Refactor baking code for Curve2D

The main change is to caculate tangent directly from bezier curve, without going
through discretized polyline, avoiding pitfalls of discretization. A similar refacor
had been applied to Curve3D.

The test cases for Curve2D is updated, comparing floating point with is_equal_approxmiate()
instead of `==`, in order to avoid float precision problem.

5 files changed, 18 insertions, 14 deletions

diff --git a/doc/classes/@GlobalScope.xml b/doc/classes/@GlobalScope.xml
index 977bcb78e9..4a6b85f229 100644
--- a/doc/classes/@GlobalScope.xml
+++ b/doc/classes/@GlobalScope.xml
@@ -115,7 +115,7 @@
 			<param index="3" name="end" type="float" />
 			<param index="4" name="t" type="float" />
 			<description>
-				Returns the derivative at the given [param t] on a one-dimensional [url=https://en.wikipedia.org/wiki/B%C3%A9zier_curve]Bezier curve[/url] defined by the given [param control_1], [param control_2], and [param end] points.
+				Returns the derivative at the given [param t] on a one-dimensional [url=https://en.wikipedia.org/wiki/B%C3%A9zier_curve]Bézier curve[/url] defined by the given [param control_1], [param control_2], and [param end] points.
 			</description>
 		</method>
 		<method name="bezier_interpolate">
@@ -126,7 +126,7 @@
 			<param index="3" name="end" type="float" />
 			<param index="4" name="t" type="float" />
 			<description>
-				Returns the point at the given [param t] on a one-dimensional [url=https://en.wikipedia.org/wiki/B%C3%A9zier_curve]Bezier curve[/url] defined by the given [param control_1], [param control_2], and [param end] points.
+				Returns the point at the given [param t] on a one-dimensional [url=https://en.wikipedia.org/wiki/B%C3%A9zier_curve]Bézier curve[/url] defined by the given [param control_1], [param control_2], and [param end] points.
 			</description>
 		</method>
 		<method name="bytes_to_var">
diff --git a/doc/classes/Curve2D.xml b/doc/classes/Curve2D.xml
index ccdf085319..b5e75dff68 100644
--- a/doc/classes/Curve2D.xml
+++ b/doc/classes/Curve2D.xml
@@ -51,7 +51,7 @@
 			<return type="Vector2" />
 			<param index="0" name="to_point" type="Vector2" />
 			<description>
-				Returns the closest baked point (in curve's local space) to [param to_point].
+				Returns the closest point on baked segments (in curve's local space) to [param to_point].
 				[param to_point] must be in this curve's local space.
 			</description>
 		</method>
@@ -94,7 +94,7 @@
 		</method>
 		<method name="sample_baked" qualifiers="const">
 			<return type="Vector2" />
-			<param index="0" name="offset" type="float" />
+			<param index="0" name="offset" type="float" default="0.0" />
 			<param index="1" name="cubic" type="bool" default="false" />
 			<description>
 				Returns a point within the curve at position [param offset], where [param offset] is measured as a pixel distance along the curve.
@@ -104,13 +104,10 @@
 		</method>
 		<method name="sample_baked_with_rotation" qualifiers="const">
 			<return type="Transform2D" />
-			<param index="0" name="offset" type="float" />
+			<param index="0" name="offset" type="float" default="0.0" />
 			<param index="1" name="cubic" type="bool" default="false" />
-			<param index="2" name="loop" type="bool" default="true" />
-			<param index="3" name="lookahead" type="float" default="4.0" />
 			<description>
 				Similar to [method sample_baked], but returns [Transform2D] that includes a rotation along the curve. Returns empty transform if length of the curve is [code]0[/code].
-				Use [param loop] to smooth the tangent at the end of the curve. [param lookahead] defines the distance to a nearby point for calculating the tangent vector.
 				[codeblock]
 				var transform = curve.sample_baked_with_rotation(offset)
 				position = transform.get_origin()
@@ -160,6 +157,13 @@
 				[param tolerance_degrees] controls how many degrees the midpoint of a segment may deviate from the real curve, before the segment has to be subdivided.
 			</description>
 		</method>
+		<method name="tessellate_even_length" qualifiers="const">
+			<return type="PackedVector2Array" />
+			<param index="0" name="max_stages" type="int" default="5" />
+			<param index="1" name="tolerance_length" type="float" default="20.0" />
