tc@amd.UUCP (Tom Crawford) (12/19/85)
*THIS BE FO' THE LINE-EATER* One method of drawing anti-aliased lines into a bit map involves linearly decreasing the intensity as you get further from the ideal line. I have heard that this produces an undesirable effect called the "Barber-pole" or Barbed-Wire" effect. Anybody know about this? Got any references? Please respond by e-mail and I will summarize. Thanks, as they say, in advance. Tom Crawford ...amdcad!amd!tc
ken@turtlevax.UUCP (Ken Turkowski) (12/20/85)
In article <2046@amd.UUCP> tc@amd.UUCP (Tom Crawford) writes: >One method of drawing anti-aliased lines into a bit map involves >linearly decreasing the intensity as you get further from the ideal >line. I have heard that this produces an undesirable effect called >the "Barber-pole" or Barbed-Wire" effect. Anybody know about this? >Got any references? I call it the twisted-rope effect. This is because you are using a poor low-pass filter, which lets in a lot of high-frequency aliases. I would instead recommend something that doesn't have sharp discontinuities in the first derivative like your tent-function does. I'm particularly fond of a Gaussian that is half-amplitude at one-pixel's distance from the line. The class of anti-aliasing you are speaking of goes something like this: 1) Calculate the perpendicular distance from the pixel to the line; this NEEDS to be done to sub-pixel resolution. 2) Use this distance as an argument to a function h() with the following properties: h(0) = 1; h(oo) = 0; (practically, though, h(x)=0, |x| > 1 to 3 pixels) h(-r) = h(r) h'(|r|) <= 0 If you know what kind of radially-symmetric impulse response g() you want for your low-pass filter, you can use what I call the Radial Line Transformation to derive a function that can be used for the lookup. oo __________ h(r) = intgrl g(\/ r^2 + y^2) dy -oo where g() is the desired radially-symmetric impulse response and h() is the lookup function. One of the reasons I like the Gaussian is that the Gaussian transforms into itself. I have not tried doing the inverse transform of the tent function (triangular pulse), but I suspect it has real nasty frequency characteristics. Can anybody out there in math-land come up with a formula for the inversion of this transform? Is it one-to-one, onto, both or neither? For more detail, including anti-aliasing for polygons, see: Turkowski, K. "Anti-aliasing through the Use of Coordinate Transformations", ACM Transactions on Graphics, vol. 1, no. 3, July 1982, pp.215-234 -- Ken Turkowski @ CIMLINC, Menlo Park, CA UUCP: {amd,decwrl,hplabs,seismo,spar}!turtlevax!ken ARPA: turtlevax!ken@DECWRL.DEC.COM