Is there a Polar transformation available in CSS3?

Converting a line into a ring is a straightforward process in graphic design software like GIMP:

https://i.sstatic.net/7lQZe.png
(source: adamhaskell.net)

I'm exploring the possibility of achieving the same effect using CSS.

Here's what I've figured out so far:

  • The algorithm mentioned above maps x to r and y to θ
  • To do this, x is scaled to the range of [0,w/2], where w represents the image width
  • Similarly, y is scaled to the range of [0,2π]
  • To reverse the transformation from polar coordinates to Cartesian: xc = rp*cos(θp) and yc = rp*sin(θp)
  • The outcome is then shifted so that the origin aligns with the center of the image.
  • Therefore, we have:

 

x' = (x/2)*cos(y/h*2π) + w/2;  
y' = (x/2)*sin(y/h*2π) + h/2;

All seems well, but how can I implement such a transformation in CSS? Since conventional keywords might not be applicable, the solution likely involves a Matrix transform. However, constructing a matrix based on the given equations poses a challenge, let alone representing it within a CSS transform.

Is there anyone who can assist me with this final step?

csscss-transforms

Answer №1

While I haven't had the opportunity to work extensively with CSS transform matrices, it seems that achieving your desired outcome is not feasible. Transform matrices perform linear transformations, which always result in mapping a straight line to another straight line or potentially to 0. For further exploration on this topic, you can refer to Wikipedia's comprehensive information.

In conclusion, utilizing matrices will not allow for the transformation of a straight line into a circle.

Answer №2

Discover the beauty of creating two symmetrical third order Bezier curves with ease.

Embrace the formula Y(t) = (t^3, t^2, t, 1) * M * (P0, P1, P2, P3).

In this equation, t represents time and P0 - P3 symbolize the control points' coordinates. Remember, the vector must be vertical for accurate representation.

Y(t) signifies the curve's coordinate, while matrix M takes the form of a 4*4 structure: row 1 (-1, 3, -3, 1), row 2 (3, -6, -3, 0), row 3 (-3, 3, 0, 0), row 4 (1, 0, 0, 0).

Take the next step by defining a function to determine the control points based on your line's coordinate system.

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