Nephroid as an envelope, mathematical line art, code for the animation. #shorts

Zak's Lab منتشر شده در تاریخ 1400/04/16

1.4 هزار بار بازدید - 3 سال پیش - Nephroid as an envelope, mathematical

Nephroid as an envelope, mathematical line art, code for the animation.

We plot two points revolving on a circle, with one point moving three times as fast as the slow one. Line segments connecting the points are plotted, and the envelope of these line segments forms a nephroid curve or two cusped hypocycloid.

Code for the nephroid animation is written for wxMaxima, but it is useful as pseudocode for any similar system.

wxMaxima code:

kill(all)$
/*two points traveling on a circle of radius 3, one of the points moving three times as fast*/
p1(t):=points([[3*cos(.04*t),3*sin(.04*t)]])$
p1x(t):=3*cos(.04*t)$
p1y(t):=3*sin(.04*t)$
p2(t):=points([[3*cos(.12*t),3*sin(.12*t)]])$
p2x(t):=3*cos(.12*t)$
p2y(t):=3*sin(.12*t)$

/*line connecting the two points*/
line1(t):=parametric((1-i)*p1x(t)+i*p2x(t),(1-i)*p1y(t)+i*p2y(t),i,0,1)$

/*make a list of lists to add to the parametric set at each step*/;
innerlist:[]$
radiuslist:[]$
for j from 1 thru 160 do(
innerlist:append(innerlist,
[line1(j)]
)
)$
templist:[]$
for n from 1 thru 160 do(

for m from 1 thru n do(

templist:append(templist,
[innerlist[m]])
),

radiuslist:append(radiuslist,[templist]),

templist:[]

)$
wxplot_size:[1000,1000]$
wxanimate_framerate:20$
rlist:makelist(i,i,1,160)$
with_slider_draw(
r,rlist,
nticks=1000,
xrange=[-3.2,3.2],
yrange=[-3.2,3.2],
xtics=false,
ytics=false,
color=black,

color=black,
line_width=2,
parametric(3*cos(t),3*sin(t),t,0,2*%pi),

color=blue,
line_width=2,
radiuslist[r],

point_type=7,
point_size=2,
color=red,
p1(r),
p2(r)

);

3 سال پیش در تاریخ 1400/04/16 منتشر شده است.

1,482 بـار بازدید شده

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