Rigidbody or Transform Movement

[ATHellboy]

Using OffsetRadius or not is I think just a detail. The important thing is to use like you said pseudo gravity and velocity to have a good looking jump. Once you calculated the height using that, you can either apply it by modifying directly the transform, or consider the difference between the desired height and the spline's height, and apply that through the OffsetRadius

FYI, OffsetRadius is used for jumping in example scene 50_EndlessRunner

As I figured out, OffsetRadius is based on Y axis of spline. So using OffsetRadius doesn't help me to implement jump and fall.

I've checked out scene 50_EndlessRunner but it is not a good jump really. As I said when the character is on air it should not depends on Y axis of spline or ground if it depends on Y axis then jumping effect is incorrect. As you can see in this gif from scene 50_EndlessRunner (I just change the spline a little bit for showing incorrect jumping): https://gyazo.com/acf01a2dbb59e06e086e75e5f821928f