# Documentation of quiver_scale

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## Function Synopsis

`hh = quiver_scale(varargin)`

## Help text

```QUIVER_SCALE Quiver plot.
QUIVER_SCALE(X,Y,U,V) plots velocity vectors as arrows with
components (u,v) at the points (x,y).  The matrices X,Y,U,V must all
be the same size and contain corresponding position and velocity
components (X and Y can also be vectors to specify a uniform grid).
QUIVER_SCALE automatically scales the arrows to fit within the grid.

QUIVER_SCALE(U,V) plots velocity vectors at equally spaced points in
the x-y plane.

QUIVER_SCALE(U,V,S) or QUIVER_SCALE(X,Y,U,V,S) automatically scales
the arrows to fit within the grid and then stretches them by S.  Use
S=0 to plot the arrows without the automatic scaling.

QUIVER_SCALE(U,V,S) with S < 0, automatically scales the arrows so
that arrows of magnitude (or wind speed) abs(s) are assigned to the
reference length.

QUIVER_SCALE(...,LINESPEC) uses the plot linestyle specified for
the velocity vectors.  Any marker in LINESPEC is drawn at the base
instead of an arrow on the tip.  Use a marker of '.' to specify
no marker at all.  See PLOT for other possibilities.

QUIVER_SCALE(...,'filled') fills any markers specified.

H = QUIVER_SCALE(...) returns a vector of line handles.

Example:
[x,y] = meshgrid(-2:.2:2,-1:.15:1);
z = x .* exp(-x.^2 - y.^2); [px,py] = gradient(z,.2,.15);
contour(x,y,z), hold on
quiver(x,y,px,py), hold off, axis image

```

## Cross-Reference Information

This function calls This function is called by

## Listing of function quiver_scale

```function hh = quiver_scale(varargin)

%   Clay M. Thompson 3-3-94
%   Copyright 1984-2001 The MathWorks, Inc.
%   \$Revision: 5.20 \$  \$Date: 2001/04/15 12:03:54 \$
%
%   Modified by Dan Vimont, July 17, 2002
%   Changes include autoscale < 0 option, and redoing the arrowhead so
%   that it doesn't get all distorted.

alpha = 0.25; % Size of arrow head relative to the length of the vector
beta = 0.25;  % Width of the base of the arrow head relative to the length
autoscale = 1; % Autoscale if ~= 0 then scale by this.
plotarrows = 1; % Plot arrows
sym = '';

filled = 0;
ls = '-';
ms = '';
col = '';

nin = nargin;
% Parse the string inputs
while isstr(varargin{nin}),
vv = varargin{nin};
if ~isempty(vv) & strcmp(lower(vv(1)),'f')
filled = 1;
nin = nin-1;
else
[l,c,m,msg] = colstyle(vv);
if ~isempty(msg),
error(sprintf('Unknown option "%s".',vv));
end
if ~isempty(l), ls = l; end
if ~isempty(c), col = c; end
if ~isempty(m), ms = m; plotarrows = 0; end
if isequal(m,'.'), ms = ''; end % Don't plot '.'
nin = nin-1;
end
end

error(nargchk(2,5,nin));

% Check numeric input arguments
if nin<4, % quiver(u,v) or quiver(u,v,s)
[msg,x,y,u,v] = xyzchk(varargin{1:2});
else
[msg,x,y,u,v] = xyzchk(varargin{1:4});
end
if ~isempty(msg), error(msg); end

if nin==3 | nin==5, % quiver(u,v,s) or quiver(x,y,u,v,s)
autoscale = varargin{nin};
end

% Scalar expand u,v
if prod(size(u))==1, u = u(ones(size(x))); end
if prod(size(v))==1, v = v(ones(size(u))); end

if autoscale > 0,
% Base autoscale value on average spacing in the x and y
% directions.  Estimate number of points in each direction as
% either the size of the input arrays or the effective square
% spacing if x and y are vectors.
if min(size(x))==1, n=sqrt(prod(size(x))); m=n; else [m,n]=size(x); end
delx = diff([min(x(:)) max(x(:))])/n;
dely = diff([min(y(:)) max(y(:))])/m;
del = delx.^2 + dely.^2;
if del>0
len = sqrt((u.^2 + v.^2)/del);
maxlen = max(len(:));
else
maxlen = 0;
end

if maxlen>0
autoscale = autoscale*0.9 / maxlen;
else
autoscale = autoscale*0.9;
end
u = u*autoscale; v = v*autoscale;
elseif autoscale < 0,
%  Base autoscale on a specified magnitude of the given vector.
u = -1*u./autoscale; v = -1*v./autoscale;
end

ax = newplot;
next = lower(get(ax,'NextPlot'));
hold_state = ishold;

% Make velocity vectors
x = x(:).'; y = y(:).';
u = u(:).'; v = v(:).';
uu = [x;x+u;repmat(NaN,size(u))];
vv = [y;y+v;repmat(NaN,size(u))];

h1 = plot(uu(:),vv(:),[col ls]);

if plotarrows,
% Make arrow heads and plot them

len = sqrt(u.^2 + v.^2);

%orig  hu = [x+u-alpha*(u+beta*(v+eps));x+u; ...
%orig        x+u-alpha*(u-beta*(v+eps));repmat(NaN,size(u))];

hu = [x+u-alpha*len.*sin(atan2(u,v)-0.5); x+u; ...
x+u-alpha*len.*cos(atan2(v,u)-0.5); repmat(NaN,size(u))];

%orig  hv = [y+v-alpha*(v-beta*(u+eps));y+v; ...
%orig        y+v-alpha*(v+beta*(u+eps));repmat(NaN,size(v))];

hv = [y+v-alpha*len.*cos(atan2(u,v)-0.5); y+v; ...
y+v-alpha*len.*sin(atan2(v,u)-0.5); repmat(NaN,size(v))];

hold on
h2 = plot(hu(:),hv(:),[col ls]);
hold off
else
h2 = [];
end

if ~isempty(ms), % Plot marker on base
hu = x; hv = y;
hold on
h3 = plot(hu(:),hv(:),[col ms]);
if filled, set(h3,'markerfacecolor',get(h1,'color')); end
else
h3 = [];
end

if ~hold_state, hold off, view(2); set(ax,'NextPlot',next); end

if nargout>0, hh = [h1;h2;h3]; end
```