Answers for "What is the best way to map the curve of a jump?"
http://answers.unity.com/questions/950561/what-is-the-best-way-to-map-the-curve-of-a-jump.html
The latest answers for the question "What is the best way to map the curve of a jump?"Answer by AlwaysSunny
http://answers.unity.com/answers/950804/view.html
If you have sufficient knowns (you do) you can discover your unknowns.
Have a look at [the "big four" kinematic equations.][1]
You'll need to run the equation several times in a loop with different TIME values to build a prediction. The more iterations (with smaller time steps) the greater the fidelity of the prediction. Each discovered displacement will be a point in the parabola you are creating.
Your goal is the DISPLACEMENT, so methinks
d = (v' * t) + (1/2)(a)(t^2)
is the formula you need. Your ACCELERATION is Physics.gravity. The INITIAL VELOCITY is going to be *the velocity your object would have if he jumped during that frame.* This can be worked out by knowing *the direction and magnitude of the force vector you would apply* and the object's mass.
At each iteration, you may want to also know the FINAL VELOCITY, which would give you the direction of the ray you'd cast to check for a valid landing. There's a formula for that there too. Note this step is somewhat optional. A raycast "down" should be sufficient, perhaps with a "suggestion" of the jump's X direction for added insurance.
This approach will not help you discover any obstacles in the path; for that, you'd have to ray- or sphere-cast along each segment of the parabola. For anything more sophisticated like prediction of reactions to obstacles, you'd need a recursive function that tests for obstacles with each iteration.
[1]: http://www.physicsclassroom.com/class/1DKin/Lesson-6/Kinematic-EquationsMon, 20 Apr 2015 11:43:27 GMTAlwaysSunny