I'm trying to generate a spherical polygon on a unit-sphere from a set of points, but I'm running into some trouble. I've looked through previous answers to questions similar to/identical to mine:

Fast spherical polygon

An efficient circular arc primitive for Graphics3D

Geodesics on a sphere

but I am struggling to implement any of these methods myself. My problem is straightforward. Given a set of points lying on a sphere, I simply want to draw a spherical polygon by connecting the points with geodesics and then fill the area the polygon encloses with some color. I'm also trying to plot a curve that the polygon approximates and have that fill with a different color on a different plot as well.

For example, the points given by:

pts = Table[{Sin[t], Sin[t]*Cos[t], Cos[t]^2}, {t, 0, Pi, .1}]
Show[ContourPlot3D[
x^2 + y^2 + z^2 == 1, {x, -1, 1}, {y, -1, 1}, {z, -1, 1}, 
ContourStyle -> Opacity[0.3], Mesh -> None], ListPointPlot3D[pts], 
Boxed -> False, Axes -> False]

[![enter image description here][1]][1] [![enter image description here][2]][2] And the curve:

Show[ContourPlot3D[
x^2 + y^2 + z^2 == 1, {x, -1, 1}, {y, -1, 1}, {z, -1, 1}, 
ContourStyle -> Opacity[0.3], Mesh -> None], 
ParametricPlot3D[{Sin[t], Sin[t]*Cos[t], Cos[t]^2}, {t, 0, Pi}], 
Boxed -> False, Axes -> False
]

[![enter image description here][3]][3]

These problems appear to be answered in the links I've included, but I can't implement my own set of points for some reason. I've tried replicating Joseph O'Rourke's result from Geodesics on a sphere which is what I'm trying to make in the first place but to no avail. [1]: https://i.sstatic.net/zuytg.png [2]: https://i.sstatic.net/n2pIA.png [3]: https://i.sstatic.net/Xqh4R.png

I'm trying to generate a spherical polygon on a unit-sphere from a set of points, but I'm running into some trouble. I've looked through previous answers to questions similar to/identical to mine:

Fast spherical polygon

An efficient circular arc primitive for Graphics3D

Geodesics on a sphere

However, I am struggling to implement any of these methods myself. My problem is straightforward. Given a set of points lying on a sphere, I simply want to draw a spherical polygon by connecting the points with geodesics and then fill the area the polygon encloses with some color. I'm also trying to plot a curve that the polygon approximates and have that filled with a different color on a different plot as well.

For example, the points given by:

pts = Table[{Sin[t], Sin[t]*Cos[t], Cos[t]^2}, {t, 0, Pi, .1}]

Show[
  ContourPlot3D[x^2 + y^2 + z^2 == 1, {x, -1, 1}, {y, -1, 1}, {z, -1, 1}, 
    ContourStyle -> Opacity[0.3], Mesh -> None], 
  ListPointPlot3D[pts], 
  Boxed -> False, Axes -> False]

And the curve:

Show[
  ContourPlot3D[x^2 + y^2 + z^2 == 1, {x, -1, 1}, {y, -1, 1}, {z, -1, 1}, 
    ContourStyle -> Opacity[0.3], Mesh -> None], 
 ParametricPlot3D[{Sin[t], Sin[t]*Cos[t], Cos[t]^2}, {t, 0, Pi}], 
 Boxed -> False, Axes -> False]

These problems appear to be answered in the links I've included, but I can't implement my own set of points for some reason. I've tried replicating Joseph O'Rourke's result from Geodesics on a sphere, which is what I'm trying to make in the first place, but to no avail.