polar2cart: Polar to Cartesian Coordinate Reconstruction

Converting polar representation back to rectangular coordinates

The polar2cart functions perform the inverse transformation of cart2polar, reconstructing Cartesian coordinates from polar and spherical representations.

2D Cartesian Reconstruction

For polar coordinates $(\theta, r)$, the Cartesian reconstruction produces $(x, y)$:

$x = r \cos(\theta)$ $y = r \sin(\theta)$

3D Cartesian Reconstruction

For spherical coordinates $(r, \phi, \theta)$, the Cartesian reconstruction produces $(x, y, z)$:

$x = r \cos(\theta) \sin(\phi)$ $y = r \sin(\theta) \sin(\phi)$ $z = r \cos(\phi)$

Function Variants

Function	Input	Output	Description
polar2cart(polar)	vec2	vec2	2D polar to Cartesian $(\theta,r) \rightarrow (x,y)$
polar2cart3D(r,phi,theta)	float,float,float	vec3	3D spherical to Cartesian

ライブエディター

const fragment = () => {
      const r = 0.3
      const phi = uv.x.mul(3.14)
      const theta = uv.y.mul(6.28)
      const sphere3d = polar2cart3D(r, phi, theta)
      const projection = sphere3d.xy.add(0.5)
      const depth = sphere3d.z.mul(2).add(0.5)
      return vec4(vec3(projection, depth), 1)
}

結果

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