Thanks for your interest. Have a good sleep! Richard Donovan
> On 15 Aug 2022, at 11:54, Elijah Stone <elro...@elronnd.net> wrote: > > Was about to go to bed, but this tickled my imagination, so I will say a > little something. > > Rather than calculus, I would do this as an implicit curve. > > Start off with the signed distance function of a circle: > > sdc=. ]: -~ +/&.:*: > > Then that of a box, taken from > https://iquilezles.org/articles/distfunctions2d/: > > sdb=. (+/&.:*:@:(0&>.) + 0 <. >./)@:(]: -~ |) > > Both of these are adverbs, taking a radius as an operand and then a vector > coordinate as an argument. (The latter can also be given a vector, in which > case it calculates the distance to an n-dimensional rectangle, but that is > irrelevant here.) > > Then, we are looking for the case when the distance to the box is equal to > the distance to the circle. Such points will be inside the square, but > outside the circle, so the distance functions of those shapes will have > opposite sign, and we can just add them together: > > sdsquircle=. 1 sdc + 1 sdb > > sdsquircle is not, strictly speaking, a signed distance function. However, > like a signed distance function, it has a value of 0 when applied to a > coordinate on the squircle; and it is negative inside, and positive outside. > So it is trivial to render the shape from it. > > I can expand further on this tomorrow, but I really must be getting to bed > now. > > -E > >> On Mon, 15 Aug 2022, Richard Donovan wrote: >> >> Hi >> >> I want to construct and plot a Squircle in J. >> >> There is a lengthy article in Wikipedia but in simple language I want my >> Squircle to be defined as the continuous line between a unit circle and the >> unit square that encloses it such that every point on the Squircle is the >> mean of the nearest points of the circle and the square. >> >> Thus, the mean is zero at the four points where the circle and the square >> touch, and a maximum of (-: @ <: @ %:2) at the four corners of the square. >> >> Each intermediate point between 0 degrees and 90 degrees will be somewhere >> in the middle. >> >> I suspect the calculation of the intermediate points is a calculus function? >> >> Has anyone a good idea for performing that calculation? Could the J function >> “ plot “ then draw the Squircle? >> >> Thanks >> >> Richard Donovan >> ---------------------------------------------------------------------- >> For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
