video/.claude/skills/manimgl-best-practices/references/equation_transforms.md

Equation Transforms - Reference Guide

Example file: examples/equation_transforms.py

User Query Scenarios

This example addresses queries like:

• "Show step-by-step equation derivation"
• "Animate the quadratic formula derivation"
• "Highlight parts of an equation"
• "Show variable substitution with color tracking"
• "Add braces to explain equation parts"

Scene Thinking Process (3b1b Style)

1. Core Concept

Mathematical Derivations: Step-by-step equation manipulation is clearer when terms are color-coded and transformations are animated smoothly.

2. Technical Implementation

Color-Coded Terms with t2c

eq = Tex(
    r"ax^2 + bx + c = 0",
    t2c={"a": RED, "b": GREEN, "c": BLUE, "x": YELLOW}
)

Smooth Equation Transformation

eq1 = Tex(r"ax^2 + bx + c = 0", t2c=colors)
eq2 = Tex(r"x^2 + \frac{b}{a}x + \frac{c}{a} = 0", t2c=colors)
self.play(TransformMatchingTex(eq1.copy(), eq2))

Key insight: TransformMatchingTex matches characters between equations and morphs them smoothly.

Highlighting with SurroundingRectangle

part = eq[r"a^2"]  # Select by tex string
rect = SurroundingRectangle(part, color=RED, buff=0.05)
self.play(ShowCreation(rect))

Brace Annotations

brace = Brace(eq["F"], UP, color=BLUE)
label = brace.get_text("Force", font_size=30)
self.play(GrowFromCenter(brace), FadeIn(label, UP))

3. Scene Variants

Scene	Purpose
QuadraticFormula	Full derivation with step labels
HighlightAndTransform	Highlighting + visual proof
BraceAnnotations	F=ma with labeled parts
ColorCodedSubstitution	u-substitution with tracking

Key Patterns

Pattern: Step Labels

step_label = Text("Divide by a", font_size=24, color=GREY)
step_label.next_to(eq2, LEFT, buff=0.5)
self.play(FadeIn(step_label, LEFT))

Pattern: Final Answer Box

final = Tex(r"x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}")
box = SurroundingRectangle(final, color=GOLD, buff=0.2)
self.play(ShowCreation(box))

Pattern: Selecting Equation Parts

# By tex substring
eq["x^2"]  # Returns submobject matching "x^2"
eq[r"\frac{b}{a}"]  # LaTeX commands work too

# By index
eq[0]  # First character/group

Run Commands

manimgl equation_transforms.py QuadraticFormula -w
manimgl equation_transforms.py HighlightAndTransform -w
manimgl equation_transforms.py BraceAnnotations -w
manimgl equation_transforms.py ColorCodedSubstitution -w