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](https://mathematica.stackexchange.com/questions/144167/fast-spherical-polygon)

[An efficient circular arc primitive for Graphics3D](https://mathematica.stackexchange.com/questions/10957/an-efficient-circular-arc-primitive-for-graphics3d/10994#10994)

[Geodesics on a sphere](https://mathematica.stackexchange.com/questions/154068/geodesics-on-a-sphere?noredirect=1&lq=1)

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}]

```

[![enter image description here](https://i.stack.imgur.com/zuytg.png)](https://i.stack.imgur.com/zuytg.png)

```
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](https://i.stack.imgur.com/n2pIA.png)](https://i.stack.imgur.com/n2pIA.png)

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](https://i.stack.imgur.com/Xqh4R.png)](https://i.stack.imgur.com/Xqh4R.png)

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](https://mathematica.stackexchange.com/questions/154068/geodesics-on-a-sphere?noredirect=1&lq=1), which is what I'm trying to make in the first place, but to no avail.