docs: expand Manim CE reference docs with additional API coverage

Add geometry mobjects, movement/creation animations, and LaTeX
environments to the skill's reference docs. All verified against
Manim CE v0.20.1.

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

skills/creative/manim-video/SKILL.md

@@ -24,7 +24,7 @@ This is educational cinema. Every frame teaches. Every animation reveals structu
 
 ## Prerequisites
 
-Run `scripts/setup.sh` to verify all dependencies. Requires: Python 3.10+, Manim Community Edition (`pip install manim`), LaTeX (`texlive-full` on Linux, `mactex` on macOS), and ffmpeg.
+Run `scripts/setup.sh` to verify all dependencies. Requires: Python 3.10+, Manim Community Edition v0.20+ (`pip install manim`), LaTeX (`texlive-full` on Linux, `mactex` on macOS), and ffmpeg. Reference docs tested against Manim CE v0.20.1.
 
 ## Modes
 

skills/creative/manim-video/references/animations.md

@@ -50,6 +50,31 @@ self.play(circle.animate.set_color(RED))
 self.play(circle.animate.shift(RIGHT * 2).scale(0.5))  # chain multiple
 ```
 
+## Additional Creation Animations
+
+```python
+self.play(GrowFromPoint(circle, LEFT * 3))     # scale 0 -> 1 from a specific point
+self.play(GrowFromEdge(rect, DOWN))             # grow from one edge
+self.play(SpinInFromNothing(square))            # scale up while rotating (default PI/2)
+self.play(GrowArrow(arrow))                     # grows arrow from start to tip
+```
+
+## Movement Animations
+
+```python
+# Move a mobject along an arbitrary path
+path = Arc(radius=2, angle=PI)
+self.play(MoveAlongPath(dot, path), run_time=2)
+
+# Rotate (as a Transform, not .animate — supports about_point)
+self.play(Rotate(square, angle=PI / 2, about_point=ORIGIN), run_time=1.5)
+
+# Rotating (continuous rotation, updater-style — good for spinning objects)
+self.play(Rotating(gear, angle=TAU, run_time=4, rate_func=linear))
+```
+
+`MoveAlongPath` takes any `VMobject` as the path — use `Arc`, `CubicBezier`, `Line`, or a custom `VMobject`. Position is computed via `path.point_from_proportion()`.
+
 ## Emphasis Animations
 
 ```python

skills/creative/manim-video/references/equations.md

@@ -65,6 +65,57 @@ MathTex(r"\vec{v}")                       # vector
 MathTex(r"\lim_{x \to \infty} f(x)")    # limit
 ```
 
+## Matrices
+
+`MathTex` supports standard LaTeX matrix environments via `amsmath` (loaded by default):
+
+```python
+# Bracketed matrix
+MathTex(r"\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}")
+
+# Parenthesized matrix
+MathTex(r"\begin{pmatrix} a & b \\ c & d \end{pmatrix}")
+
+# Determinant (vertical bars)
+MathTex(r"\begin{vmatrix} a & b \\ c & d \end{vmatrix}")
+
+# Plain (no delimiters)
+MathTex(r"\begin{matrix} x_1 \\ x_2 \\ x_3 \end{matrix}")
+```
+
+For matrices you need to animate element-by-element or color individual entries, use the `IntegerMatrix`, `DecimalMatrix`, or `MobjectMatrix` mobjects instead — see `mobjects.md`.
+
+## Cases and Piecewise Functions
+
+```python
+MathTex(r"""
+    f(x) = \begin{cases}
+        x^2    & \text{if } x \geq 0 \\
+        -x^2   & \text{if } x < 0
+    \end{cases}
+""")
+```
+
+## Aligned Environments
+
+For multi-line derivations with alignment, use `aligned` inside `MathTex`:
+
+```python
+MathTex(r"""
+    \begin{aligned}
+        \nabla \cdot \mathbf{E} &= \frac{\rho}{\epsilon_0} \\
+        \nabla \cdot \mathbf{B} &= 0 \\
+        \nabla \times \mathbf{E} &= -\frac{\partial \mathbf{B}}{\partial t} \\
+        \nabla \times \mathbf{B} &= \mu_0 \mathbf{J} + \mu_0 \epsilon_0 \frac{\partial \mathbf{E}}{\partial t}
+    \end{aligned}
+""")
+```
+
+Note: `MathTex` wraps content in `align*` by default. Override with `tex_environment` if needed:
+```python
+MathTex(r"...", tex_environment="gather*")
+```
+
 ## Derivation Pattern
 
