit/normalized, then this can be simplified further). |
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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: |
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<source lang="C++"> |
<source lang="C++"> |
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// https://gamedev.stackexchange.com/a/4472 |
// https://gamedev.stackexchange.com/a/4472 |
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// a0 and a1 are in radians (always positive) |
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float delta_angle(float a0, float a1) |
float delta_angle(float a0, float a1) |
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{ |
{ |
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Latest revision as of 12:21, 21 April 2020
In general, the smallest angle (angular distance) between two vectors is given by:
(if and are unit/normalized, then this can be simplified further).
Given two angles and , you could substitute and above, or you could use the following code:
![{\displaystyle A=\left[\cos a_{0},\sin a_{0}\right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/41d79c2cfa41f0a5d487eea6ee71ed161a83543d)
![{\displaystyle B=\left[\cos a_{1},\sin a_{1}\right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4e74496032f5970d3db2c3e31018091bf5339c5b)
// https://gamedev.stackexchange.com/a/4472
// a0 and a1 are in radians (always positive)
float delta_angle(float a0, float a1)
{
return M_PI - fabs(fabs(a1 - a0) - M_PI);
}