dear fellow scholars, this is two minute paperswith kã¡roly zsolnai-fehã©r. subsurface scattering means that not everyray of light is reflected or absorbed on the surface of a material, but some of it mayget inside somewhere, and come out somewhere else. for instance, our skin is a great and fairlyunknown example of that.
new materials for 3d printing, we can witness this beautiful effect if weplace a strong light source behind our ears. note that many other materials, such as plantleaves, many fruits such as apples and oranges, wax, marble also have subsurface scattering. the more we look at objects like these, themore we recognize how beautiful and ubiquitous
subsurface scattering and translucency isin mother nature. and today, our main question is whether wecan reproduce this kind of effect with 3d printed materials. the input would be a real material, such asthese slabs, and the output would be an arbitrary shaped 3d printed material with similar scatteringproperties. something that looks similar. what you see here is already the result ofthe 3d printing process, and wow, they look very tasty indeed. the process starts with a measurement apparatuswhere we grab a real material, and create
a diffusion profile from it that describeshow light scatters inside of this material. we have talked quite a bit about diffusionprofiles before, i've put some links to earlier episodes in the video description box. if you check it out, you'll see how we canadd subsurface scattering to an already existing image by "kind of" multiplying it with another image. this is another one of those amazing inventionsof mankind. now, onto 3d printing. when we would like to 3d print something,we basically have a few different materials to work with, and we have to specify a shape.
this shape is approximated with a three-dimensionalgrid. each of these tiny grid elements typicallyhave the thickness of several microns, which basically means a tiny fraction of the diameterof one hair strand, and we like to call these elements voxels. now, before printing, we have to specify whatkind of material we'd like to fill each of these voxels with. this is the general workflow for most 3d printers. what is specific to this work is that, afterthat, we have to take one column of this material, and look at the scattering properties of it.
let's call this column one stacking. we could measure that stacking by hand andsee how it relates to the original target material, and we are trying to minimize thedifference between the two. however, it would take millions of tries andwould likely take a lifetime to print just one high-quality reproduction. so basically, we have an optimization problemwhere we're looking for a stacking that will appear similar to the chosen diffusion profiles. the difference between the appearance of thetwo is to be minimized. however, we have to realize, that in physics,the laws of light scattering are well understood,
and the wonderful thing is that instead ofprinting a real object, we could just use a light simulation program to tell us howclose the results should be. now, this would work great, but it would stilltake an eternity because simulating light scattering through a stack of materials wouldtake the very least, several seconds. and we have to try up to millions of stackingsfor each column, and there is a lot of columns to compute. why a lot of different columns? well, it's because we have a heterogeneousproblem, which means that the whole material can contain variations in color and scatteringproperties.
the geometry may also be uneven, so this isa vastly more difficult formulation of the initial problem. a classical light simulation program wouldbe able to solve this, well, in a matter of years. however, there is a wonderful tool that isable to almost immediately tell us how much light is scattering inside of a stack of aton of different materials. an almost instant multi-layer scattering tool,if you will. it really is a miracle that we can get theresults for something so quickly that would otherwise require following the paths of millionsof light rays.
we call this technique the hankel transform. the mathematical description of it is absolutelybeautiful, but i personally think the best way of motivating these techniques is throughapplication. like this one. imagine that many mathematicians have to studythis transform without ever hearing what it can be used for. these are not some dry and tedious materialsthat one has to memorize - we can do miracles with these inventions, and i feel that peopleneed to know about that! with the use of the hankel transform and someadditional optimizations, one can efficiently
find solutions that lead to high-quality reproductionsof the input material. excellent piece of work, definitely one ofmy favorites in 3d fabrication. as always, we'd love to read your feedbackon this episode, let us know whether you have found it understandable! i hope you did! also, a quick shoutout to betterexplained.com. please note that this is not a sponsored message. it has multiple slogans, such as "math lessonsfor lasting insight" or "math without endless memorization".
this webpage is run by kalid azad, and containstons of intuitive math lessons i wish i had access to during my years at the university. for instance, here is his guide on fouriertransforms, which is a staple technique in every mathematician's and engineer's skillset, and is a prerequisite to understanding
the hankel transform. if you wish to learn mathematics, definitelycheck this website out, and if you don't wish to learn mathematics, then also definitelycheck this website out. thanks for watching, and for your generous support, and i'll see you next time!
