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lcz

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6 years, 128 days
changsha, China
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Is there a more versatile way to draw th...

lcz 994 Maple 2020
March 11 2021
0 0

I read the code in the link below and have some thoughts on drawing the graph.

https://www.mapleprimes.com/questions/216092-Options-For-Graph-Drawing-In-The-GraphTheory

restart:
with(GraphTheory):
with(SpecialGraphs): 
G     := PetersenGraph();:
POS := GetVertexPositions(G);
EG   := Edges(G); 
PLOT(
   seq( CURVES([POS[EG[i][1]], POS[EG[i][2]]], LINESTYLE(3) ), i=1..numelems(Edges(G))),
   POINTS(POS, SYMBOL(_SOLIDBOX, 35), COLOR(RGB, 1, 1, 0)),
   seq(TEXT(POS[i], i), i=1..numelems(Vertices(G))),
   AXESSTYLE(NONE)
)
 

 

But if we want to change the edge to a curvilinear style, it seems very difficult. We know  PetersenGraph is 1-planar graph.  The following picture is one of  its 1-plane drawing.  That is  also what I want to draw .

 

PS: A 1-planar graph is a graph that can be drawn in the Euclidean plane in such a way that each edge has at most one crossing point, where it crosses a single additional edge. 

Although I asked a similar question, but it uses too many special curve functions and the method is relatively isolated. Because the cycle graph is too special.  https://www.mapleprimes.com/questions/228987--Can-We-Draw-Curved-Edges-In-The-Graph

I also noticed the optional items of the edge style.  But there are no curves, such as arcs, parabola, etc.

The plot style must be one of line, point, pointline, polygon (patchnogrid), or polygonoutline (patch).  

I am trying to draw a parabola, it seems to be quite difficult. And it completely deviated from the use of graph theory package.

drawarc :=proc(A,B,C,ecolor);

local  c,ax,cx ,ay,cy,ox,oy,oo,x,y,b,a,an_end,an_start,r,yuanhu:
ax :=evalf(geometry)[HorizontalCoord](A):
cx :=evalf(geometry)[HorizontalCoord](C):
ay :=evalf(geometry)[VerticalCoord](A):
cy :=evalf(geometry)[VerticalCoord](C):

geometry[circle](c,[ A ,B ,C], [x,y],'centername' =o):

ox :=evalf(geometry[HorizontalCoord] (o)):
oy :=evalf(geometry[ VerticalCoord] (o)):

if(cx -ox)>0 then
b :=arctan((cy -oy) /(cx -ox)):
elif(cx -ox)=0 and (cy -oy)>0 then

b :=Pi/2 :
elif(cx -ox)=0 and (cy -oy)<0 then

b :=-Pi/ 2 :
else 
b :=Pi +arctan((cy -oy) /(cx -ox)):
fi :
if(ax -ox)>0 then 
a :=arctan((ay -oy) /(ax -ox)):
elif(ax -ox)=0 and (ay -oy)>0 then

a :=Pi /2 :
elif(ax -ox)=0 and (ay -oy)<0 then

a :=-Pi/ 2 ;
else 
a :=Pi +arctan((ay -oy)/ (ax -ox)):
fi ;
if(evalf(b)<evalf(a))then
an_start :=a :
else
an_start :=a +2*Pi :
fi :
an_end :=b :

r :=geometry[ radius] (c); 
yuanhu :=plottools[ arc] ([ ox , oy] , r , an_start..an_end):

plots[ display] (yuanhu , scaling =constrained, color =ecolor,axes=none);

end :

geometry[point] (a , -3 .00 , 1 .70);
geometry[point] (b , 0 .35 , -0 .45);
geometry[point] (c , 3 .13 , 1 .86);
l :=[a , b , c] ;
drawarc(a,b,c,blue);

I would like to ask maple if there is a more versatile and simpler way to draw a curve of  graph drawing.

drawarcs:=proc(VL ::list , ecolor , scope);
local i , num , arcs , arc_text , vl , display_set ;
vl :=VL ;
num:=nops(vl);
arcs :={};
i:=1;
if num <3 then 
"There isn' t enough points in the point list." ;
return ;
elif irem(num-1 , 2)<>0 then  
"The number of the list must be multiple of 2 when it minus 1 .";
fi :
while i <num do
arcs :={drawarc(vl[i] ,vl[i +1] , vl[i +2],ecolor),op(arcs)};
i:=i +2 ;
od ;
arc_text :=geometry[ draw] ({vl[1] , vl[num] }, printtext =true , color =ecolor);
display_set:={op(arcs),arc_text};
plots[ display] (display_set , view =[ -abs(scope)..abs(scope), -abs(scope)..abs(scope)] , scaling =constrained,axes=none);
end proc:
geometry[ point] (v1 , 0 ,0):
geometry[ point] (a , 3, 9):
geometry[ point] (b , 7, 9):
geometry[ point] (c, 6,8):
geometry[ point] (d , 12,9):
geometry[ point] (e , 7 ,2):
geometry[ point] (v3 , 9 ,0):
vl:=[ v1,a,b,c,d,e,v3] :
drawarcs(vl,red,20);

