Use Curvenote
Coordinate Transformation
How do you change from a radial coordinate system to Cartesian coordinate system?!
Cartesian Coordinate System
- $x$
-
- $y$
-
Radial Coordinate System
- $r$
-
- $\theta$
-
°
Cartesian Update- $x$
x =
<r-dynamic :value="x" :change="{x: value}"></r-dynamic>
Cartesian Update - $y$
y =
<r-dynamic :value="y" :change="{y: value}"></r-dynamic>
Radius Update - $r$
r &= \sqrt{x^2 + y^2} = \\
x &= r \cos(\operatorname{atan2}(y, x)) = \\
y &= r \sin(\operatorname{atan2}(y, x)) =
<r-dynamic :value="Math.sqrt(x*x + y*y)" :change="{
x: value * Math.cos(Math.atan2(y, x)),
y: value * Math.sin(Math.atan2(y, x))
}"></r-dynamic>
Theta Update - $\theta$
\theta &= \operatorname{atan2}(y, x) = \\
x &= \sqrt{x^2 + y^2} \cos( \theta ) = \\
y &= \sqrt{x^2 + y^2} \sin( \theta ) =
<r-dynamic :value="Math.atan2(y, x)" :change="{
x: Math.sqrt(x*x + y*y) * Math.cos(value),
y: Math.sqrt(x*x + y*y) * Math.sin(value)
}"></r-dynamic>
Made with love by 
Curvenote
Last updated August 24th, 2021