Desmos Graphing in Obsidian

⚠️ CRITICAL: Dual Parser System

The plugin uses different parsers for different parts:

pi

left=-2*pi+0.5

\pi

\sqrt{x}

y=\sqrt{x}+\pi

\pi

\sqrt{x}

(\pi/2, 1)

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" (p*i)
(pi/2, 0)                 # Error: "Too many variables" ← Points need LaTeX!
y=x/sqrt(3)|0<=x<=sqrt(3) # Error: "Too many variables" (s*q*r*t)

Key rule:

\sqrt{x}

x^0.5

Code Block Format

```desmos-graph
[settings]
---
[equations]
```

• Settings (optional) above

  ---

  , equations below
• Each equation on its own line
• Use

  |

  to add styling/restrictions to equations

Quick Start

Basic Function

```desmos-graph
y=x^2
y=\sin(x)|blue
```

With Settings

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

Points and Labels

```desmos-graph
(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)

(pi/2, 0)

Essential Settings

width

height

left

right

bottom

top

grid

degreeMode

radians

degrees

Additional Settings

hideAxisNumbers

xAxisLabel

yAxisLabel

xAxisLogarithmic

yAxisLogarithmic

defaultColor

Settings use

=

;

left=-2*pi

Equation Styling

Use

|

equation|color|style|restrictions|label

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

⚠️ CRITICAL:

|

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

#rgb

#ff6600

#f60

⚠️

gray

grey

• Light gray:

  #c0c0c0

• Medium gray:

  #808080

• Dark gray:

  #404040

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

Line & Point Styles

solid

point

dashed

open

dotted

cross

Labels

(1, 2)|label

(1, 2)|label:Point A

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!

x/2<y

\frac{x}{2}<y

x^0.5<2

\sqrt{x}<2

^0.5

\sqrt

0<x<3^0.5

0<x<sqrt(3)

sqrt()

x>-1.5708

x>-pi/2

pi

0<x<1

\{0<x<1\}

The plugin auto-wraps restrictions with

{}

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

y=x^2

x^2+y^2=25

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

r=1+\cos(\theta)

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

(3, 4)

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

```desmos-graph
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

```desmos-graph
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

```desmos-graph
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

```desmos-graph
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

2*pi

\pi

3*\pi/2

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