try.mwtry.mw

The above program is too cumbersome and not robust

macro(GS=GetVertexPositions):
with(GraphTheory):
with(SpecialGraphs): 
G     := PetersenGraph():
POS := GetVertexPositions(G):
EG   := Edges(G) minus {{6,10},{6,7}}:
s1:=PLOT(
   seq( CURVES([POS[EG[i][1]], POS[EG[i][2]]], LINESTYLE(3) ), i=1..numelems(Edges(G))-2),
   POINTS(POS, SYMBOL(_SOLIDBOX, 35), COLOR(RGB, 1, 1, 0)),
   seq(TEXT(POS[i], i), i=1..numelems(Vertices(G))),
   AXESSTYLE(NONE)
):
geometry[ point] (a,op(GS(G)[6])):
geometry[ point] (b , op(GS(G)[7])):
geometry[ point] (c , op(GS(G)[10])):
geometry[ point] (d ,op(GS(G)[8])[1]+0.3,op(GS(G)[8])[2]-0.5):
geometry[ point] (d2 ,op(GS(G)[9])[1]-0.3,op(GS(G)[9])[2]-0.5):
s2:=drawarc(a,d,b,red):
s3:=drawarc(c,d2,a,red):
plots:-display({s1,s2,s3});
 

 

 

 

 

why my question have been deleted...

lcz 994 MaplePrimes
deleted duplicate-question
March 11 2021
0 0

Dear administration, I hope you all are good,why my question have been deleted? My question is a little similar to the one before, but there are still a lot of differences.I didn't do a backup which was bad.Once deleted, there is no chance of modification.

simplify ceil and floor2.0...

lcz 994 Maple 2020
simplify floor ceil
February 05 2021
2 0

 12 yeas later, the probelm  is not still improved in following links 

https://www.mapleprimes.com/posts/38473-Simplify-Ceil-And-Floor

simplify(ceil(x)+floor(-x));

                         floor(-x) + ceil(x)



I think extending simplify by Joe Riel 8221  is a little complicated. 

restart;
`simplify/ceil` := proc(ex)
    evalindets(ex, 'specfunc(anything,ceil)', x -> -floor(-op(x)));
end proc:

simplify(floor(-x) + ceil(x));

 It seems that maple know  ceil(x)=-floor(-x) 

 

why does not maple2020 still handle that?  

 

 

coordinate axis tickmarks...

lcz 994 Maple 2020
axis plotting tickmarks
January 11 2021
3 2

A torus can be defined parametrically by:

{\displaystyle {\begin{aligned}x(\theta ,\varphi )&=(R+r\cos \theta )\cos {\varphi }\\y(\theta ,\varphi )&=(R+r\cos \theta )\sin {\varphi }\\z(\theta ,\varphi )&=r\sin \theta \end{aligned}}}

where θ, φ are angles which make a full circle, so that their values start and end at the same point, R is the distance from the center of the tube to the center of the torus, r  is the radius of the tube.

R:=10:
r:=5:
plot3d( [ ( R+r(u,v)*cos(v))*sin(u),
          ( R+r(u,v)*cos(v))*cos(u),
            r*sin(v)
        ],
            u=0..2*Pi,
            v=0..2*Pi,style=patchnogrid,
            scaling=constrained,
          scaling=constrained,
coordinateview=[-15..15, -15..15,-5..5],
lightmodel=light3, viewpoint = circleleft);

I set range [-5..5] of the Z axis，but  the range of  Z axis tickmarks  in the above image maybe in [-4.5..4.5] .

How to have tickmarks included at -5 and 5 on the Z axis?

The Sum is not what I want...

lcz 994 Maple 2020
subscript indexed
December 30 2020
2 10

The code 

S:=sum(1/x__i,i=1..5)

will give us the following ouput

Why not 

S:=add(1/x__i,i=1..5)

 also give same result. why?How to do?

I also note that:

S:=add(1/x||i,i=1..5)

S:=sum(1/x||i,i=1..5)

 

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