how to create this surface model as attached files

In the Inventor it is possible to arrange the "spikes" after a route but on a flat surface.

I don't know of an easy way to pattern the spikes with CATIA V5, since each one is at a different angle (assuming each one is normal to the surface). But here's how I would model this:

1. I would use the Part Design workbench to model this as a solid.
2. make a Shaft feature for the revolved base
3. add a spline on the face for the path of the spikes
4. add the points on the spline with the Point And Plane Repetition tool
5. add the first spike as a Shaft feature
6. use a PowerCopy to quickly create all the other spikes at each point, normal to the face.

(I don't have access to CATIA right now, but maybe someone could make a video tutorial for you)

In Inventor you can project a 2d sketch onto the surface and then use the resulting 3d sketch as a path for a pattern.