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Removing trailing whitespace
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@@ -201,7 +201,7 @@ that hasn't been translated, rotated or scaled.
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var m = Transform2D()
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print(m)
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# prints: ((1, 0), (0, 1), (0, 0))
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.. code-tab:: csharp
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@@ -442,7 +442,7 @@ If the matrix is orthonormal, then:
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.. tabs::
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.. code-tab:: gdscript GDScript
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# if m is orthonormal, then
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pos = mi.xform(pos)
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# is the same is
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@@ -158,7 +158,7 @@ the velocity to the current position.
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.. image:: img/vector_movement1.png
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.. tip:: Velocity measures the **change** in position per unit of time. The
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.. tip:: Velocity measures the **change** in position per unit of time. The
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new position is found by adding velocity to the previous position.
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- Pointing toward a target
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@@ -189,14 +189,14 @@ by its magnitude:
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.. code-tab:: gdscript GDScript
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var a = Vector2(2, 4)
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var m = sqrt(a.x*a.x + a.y*a.y) # get magnitude "m" using the Pythagorean theorem
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var m = sqrt(a.x*a.x + a.y*a.y) # get magnitude "m" using the Pythagorean theorem
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a.x /= m
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a.y /= m
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.. code-tab:: csharp
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var a = new Vector2(2, 4);
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var m = Mathf.Sqrt(a.x*a.x + a.y*a.y); // get magnitude "m" using the Pythagorean theorem
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var m = Mathf.Sqrt(a.x*a.x + a.y*a.y); // get magnitude "m" using the Pythagorean theorem
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a.x /= m;
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a.y /= m;
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@@ -249,7 +249,7 @@ to handle this. Here is a GDScript example of the diagram above using a
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move_and_collide(reflect)
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.. code-tab:: csharp
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// KinematicCollision2D contains information about the collision
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KinematicCollision2D collision = MoveAndCollide(_velocity * delta);
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if (collision != null)
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@@ -270,13 +270,13 @@ direction, a scalar value has only magnitude.
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The formula for dot product takes two common forms:
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.. math::
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A \cdot B = \left \| A \right \|\left \| B \right \|\cos \Theta
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and
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.. math::
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A \cdot B = A_{x}B_{x} + A_{y}B_{y}
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However, in most cases it is easiest to use the built-in method. Note that
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@@ -261,7 +261,7 @@ Code should be something like this:
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break; // with one that fails, it's enough
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}
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}
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Pretty cool, huh? But this gets much better! With a little more effort,
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similar logic will let us know when two convex polygons are overlapping
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too. This is called the Separating Axis Theorem (or SAT) and most
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@@ -328,7 +328,7 @@ Code should be something like this:
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break;
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}
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}
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if (allOut)
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{
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// a separating plane was found
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@@ -353,7 +353,7 @@ Code should be something like this:
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break;
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}
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}
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if (allOut)
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{
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overlapping = false;
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@@ -481,7 +481,7 @@ So the final algorithm is something like:
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print("Polygons collided!")
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.. code-tab:: csharp
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var overlapping = true;
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foreach (Plane plane in planesOfA)
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@@ -520,7 +520,7 @@ So the final algorithm is something like:
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break;
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}
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}
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if (allOut)
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{
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overlapping = false;
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