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Use direction_to, remove code example for manually normalizing (#3330)

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Also link to matrices and transforms and 3Blue1Brown from within the advanced vector math article.
This commit is contained in:
Aaron Franke
2020-03-31 10:06:18 -04:00
committed by GitHub
parent 76ae949feb
commit a9ef557151
2 changed files with 19 additions and 24 deletions
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32
tutorials/math/vector_math.rst
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@@ -188,25 +188,8 @@ Normalization
**Normalizing** a vector means reducing its length to ``1`` while
preserving its direction. This is done by dividing each of its components
by its magnitude:
.. tabs::
.. code-tab:: gdscript GDScript
var a = Vector2(2, 4)
var m = sqrt(a.x*a.x + a.y*a.y) # get magnitude "m" using the Pythagorean theorem
a.x /= m
a.y /= m
.. code-tab:: csharp
var a = new Vector2(2, 4);
var m = Mathf.Sqrt(a.x*a.x + a.y*a.y); // get magnitude "m" using the Pythagorean theorem
a.x /= m;
a.y /= m;
Because this is such a common operation, ``Vector2`` and ``Vector3`` provide
a method for normalizing:
by its magnitude. Because this is such a common operation,
``Vector2`` and ``Vector3`` provide a method for normalizing:
.. tabs::
.. code-tab:: gdscript GDScript
@@ -291,12 +274,12 @@ the order of the two vectors does not matter:
.. code-tab:: gdscript GDScript
var c = a.dot(b)
var d = b.dot(a) # these are equivalent
var d = b.dot(a) # These are equivalent.
.. code-tab:: csharp
float c = a.Dot(b);
float d = b.Dot(a); // these are equivalent
float d = b.Dot(a); // These are equivalent.
The dot product is most useful when used with unit vectors, making the
first formula reduce to just ``cosθ``. This means we can use the dot
@@ -319,7 +302,8 @@ zombies ``A`` and ``B``. Assuming a zombie's field of view is **180°**, can the
The green arrows ``fA`` and ``fB`` are **unit vectors** representing the
zombies' facing directions and the blue semicircle represents its field of
view. For zombie ``A``, we find the direction vector ``AP`` pointing to
the player using ``P - A`` and normalize it. If the angle between this
the player using ``P - A`` and normalize it, however, Godot has a helper
method to do this called ``direction_to``. If the angle between this
vector and the facing vector is less than 90°, then the zombie can see
the player.
@@ -328,13 +312,13 @@ In code it would look like this:
.. tabs::
.. code-tab:: gdscript GDScript
var AP = (P - A).normalized()
var AP = A.direction_to(P)
if AP.dot(fA) > 0:
print("A sees P!")
.. code-tab:: csharp
var AP = (P - A).Normalized();
var AP = A.DirectionTo(P);
if (AP.Dot(fA) > 0)
{
GD.Print("A sees P!");