 ```python

skills/creative/manim-video/references/mobjects.md

@@ -35,6 +35,52 @@ rrect = RoundedRectangle(corner_radius=0.3, width=4, height=2)
 brace = Brace(rect, DOWN, color=YELLOW)
 ```
 
+## Polygons and Arcs
+
+```python
+# Arbitrary polygon from vertices
+poly = Polygon(LEFT, UP * 2, RIGHT, color=GREEN, fill_opacity=0.3)
+
+# Regular n-sided polygon
+hexagon = RegularPolygon(n=6, color=TEAL, fill_opacity=0.4)
+
+# Triangle (shorthand for RegularPolygon(n=3))
+tri = Triangle(color=YELLOW, fill_opacity=0.5)
+
+# Arc (portion of a circle)
+arc = Arc(radius=2, start_angle=0, angle=PI / 2, color=BLUE)
+
+# Arc between two points
+arc_between = ArcBetweenPoints(LEFT * 2, RIGHT * 2, angle=TAU / 4, color=RED)
+
+# Curved arrow (arc with tip)
+curved_arrow = CurvedArrow(LEFT * 2, RIGHT * 2, color=ORANGE)
+```
+
+## Sectors and Annuli
+
+```python
+# Sector (pie slice)
+sector = Sector(outer_radius=2, start_angle=0, angle=PI / 3, fill_opacity=0.7, color=BLUE)
+
+# Annulus (ring)
+ring = Annulus(inner_radius=1, outer_radius=2, fill_opacity=0.5, color=GREEN)
+
+# Annular sector (partial ring)
+partial_ring = AnnularSector(
+    inner_radius=1, outer_radius=2,
+    angle=PI / 2, start_angle=0,
+    fill_opacity=0.7, color=TEAL
+)
+
+# Cutout (punch holes in a shape)
+background = Square(side_length=4, fill_opacity=1, color=BLUE)
+hole = Circle(radius=0.5)
+cutout = Cutout(background, hole, fill_opacity=1, color=BLUE)
+```
+
+Use cases: pie charts, ring progress indicators, Venn diagrams with arcs, geometric proofs.
+
 ## Positioning
 
 ```python
@@ -99,6 +145,29 @@ class NetworkNode(Group):
         self.add(self.circle, self.label)
 ```
 
+## Matrix Mobjects
+
+Display matrices as grids of numbers or mobjects:
+
+```python
+# Integer matrix
+m = IntegerMatrix([[1, 2], [3, 4]])
+
+# Decimal matrix (control decimal places)
+m = DecimalMatrix([[1.5, 2.7], [3.1, 4.9]], element_to_mobject_config={"num_decimal_places": 2})
+
+# Mobject matrix (any mobject in each cell)
+m = MobjectMatrix([
+    [MathTex(r"\pi"), MathTex(r"e")],
+    [MathTex(r"\phi"), MathTex(r"\tau")]
+])
+
+# Bracket types: "(" "[" "|" or "\\{"
+m = IntegerMatrix([[1, 0], [0, 1]], left_bracket="[", right_bracket="]")
+```
+
+Use cases: linear algebra, transformation matrices, system-of-equations coefficient display.
+
 ## Constants
 
 Directions: `UP, DOWN, LEFT, RIGHT, ORIGIN, UL, UR, DL, DR`