31:[] 2f:{"title":"3D Free Form Region Arithmatic","cells":[{"id":0,"value":"md`# 3D Free Form Region Arithmatic`","pinned":false,"hidden":false,"mode":"ojs"},{"id":31,"value":"md`Prof. Mc Clure suggested that we use Wofram Cloud's native 3D renderer since the Observable implementation might be difficult if we deal with raw polygons. \n\nIMHO Wolfram Cloud native renderer has come a long way but has lots of limitations that I rather use Three.js or other platforms in future. \n\nThe user enters Free Form English description of the differences between the 3D regions, in this case Implicit Regions, there is a Natural Language Free Form grammar live at Wolfram Cloud awaiting to parse and interpret and the output is an embeddable cloud object.\n\nThis a new innovative approach for Cloud API to connect very different software systems with little training on the part of the programmers. For example you can use the Free Form grammar to construct and query expressions in Mathematica without any need to learn or install that behemoth!\n\n`","pinned":false,"hidden":false,"mode":"ojs"},{"id":15,"value":"html``","pinned":true,"hidden":false,"mode":"ojs"},{"id":11,"value":"url = cloudObject + encodeURIComponent(query)","pinned":true,"hidden":false,"mode":"ojs"},{"id":42,"value":"md`Free Form input:\n\ndifference region1 from region2 from region3\n\nYou can use booleans and inequalities and many other standard goodies. \n\n`","pinned":false,"hidden":false,"mode":"ojs"},{"id":9,"value":"query = \"difference x^2 + y^2 + z^2 == 1 from 0.5*x^2 + 0.9*y^2 + (z - 1/2)^2 < 1/3 from x^2 + z^2 <= 1/3\"","pinned":true,"hidden":false,"mode":"ojs"},{"id":55,"value":"md`No lets try a solid sphere and scoope regions off of it:\n\ndifference x^2 + y^2 + z^2 < 1 from (x - 3/4)^2 + y^2 + z^2 < 1 from x^2 + z^2 <= 1/8\n\nThis is a good example to pointout some serious limitations of some operations on the regions in Mathematica. \n\nWe can decrease the volume of the cells in Discretization algorithm but time to compute increases as in n^2 if n is the subdivision of parametric spaces. \n\nEven with these limitations for much of the region computing we are able to provide serious applications. \n\n`","pinned":false,"hidden":false,"mode":"ojs"},{"id":49,"value":"query2 = \"difference x^2 + y^2 + z^2 < 1 from (x - 3/4)^2 + y^2 + z^2 < 1 from x^2 + z^2 <= 1/8\"","pinned":true,"hidden":false,"mode":"ojs"},{"id":51,"value":"url2 = cloudObject + encodeURIComponent(query2)","pinned":true,"hidden":false,"mode":"ojs"},{"id":53,"value":"html``","pinned":true,"hidden":false,"mode":"ojs"},{"id":7,"value":"cloudObject = \"https://www.wolframcloud.com/obj/ccn/Plot3DEmbed?x=\"","pinned":true,"hidden":false,"mode":"ojs"}],"files":"$W31","stdlib":"1","titling":"auto"}