Desmos Graphing in Obsidian

⚠️ CRITICAL: Dual Parser System

The plugin uses different parsers for different parts:

Location Parser pi sqrt Example

Settings mathjs pi

left=-2*pi+0.5

Equations Desmos (LaTeX) \pi

\sqrt{x}

y=\sqrt{x}+\pi

Points Desmos (LaTeX) \pi

\sqrt{x}

(\pi/2, 1)

Restrictions plain math numeric x^0.5

x>-1.5708

✅ CORRECT left=-0.5; right=2*pi+0.5

y=\sqrt{x}|blue y=x/\sqrt{3}|green|0<=x<=3^0.5 (\pi/2, 0)|label:cos(90°)=0

❌ WRONG (will error) left=-2*\pi # Error: "Syntax error in part '\pi'" y=\sin(x+pi/4) # Error: "Too many variables" (pi) (pi/2, 0) # Error: "Too many variables" ← Points need LaTeX! y=x/sqrt(3)|0<=x<=sqrt(3) # Error: "Too many variables" (sqrt)

Key rule: \sqrt{x} in equations, x^0.5 in restrictions!

Code Block Format

[settings]
---
[equations]

• Settings (optional) above --- , equations below

• Each equation on its own line

• Use | to add styling/restrictions to equations

Quick Start

Basic Function

y=x^2
y=\sin(x)|blue

With Settings

left=-2*pi; right=2*pi
bottom=-2; top=2
---
y=\sin(x)|red
y=\cos(x)|blue|dashed

Points and Labels

(0, 0)|label:Origin
(3, 4)|red|label:Point A
(\pi/2, 1)|blue|label:π/2    # Use \pi in coordinates!
y=x|dashed

⚠️ Points use LaTeX: (\pi/2, 0) not (pi/2, 0)

Essential Settings

Setting Default Description

width

600 Graph width in pixels

height

400 Graph height in pixels

left

-10 Left boundary

right

10 Right boundary

bottom

-7 Bottom boundary

top

7 Top boundary

grid

true Show grid lines

degreeMode

radians radians or degrees

Additional Settings

Setting Default Description

hideAxisNumbers

false Hide axis number labels

xAxisLabel

Custom x-axis label

yAxisLabel

Custom y-axis label

xAxisLogarithmic

false Logarithmic x-axis scale

yAxisLogarithmic

false Logarithmic y-axis scale

defaultColor

Default color for all equations

Settings use = for values, separated by ; or newlines. Bounds accept math expressions: left=-2*pi

Equation Styling

Use | (pipe) to add styling after an equation:

equation|color|style|restrictions|label

Segment order is flexible - the parser auto-detects each segment type.

⚠️ CRITICAL: | is RESERVED as delimiter!

The pipe character cannot appear in equations or labels:

(1, 0)|label:|v|=5 # ❌ Error: label parsed as empty (1, 0)|label:∥v∥=5 # ✅ Use Unicode ∥ (U+2225) y=|x| # ❌ Error: pipes split the equation y=abs(x) # ✅ Use abs() function

Colors

Supported names: red , green , blue , yellow , orange , purple , cyan , magenta , black , white

Hex codes: #rrggbb or #rgb (e.g., #ff6600 , #f60 )

⚠️ gray /grey are NOT supported! Use hex instead:

• Light gray: #c0c0c0

• Medium gray: #808080

• Dark gray: #404040

y=x|gray # ❌ Error: parsed as restriction y=x|#808080 # ✅ Correct

Line & Point Styles

Line Point Effect

solid

point

Default (solid/filled)

dashed

open

Dashed/open circle

dotted

cross

Dotted/X mark

Labels

(1, 2)|label shows "(1, 2)", (1, 2)|label:Point A shows custom text

Restrictions

Limit where equations are drawn:

y=x^2|0<x<5 # Only draw for 0 < x < 5 y=\sin(x)|x>0|y>0 # Multiple restrictions y=2x|0<=x<=1 # <= and >= supported y=\tan(x)|x>-1.5708|x<1.5708 # Use numeric values (π/2≈1.5708)

⚠️ CRITICAL: Use plain math, NOT LaTeX in restrictions!

