[Scilab-users] Regarding multiply-armed equiangular (or Logarithmic) spirals

[Samuel Gougeon]

Le 17/09/2012 17:56, bkpsusmitaa a écrit :
> .../...
> Will you please explain the steps,
> .../...
>    
Each branch must be generated apart. When with
plot(X,Y)
X and Y are matrices of the same sizes, each column of X and respectively Y
is considered as an individual curve. So if X and Y have N columns,
N curves will be plotted by the single plot(X,Y) instruction

As a first step, it is easier to generate branches in polar coordinates.
So we must generate a matrix A of angles and a matrix R of radii.
Radii are chosen to drive the angles. The set of radii is the same
for all branches. With
a = (0:11)/12*360;       // starting angles
r = (0:30)'              // range of radii
R = r*ones(a)            // matrix of radii for all branches

all columns of R are the same, and there are as many columns as angle 
steps in a.
Then, we must generate angles.
Each branch (column) has a specific starting angle (from the center). It 
is respectively
replicated with
A = ones(r)*a
for all radii (rows).
Then we must add to A a angular drift describing the spiral. This the
r*ones(a)
contribution, leading to
A = ones(r)*a + r*ones(a)

If you want to twist more branches, you can amplify the angular drift, 
chosing for instance
A = ones(r)*a + 3*r*ones(a)

Then, the polar to cartesian transform of coordinates must be
applided, because plot() works with cartesian coordinates.
This is the part
X = R.*cosd(A)           // polar to cartesian transform
Y = R.*sind(A)           // ..

And finally we plot the result, and tune the axes to isometric scales:
plot(X,Y)
ax = gca();
ax.isoview = "on";

With the amplified twist (still proportional to radii, but here x3) , 
this gives:


Samuel

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