SurfaceProjection.html

Surface Projection

Example from the PscFunctions package

It is possible to obtain a parametric equation of projection region of a surface onto the oblique plane .
The PscFunctions package contains several routines for generation equations of surfaces of solids of standard form. Here we use SRegularPyramid routine for generating parametric equation of the pyramidal surface and SProjection routine for generating equation of projection of the pyramid.

> restart;
with(PscFunctions):
px,py,pz:=SRegularPyramid(6,2,1):
ps:=plot3d([px(u,v),py(u,v),pz(u,v)],u=0..6,v=0..3,scaling=CONSTRAINED,grid=[25,13],axes=BOXED):
xp,yp,zp:=SProjection([px,py,pz],[1,0,0,-3/2]):
pc:=plot3d([xp(u,v),yp(u,v),zp(u,v)],u=0..6,v=0..3,axes=BOXED,scaling=CONSTRAINED,labels=["X","Y","Z"],style=patchnogrid):
plots[display](pc,ps,orientation=[-130,60]);
`Parametric equation of the pyramid`;
'x'=px(u,v);
'y'=py(u,v);
'z'=pz(u,v);

Here is a similar example of generating equation of projection of a cube onto the oblique plane.

> Cube:=SCuboid(2,2,2):
xc:=(u,v)->Cube[1](u,v)-1:
yc:=(u,v)->Cube[2](u,v)-1:
zc:=(u,v)->Cube[3](u,v)-1:
cs:=plot3d([xc(u,v),yc(u,v),zc(u,v)],u=0..8,v=-2..4,scaling=CONSTRAINED,grid=[25,19],axes=BOXED):
xp,yp,zp:=SProjection([xc,yc,zc],[1,1,1,-4]):
pc:=plot3d([xp(u,v),yp(u,v),zp(u,v)],u=0..8,v=-2..4,axes=BOXED,scaling=CONSTRAINED,labels=["X","Y","Z"],style=patchnogrid):
plots[display](pc,cs,orientation=[-20,60]);
`Parametric equation of projection of the cube`;
print('x'=xp(u,v));
print('y'=yp(u,v));
print('z'=zp(u,v));