More Miscellaneous Projections

> s:='s':

Wiechel "Catherine Wheel"

> mapcoords(Wiechel,
input = [lambda,phi],
coords = [s=cos(lambda),v=cos(phi),w=sin(phi),
[r*(sin(lambda)*v-(1-w)*s),-r*(s*v+(1-w)*sin(lambda))]],
params = [r],
view = [-180..180,-80..85,13,7,-115..115,-115..115]);

> coordplot(Wiechel,scaling=constrained);

> changecoords(world[1866],Wiechel);

Collignon Triangle

> mapcoords(Collignon,
input = [lambda,phi],
coords = [s=sqrt(1-sin(phi)),
[r*lambda*s*2/sqrt(Pi),r*sqrt(Pi)*(1-s)]],
params = [r],
view = [-180..180,-90..90,13,7,-300..300,-50..110]);

Warning: coordinates already exists, system redefined.

Warning: default information already exists, redefining.

> coordplot(Collignon,scaling=constrained);

> changecoords(world[50],Collignon);

"Lagrange" Projection (actually, another of Lambert's)

> mapcoords(Lagrange,
input = [lambda,phi],
coords = [p1 = arcsin(tan(phi/2)),
c = cos(p1),
t = 1+c*cos(lambda/2),
[4*r*c*sin(lambda/2)/t,4*r*sin(p1)/t]],
params = [r],
view = [-180..180,-90..90,13,9,-300..300,-300..300]);

Warning: coordinates already exists, system redefined.

> coordplot(Lagrange,scaling=constrained);

> lg1:=changecoords(world[ng,50],Lagrange):

> lg2:=coordplot(Lagrange,scaling=constrained):

> plots[display]({lg1,lg2});

Briesemeister Projection

> mapcoords(Briesemeister,
input = [lambda,phi],
coords = [Phi = arcsin((sin(phi)-cos(phi)*cos(lambda-0*Pi/180))/sqrt(2)),
Lambda = arccos((sin(phi)+cos(phi)*cos(lambda-0*Pi/180))/sqrt(2)/cos(Phi)),
d = 2/(1+cos(Phi)*cos(Lambda/2)),
['sign'(lambda)*r*sqrt(3.5*d)*cos(Phi)*sin(Lambda/2), r*sqrt(2*d)*sin(Phi)/sqrt(1.75)]],
params = [r,_theta1],
view = [-180..180,-90..90,13,7,-180..180,-90..90]);

> brmap:=changecoords(world[50],Briesemeister):

> br2:=removelines(brmap):

> br2;

> coordplot(Briesemeister,scaling=constrained);

>

>