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Question: How to diplay lots of curves

Question:How to diplay lots of curves

Traruh Synred 55 Maple 2018
vector plotting display
December 01 2023
1

Using Maple-18 on Window 11...

I have a set of curves in a Maple 'vector.' I want to plot them all on the same figure, but if call 'display' with the vector it makes separate plots for each one. I have to all it with each plot individual to get them on the same plot:

lc is a 'vector' of curves (I use 'vector' because I want to append and that doesn't work for 'list')

display(lc) -- plots a separate plot for each element of lc

display(lc[1], lc[2], lc[3],...) puts them all on one plot as needed, but as there will be a large numbe of curvesr it's extremely tedious.

It is a Huygens principle based simulation of diffraction.

> 

restart
> 

estart; with(Physics); with(LinearAlgebra); with(VectorCalculus); with(Optimization); with(Statistics); with(ArrayTools); with(plots); with(plottools); with(Threads); with(MmaTranslator[Mma]), with(StringTools); with(CodeGeneration); with(ImageTools); with(ImageTools:-Draw); VectorCalculus:-`*`(Setup(mathematicalnotation = true), Setup(coordinatesystems = cartesian))

estart

  

[annulus, arc, arrow, circle, cone, cuboid, curve, cutin, cutout, cylinder, disk, dodecahedron, ellipse, ellipticArc, exportplot, extrude, getdata, hemisphere, hexahedron, homothety, hyperbola, icosahedron, importplot, line, octahedron, parallelepiped, pieslice, point, polygon, prism, project, rectangle, reflect, rotate, scale, sector, semitorus, sphere, stellate, tetrahedron, torus, transform, translate]

  

`Default differentiation variables for d_, D_ and dAlembertian are:`*{X = (x, y, z, t)}

  

`Systems of spacetime Coordinates are:`*{X = (x, y, z, t)}

 (1)
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NULL
> 

NULL

 

> 

radius := 1.0

1.0

 (2)
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NULL
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NULL
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``
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NULL
> 

alpha := sin((1/4)*Pi)

(1/2)*2^(1/2)

 (3)
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step := .2

.2

 (4)
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radius := 100.0

100.0

 (5)
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l1 := line([0, 0], [100, 100])

CURVES([[0., 0.], [100., 100.]])

 (6)
> 

loAng := 0.

0.

 (7)
> 

hiAng := (1/2)*Pi

(1/2)*Pi

 (8)
> 

c1 := arc([0, 0.], radius, loAng .. Pi, color = "red")
> 

c2 := arc([step, 0.], -alpha*step+radius, loAng .. hiAng, color = "blue")
> 

c3 := arc([2*step, 0.], -2*alpha*step+radius, loAng .. Pi, color = "purple")
> 

c4 := arc([3*step, 0.], -3*alpha*step+radius, loAng .. Pi, color = "black")
> 

plots[display](l1, c1, c2, c3, c4, view = [0. .. radius, 0 .. radius])

 
> 

`cir≔arc`([x, 0.], radius-step, loAng .. hiAng, i, color = "red")

`cir≔arc`([x, 0.], 99.8, 0. .. (1/2)*Pi, i, color = "red")

 (9)
> 

``
> 

xLimitWall := 500.0; nScatter := 20; step := xLimitWall/(nScatter+1); x := 0.; for i from 0 to nScatter do x := x+step; cir := arc([x, 0.], radius-step, 0 .. Pi, color = "red"); if i = 0 then lc := Vector([cir]) else i; cir; Append(lc, cir) end if end do; lc

xLimitWall := 500.0

  

nScatter := 20

  

step := 23.80952381

  

x := 0.

  

x := 23.80952381

  

cir := CURVES(Vector(4, {(1) = ` 200 x 2 `*Matrix, (2) = `Data Type: `*float[8], (3) = `Storage: `*rectangular, (4) = `Order: `*Fortran_order}), COLOUR(RGB, 1.00000000, 0., 0.))

  

x := 47.61904762

  

cir := CURVES(Vector(4, {(1) = ` 200 x 2 `*Matrix, (2) = `Data Type: `*float[8], (3) = `Storage: `*rectangular, (4) = `Order: `*Fortran_order}), COLOUR(RGB, 1.00000000, 0., 0.))

  

x := 71.42857143

  

cir := CURVES(Vector(4, {(1) = ` 200 x 2 `*Matrix, (2) = `Data Type: `*float[8], (3) = `Storage: `*rectangular, (4) = `Order: `*Fortran_order}), COLOUR(RGB, 1.00000000, 0., 0.))

  

x := 95.23809524

  

cir := CURVES(Vector(4, {(1) = ` 200 x 2 `*Matrix, (2) = `Data Type: `*float[8], (3) = `Storage: `*rectangular, (4) = `Order: `*Fortran_order}), COLOUR(RGB, 1.00000000, 0., 0.))

  

x := 119.0476190

  

cir := CURVES(Vector(4, {(1) = ` 200 x 2 `*Matrix, (2) = `Data Type: `*float[8], (3) = `Storage: `*rectangular, (4) = `Order: `*Fortran_order}), COLOUR(RGB, 1.00000000, 0., 0.))

