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" (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} in equations, x^0.5 in restrictions!

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) 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

```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, 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