Spline Toolbox

Example: Sphere

As a surface example, the command rsmak('southcap') provides a 3-vector valued rational bicubic polynomial whose values on the unit square [-1 .. 1]^2 fill out a piece of the unit sphere. Adjoin to it five suitable rotates of it and you get the unit sphere exactly. For illustration, the following commands generate 2/3 of that sphere, as shown in Figure 2-15.

• southcap = rsmak('southcap'); fnplt(southcap)
  xpcap = fncmb(southcap,[0 0 -1;0 1 0;1 0 0]);
  ypcap = fncmb(xpcap,[0 -1 0; 1 0 0; 0 0 1]);
  northcap = fncmb(southcap,-1);
  hold on, fnplt(xpcap), fnplt(ypcap), fnplt(northcap)
  axis equal, shading interp, view(-115,10), axis off, hold off
  
  
  

Figure 2-15: Part of a Sphere Formed by Four Rotates of a Quartic Rational

Example: Circle

rsform