This is a list of the FIVE (plus one!) measures of distance that every #gamedev should know!
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Starting from the most well-known one...
1โฃ EUCLIDEAN DISTANCE ๐
Measures the distance between two points, using the Pythagorean theorem.
In Unity: Vector3.Distance(A,B).
๐งต๐
Starting from the most well-known one...
1โฃ EUCLIDEAN DISTANCE ๐
Measures the distance between two points, using the Pythagorean theorem.
In Unity: Vector3.Distance(A,B).
2โฃ VECTOR DISTANCE ๐
Is a vector that starts from ๐ ฐ๏ธ and goes to ๐ ฑ๏ธ.
It is pretty handy in LINEAR ALGEBRA, as it can avoid Trigonometry.
It has a DIRECTION, meaning that ๐ ฐ๏ธ-๐ ฑ๏ธ is not the same of ๐ ฑ๏ธ-๐ ฐ๏ธ!
In Unity, you can calculate it by simply subtracting the two vectors!
Is a vector that starts from ๐ ฐ๏ธ and goes to ๐ ฑ๏ธ.
It is pretty handy in LINEAR ALGEBRA, as it can avoid Trigonometry.
It has a DIRECTION, meaning that ๐ ฐ๏ธ-๐ ฑ๏ธ is not the same of ๐ ฑ๏ธ-๐ ฐ๏ธ!
In Unity, you can calculate it by simply subtracting the two vectors!
3โฃ COSINE DISTANCE ๐ก
It measures the alignment of two UNIT VECTORS, as the cosine of the angle between them:
๐น A โข B = +1 โ fully aligned
๐น A โข B = 0 โ orthogonal
๐น A โข B = -1 โ opposite direction
Also known as DOT PRODUCT, it is very useful for shaders!
It measures the alignment of two UNIT VECTORS, as the cosine of the angle between them:
๐น A โข B = +1 โ fully aligned
๐น A โข B = 0 โ orthogonal
๐น A โข B = -1 โ opposite direction
Also known as DOT PRODUCT, it is very useful for shaders!
3โฃbis: ORTHOGONAL PROJECTION
When the DOT PRODUCT is used on two vectors that are not UNIT VECTORS, it actually projects one onto another.
Below, you can see that A โข B actually measures the ORTHOGONAL PROJECTION of A onto B.
In Unity: Vector3.Dot(A,B)
When the DOT PRODUCT is used on two vectors that are not UNIT VECTORS, it actually projects one onto another.
Below, you can see that A โข B actually measures the ORTHOGONAL PROJECTION of A onto B.
In Unity: Vector3.Dot(A,B)
4โฃ MANHATTAN DISTANCE ๐๏ธ
Also known as TAXICAB DISTANCE, it measures the distance between two points when you cannot move diagonally. Pretty much like in a big city like Manhattan!
Both Euclidean & Manhattan are special cases of the MINKOWSKY DISTANCE.
Also known as TAXICAB DISTANCE, it measures the distance between two points when you cannot move diagonally. Pretty much like in a big city like Manhattan!
Both Euclidean & Manhattan are special cases of the MINKOWSKY DISTANCE.
5โฃ GREAT-CIRCLE DISTANCE ๐
The shortest distance between two points on the surface of a sphere.
You need to know:
๐นr: radius of the sphere
๐นฮป: longitude of both points
๐นฯ: latitude of both points
For small enough distances, it converges to the Euclidean distance.
The shortest distance between two points on the surface of a sphere.
You need to know:
๐นr: radius of the sphere
๐นฮป: longitude of both points
๐นฯ: latitude of both points
For small enough distances, it converges to the Euclidean distance.
โจ Thank you for reading! โจ
If you are interested in #gamedev, shader coding, AI & ML, follow me for more content like this! ๐
I also have a @Patreon with hundreds of Unity tutorials! Feel free to have a look! โบ๏ธ
patreon.com/AlanZucconi
If you are interested in #gamedev, shader coding, AI & ML, follow me for more content like this! ๐
I also have a @Patreon with hundreds of Unity tutorials! Feel free to have a look! โบ๏ธ
patreon.com/AlanZucconi
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