+			<description>
+			</description>
+		</method>
 	</methods>
 	<members>
 		<member name="bake_interval" type="float" setter="set_bake_interval" getter="get_bake_interval" default="5.0">
diff --git a/doc/classes/Curve3D.xml b/doc/classes/Curve3D.xml
index 851996131f..cfe2036499 100644
--- a/doc/classes/Curve3D.xml
+++ b/doc/classes/Curve3D.xml
@@ -114,7 +114,7 @@
 		</method>
 		<method name="sample_baked" qualifiers="const">
 			<return type="Vector3" />
-			<param index="0" name="offset" type="float" />
+			<param index="0" name="offset" type="float" default="0.0" />
 			<param index="1" name="cubic" type="bool" default="false" />
 			<description>
 				Returns a point within the curve at position [param offset], where [param offset] is measured as a distance in 3D units along the curve.
@@ -134,7 +134,7 @@
 		</method>
 		<method name="sample_baked_with_rotation" qualifiers="const">
 			<return type="Transform3D" />
-			<param index="0" name="offset" type="float" />
+			<param index="0" name="offset" type="float" default="0.0" />
 			<param index="1" name="cubic" type="bool" default="false" />
 			<param index="2" name="apply_tilt" type="bool" default="false" />
 			<description>
diff --git a/doc/classes/Vector2.xml b/doc/classes/Vector2.xml
index 4156030d77..1cd73688ee 100644
--- a/doc/classes/Vector2.xml
+++ b/doc/classes/Vector2.xml
@@ -93,7 +93,7 @@
 			<param index="2" name="end" type="Vector2" />
 			<param index="3" name="t" type="float" />
 			<description>
-				Returns the derivative at the given [param t] on the [url=https://en.wikipedia.org/wiki/B%C3%A9zier_curve]Bezier curve[/url] defined by this vector and the given [param control_1], [param control_2], and [param end] points.
+				Returns the derivative at the given [param t] on the [url=https://en.wikipedia.org/wiki/B%C3%A9zier_curve]Bézier curve[/url] defined by this vector and the given [param control_1], [param control_2], and [param end] points.
 			</description>
 		</method>
 		<method name="bezier_interpolate" qualifiers="const">
@@ -103,7 +103,7 @@
 			<param index="2" name="end" type="Vector2" />
 			<param index="3" name="t" type="float" />
 			<description>
-				Returns the point at the given [param t] on the [url=https://en.wikipedia.org/wiki/B%C3%A9zier_curve]Bezier curve[/url] defined by this vector and the given [param control_1], [param control_2], and [param end] points.
+				Returns the point at the given [param t] on the [url=https://en.wikipedia.org/wiki/B%C3%A9zier_curve]Bézier curve[/url] defined by this vector and the given [param control_1], [param control_2], and [param end] points.
 			</description>
 		</method>
 		<method name="bounce" qualifiers="const">
diff --git a/doc/classes/Vector3.xml b/doc/classes/Vector3.xml
index 2896408505..1d7eda6bb9 100644
--- a/doc/classes/Vector3.xml
+++ b/doc/classes/Vector3.xml
@@ -69,7 +69,7 @@
 			<param index="2" name="end" type="Vector3" />
 			<param index="3" name="t" type="float" />
 			<description>
-				Returns the derivative at the given [param t] on the [url=https://en.wikipedia.org/wiki/B%C3%A9zier_curve]Bezier curve[/url] defined by this vector and the given [param control_1], [param control_2], and [param end] points.
+				Returns the derivative at the given [param t] on the [url=https://en.wikipedia.org/wiki/B%C3%A9zier_curve]Bézier curve[/url] defined by this vector and the given [param control_1], [param control_2], and [param end] points.
 			</description>
 		</method>
 		<method name="bezier_interpolate" qualifiers="const">
@@ -79,7 +79,7 @@
 			<param index="2" name="end" type="Vector3" />
 			<param index="3" name="t" type="float" />
 			<description>
-				Returns the point at the given [param t] on the [url=https://en.wikipedia.org/wiki/B%C3%A9zier_curve]Bezier curve[/url] defined by this vector and the given [param control_1], [param control_2], and [param end] points.
+				Returns the point at the given [param t] on the [url=https://en.wikipedia.org/wiki/B%C3%A9zier_curve]Bézier curve[/url] defined by this vector and the given [param control_1], [param control_2], and [param end] points.
 			</description>
 		</method>
 		<method name="bounce" qualifiers="const">