Cross Patty (cross pattée)

max( f(abs(x), abs(y)), f(abs(y), abs(x)) ) > 0

(1) f(x,y) = ax^2 - y + b  (parabola)

a = 0.035, b = 0.85

(2) f(x,y) = x^2 + (y - a)^2 - b^2  (circle)

a = 15.6, b = 14.75

(3) f(x,y) = abs(x)^p + abs(y - a)^p - b^p  (superellipse)

a = 15.6, b = 14.75

p = 2.5, 2.4, 2.3, ...,1.5

p = 4, a = 10, b = 8

(4) f(x,y) = a[exp(-abs(x+b)^p) + exp(-abs(x-b)^p)] - y + c

p = 1.5, a = 1, b = 7, c = 2

p = 3, a = 1, b = 7, c = 2

(5) f(x,y) = a cos(bx)^p - y + c

p = 1, a = -1, b = π/7, c = 2

p = 2, a = 1, b = π/7, c = 2

p = 3, a = -1, b = π/7, c = 2

p = 4, a = 1, b = π/7, c = 2

( Mathematical software used: Graph )

Tiling using Rounded Crosses

( Mathematical software used: Graph )


Related posts:

• Rounded Cross
• Tiling using Nested Crosses

Rounded Cross - cross with rounded corners (圓角十字形)

gnuplot script:

a = 2
b = 1
c = 1
w = 8
max(x,y) = x < y ? y : x
min(x,y) = x < y ? x : y
fun(x,y) = \
  min(min(max(abs(x)-b,0)**2 + max(abs(y)-(a+b+2*c),0)**2 - c**2, \
  max(abs(x)-(a+b+2*c),0)**2 + max(abs(y)-b,0)**2 - c**2), \
  max((abs(x)-(b+c))**2 + (abs(y)-(b+c))**2 - c**2, \
  c**2 - (abs(x)-(b+2*c))**2 - (abs(y)-(b+2*c))**2))
set xrange [-w:w]
set yrange [-w:w]
set size ratio -1
set samples 512
set isosamples 512
set contour base
set cntrparam levels discrete 0.0
unset key
unset surface
set table 'fun.dat'
splot fun(x,y)
unset table
plot 'fun.dat' w l lw 1.5 lc rgb "red"

(a = 2, b = 1, c = 1)

(a = 4, b = 0.5, c = 0.5)

(a = 0, b = 0, c = 2)

(a = 0, b = 2, c = 4/3)

(a = 2, b = 0, c = 4/3)

( Mathematical softwares used: Graph, gnuplot )


Related posts:

• Tiling using Rounded Crosses
• Equation of a Rounded Rectangle

Tiling using Nested Crosses

(A) Tiling using Nested Crosses

(Nested Crosses)

(B) Tiling using Nested Crosses and Nested Squares

( Mathematical software used: GeoGebra )


Related posts:

• Tiling by Nested Polygons (1)
• Tiling by Nested Polygons (2)
• Tiling using Nested Stars (1)
• Tiling using Nested Stars (2)
• Tiling using Rounded Crosses