✅ Correct ❌ Wrong Why

x/2<y

\frac{x}{2}<y

No LaTeX commands

x^0.5<2

\sqrt{x}<2

Use ^0.5 not \sqrt

0<x<3^0.5

0<x<sqrt(3)

sqrt() → sqr*t

x>-1.5708

x>-pi/2

pi → p*i, use numeric

0<x<1

{0<x<1}

No braces needed

The plugin auto-wraps restrictions with {}

• don't add them yourself.

Hidden & Special Tags

f(x)=x^2|hidden # Define but don't display y=f(x)+1 # Use the hidden function y=\sin(x)|noline # Points only, no connecting line

Combining Styles

Order doesn't matter:

y=x^2|red|dashed|0<x<5 (1, 2)|open|blue|label:Start

Equation Types

Type Example

Explicit y=x^2

Implicit x^2+y^2=25

Parametric (\cos(t), \sin(t))

Polar r=1+\cos(\theta)

Piecewise y={x<0: -x, x}

Point (3, 4)

Function def f(x)=x^2

⚠️ Polar Equations Must Be Linear in r

Desmos only supports polar equations where r appears linearly:

r=1+\cos(\theta) # ✅ Linear in r r^2=\cos(2\theta) # ❌ Error: "must be linear in r"

Solution: Convert to parametric curve:

Lemniscate (r² = cos(2θ)) → parametric form

(\cos(t)\sqrt{\cos(2t)}, \sin(t)\sqrt{\cos(2t)})|blue

Parametric Curves Warning

⚠️ Expand parenthetical expressions to avoid parsing errors:

(2t, 4t(1-t))|blue # ⚠️ May be misinterpreted as piecewise (2t, 4t-4t^2)|blue # ✅ Expanded form is safer

Piecewise Functions

⚠️ Escape curly braces with backslash:

y={x<0: -x, x} # ❌ Error y={x<0: -x, x} # ✅ Correct

Complete Examples

Trigonometric Phase Shifts

left=-2*pi; right=2*pi
bottom=-2; top=2
---
y=\sin(x)|blue
y=\sin(x+\pi/4)|red
y=\sin(x+\pi/2)|green
y=\sin(x+\pi)|purple|dashed

Bezier Curve with Control Points

left=-0.5; right=2.5
bottom=-0.5; top=2.5
---
(2t, 4t-4t^2)|blue
(0, 0)|black|label:P0
(1, 2)|black|label:P1
(2, 0)|black|label:P2
y=2x|#808080|dashed|0<x<1
y=-2x+4|#808080|dashed|1<x<2

Easing Functions

left=-0.2; right=1.2
bottom=-0.2; top=1.2
---
y=x|dashed|black
y=1-\cos(\pi*x/2)|blue|0<=x<=1
y=\sin(\pi*x/2)|red|0<=x<=1

Cosine with Special Points

left=-0.5; right=2*pi+0.5
bottom=-1.5; top=1.5
---
y=\cos(x)|blue
(0, 1)|red|label:cos(0)=1
(\pi/2, 0)|red|label:cos(π/2)=0
(\pi, -1)|red|label:cos(π)=-1
(3*\pi/2, 0)|red|label:cos(3π/2)=0

⚠️ Note: Settings use 2pi , points use \pi , 3\pi/2 , etc.

Advanced

For complete documentation, see reference.md:

• All 13 settings with defaults and auto-adjustment rules

• Hex codes for unsupported colors (gray, pink, brown, etc.)

• 13 error messages with causes and fixes

• Detailed troubleshooting for common issues

• Polar-to-parametric conversion examples