  

x := 142.8571428

  

cir := CURVES(Vector(4, {(1) = ` 200 x 2 `*Matrix, (2) = `Data Type: `*float[8], (3) = `Storage: `*rectangular, (4) = `Order: `*Fortran_order}), COLOUR(RGB, 1.00000000, 0., 0.))

  

x := 166.6666666

  

cir := CURVES(Vector(4, {(1) = ` 200 x 2 `*Matrix, (2) = `Data Type: `*float[8], (3) = `Storage: `*rectangular, (4) = `Order: `*Fortran_order}), COLOUR(RGB, 1.00000000, 0., 0.))

  

x := 190.4761904

  

cir := CURVES(Vector(4, {(1) = ` 200 x 2 `*Matrix, (2) = `Data Type: `*float[8], (3) = `Storage: `*rectangular, (4) = `Order: `*Fortran_order}), COLOUR(RGB, 1.00000000, 0., 0.))

  

x := 214.2857142

  

cir := CURVES(Vector(4, {(1) = ` 200 x 2 `*Matrix, (2) = `Data Type: `*float[8], (3) = `Storage: `*rectangular, (4) = `Order: `*Fortran_order}), COLOUR(RGB, 1.00000000, 0., 0.))

  

x := 238.0952380

  

cir := CURVES(Vector(4, {(1) = ` 200 x 2 `*Matrix, (2) = `Data Type: `*float[8], (3) = `Storage: `*rectangular, (4) = `Order: `*Fortran_order}), COLOUR(RGB, 1.00000000, 0., 0.))

  

x := 261.9047618

  

cir := CURVES(Vector(4, {(1) = ` 200 x 2 `*Matrix, (2) = `Data Type: `*float[8], (3) = `Storage: `*rectangular, (4) = `Order: `*Fortran_order}), COLOUR(RGB, 1.00000000, 0., 0.))

  

x := 285.7142856

  

cir := CURVES(Vector(4, {(1) = ` 200 x 2 `*Matrix, (2) = `Data Type: `*float[8], (3) = `Storage: `*rectangular, (4) = `Order: `*Fortran_order}), COLOUR(RGB, 1.00000000, 0., 0.))

  

x := 309.5238094

  

cir := CURVES(Vector(4, {(1) = ` 200 x 2 `*Matrix, (2) = `Data Type: `*float[8], (3) = `Storage: `*rectangular, (4) = `Order: `*Fortran_order}), COLOUR(RGB, 1.00000000, 0., 0.))

  

x := 333.3333332

  

cir := CURVES(Vector(4, {(1) = ` 200 x 2 `*Matrix, (2) = `Data Type: `*float[8], (3) = `Storage: `*rectangular, (4) = `Order: `*Fortran_order}), COLOUR(RGB, 1.00000000, 0., 0.))

  

x := 357.1428570

  

cir := CURVES(Vector(4, {(1) = ` 200 x 2 `*Matrix, (2) = `Data Type: `*float[8], (3) = `Storage: `*rectangular, (4) = `Order: `*Fortran_order}), COLOUR(RGB, 1.00000000, 0., 0.))

  

x := 380.9523808

  

cir := CURVES(Vector(4, {(1) = ` 200 x 2 `*Matrix, (2) = `Data Type: `*float[8], (3) = `Storage: `*rectangular, (4) = `Order: `*Fortran_order}), COLOUR(RGB, 1.00000000, 0., 0.))

  

x := 404.7619046

  

cir := CURVES(Vector(4, {(1) = ` 200 x 2 `*Matrix, (2) = `Data Type: `*float[8], (3) = `Storage: `*rectangular, (4) = `Order: `*Fortran_order}), COLOUR(RGB, 1.00000000, 0., 0.))

  

x := 428.5714284

  

cir := CURVES(Vector(4, {(1) = ` 200 x 2 `*Matrix, (2) = `Data Type: `*float[8], (3) = `Storage: `*rectangular, (4) = `Order: `*Fortran_order}), COLOUR(RGB, 1.00000000, 0., 0.))

  

x := 452.3809522

  

cir := CURVES(Vector(4, {(1) = ` 200 x 2 `*Matrix, (2) = `Data Type: `*float[8], (3) = `Storage: `*rectangular, (4) = `Order: `*Fortran_order}), COLOUR(RGB, 1.00000000, 0., 0.))

  

x := 476.1904760

  

cir := CURVES(Vector(4, {(1) = ` 200 x 2 `*Matrix, (2) = `Data Type: `*float[8], (3) = `Storage: `*rectangular, (4) = `Order: `*Fortran_order}), COLOUR(RGB, 1.00000000, 0., 0.))

  

x := 499.9999998

  

cir := CURVES(Vector(4, {(1) = ` 200 x 2 `*Matrix, (2) = `Data Type: `*float[8], (3) = `Storage: `*rectangular, (4) = `Order: `*Fortran_order}), COLOUR(RGB, 1.00000000, 0., 0.))

  

Vector[column](%id = 4400555778)

 (10)
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lc[1]

CURVES(Matrix(%id = 4400554242), COLOUR(RGB, 1.00000000, 0., 0.))

 (11)
> 

lc(2)
> 

``
> 

lc
> 

lc[1]
> 

``

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