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function showinstr(mac)
if type(mac)==11 then
[in,out,txt]=string(mac)
x_message(txt)
end
endfunction
function [X,Y]=field(x,y)
// x and y are two vectors defining a grid
// X and Y are two matrices which gives the grid point coordinates
//-------------------------------------------------------------
// Copyright INRIA
[rx,cx]=size(x);
[ry,cy]=size(y);
if rx<>1, write(%io(2),"x must be a row vector");return;end;
if ry<>1, write(%io(2),"y must be a row vector");return;end;
X=x.*.ones(cy,1);
Y=y'.*.ones(1,cx);
endfunction
function [z]=dup(x,n)
// utility
// x is a vector this function returns [x,x,x,x...] or [x;x;x;x;..]
// depending on x
// Copyright INRIA
[nr,nc]=size(x)
if nr==1 then
y=ones(n,1);
z= x.*.y ;
else
if nc<>1 then
error("dup : x must be a vector");
else
y=ones(1,n);
z= x.*.y ;
end
end
endfunction
function [z] = bezier(p,t)
//comment : Computes a Bezier curves.
//For a test try:
//beziertest; bezier3dtest; nurbstest; beziersurftest; c1test;
//Uses the following functions:
//bezier, bezier3d, nurbs, beziersurface
//endcomment
//reset();
// Evaluate sum p_i B_{i,n}(t) the easy and direct way.
// p must be a k x n+1 matrix (n+1) points, dimension k.
// Copyright INRIA
n=size(p,'c')-1;// i=nonzeros(t~=1);
t1=(1-t); t1z= find(t1==0.0); t1(t1z)= ones(t1z);
T=dup(t./t1,n)';
b=[((1-t')^n),(T.*dup((n-(1:n)+1)./(1:n),size(t,'c')))];
b=cumprod(b,'c');
if (size(t1z,'c')>0); b(t1z,:)= dup([ 0*ones(1,n),1],size(t1z,'c')); end;
z=p*b';
endfunction
function bezier3d (p)
// Shows a 3D Bezier curve and its polygon
// Copyright INRIA
t=linspace(0,1,300);
s=bezier(p,t);
dh=xget("dashes");
xset("dashes",3)
param3d(p(1,:),p(2,:),p(3,:),34,45)
xset("dashes",4);
param3d(s(1,:),s(2,:),s(3,:),34,45,"x@y@z",[0,0])
xset("dashes",dh);
xtitle('A 3d polygon and its Bezier curve');
current_axe = gca();current_axe.title.font_size = 3;
endfunction
function [X,Y,Z]=beziersurface (x,y,z,n)
// Compute a Bezier surface. Return {bx,by,bz}.
// Copyright INRIA
[lhs,rhs]=argn(0);
if rhs <= 3 ; n=20;end
t=linspace(0,1,n);
n=size(x,'r')-1; // i=nonzeros(t~=1);
t1=(1-t); t1z= find(t1==0.0); t1(t1z)= ones(t1z);
T=dup(t./t1,n)';
b1=[((1-t')^n),(T.*dup((n-(1:n)+1)./(1:n),size(t,'c')))];
b1=cumprod(b1,'c');
if (size(t1z,'c')>0);
b1(t1z,:)= dup([ 0*ones(1,n),1],size(t1z,'c'));
end
n=size(x,'c')-1; // i=nonzeros(t~=1);
t1=(1-t); t1z= find(t1==0.0); t1(t1z)= ones(t1z);
T=dup(t./t1,n)';
b2=[((1-t')^n),(T.*dup((n-(1:n)+1)./(1:n),size(t,'c')))];
b2=cumprod(b2,'c');
if (size(t1z,'c')>0);
b2(t1z,:)= dup([ 0*ones(1,n),1],size(t1z,'c'));
end
X=b1*x*b2';Y=b1*y*b2';Z=b1*z*b2';
endfunction
function cplxmap(z,w,varargin)
//cplxmap(z,w,T,A,leg,flags,ebox)
//cplxmap Plot a function of a complex variable.
// cplxmap(z,f(z))
// Copyright INRIA
x = real(z);
y = imag(z);
u = real(w);
v = imag(w);
M = max(u);
m = min(u);
s = ones(size(z));
//mesh(x,y,m*s,blue*s);
//hold on
[X,Y,U]=nf3d(x,y,u);
[X,Y,V]=nf3d(x,y,v);
Colors = sum(V,'r');
Colors = Colors - min(Colors);
Colors = 32*Colors/max(Colors);
plot3d1(X,Y,list(U,Colors),varargin(:))
endfunction
function cplxroot(n,m,varargin)
//cplxroot(n,m,T,A,leg,flags,ebox)
//CPLXROOT Riemann surface for the n-th root.
// CPLXROOT(n) renders the Riemann surface for the n-th root.
// CPLXROOT, by itself, renders the Riemann surface for the cube root.
// CPLXROOT(n,m) uses an m-by-m grid. Default m = 20.
// Use polar coordinates, (r,theta).
// Cover the unit disc n times.
// Copyright INRIA
[lhs,rhs]=argn(0)
if rhs < 1, n = 3; end
if rhs < 2, m = 20; end
r = (0:m)'/m;
theta = - %pi*(-n*m:n*m)/m;
z = r * exp(%i*theta);
s = r.^(1/n) * exp(%i*theta/n);
cplxmap(z,s,varargin(:))
endfunction
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