2D projectile trajectory prediction (unity3d) - unity3d

Question

(Using unity3d 4.3 2d, it uses box2d like physics).
I have problems with predicting trajectory
I'm using:
Vector2 startPos;
float power = 10.0f;
float interval = 1/30.0f;
GameObject[] ind;
void Start (){
transform.rigidbody2D.isKinematic = true;
ind = new GameObject[dots];
for(int i = 0; i<dots; i++){
GameObject dot = (GameObject)Instantiate(Dot);
dot.renderer.enabled = false;
ind[i] = dot;
}
}
void Update (){
if(shot) return;
if(Input.GetAxis("Fire1") == 1){
if(!aiming){
aiming = true;
startPos = Input.mousePosition;
ShowPath();
}
else{
CalculatePath();
}
}
else if(aiming && !shot){
transform.rigidbody2D.isKinematic = false;
transform.rigidbody2D.AddForce(GetForce(Input.mous ePosition));
shot = true;
aiming = false;
HidePath();
}
}
Vector2 GetForce(Vector3 mouse){
return (new Vector2(startPos.x, startPos.y)- new Vector2(mouse.x, mouse.y))*power;
}
void CalculatePath(){
ind[0].transform.position = transform.position; //set frist dot to ball position
Vector2 vel = GetForce(Input.mousePosition); //get velocity
for(int i = 1; i < dots; i++){
ind[i].renderer.enabled = true; //make them visible
Vector3 point = PathPoint(transform.position, vel, i); //get position of the dot
point.z = -1.0f;
ind[i].transform.position = point;
}
}
Vector2 PathPoint(Vector2 startP, Vector2 startVel, int n){
//Standard formula for trajectory prediction
float t = interval;
Vector2 stepVelocity = t*startVel;
Vector2 StepGravity = t*t*Physics.gravity;
Vector2 whattoreturn = ((startP + (n * stepVelocity)+(n*n+n)*StepGravity) * 0.5f);
return whattoreturn;
}
Using this, I get wrong trajectory.
1. It's like gravity doesn't drag trajectory down at all, and yes i know that gravity is weak because:
t*t*Physics.gravity = 0.03^2 * vector2(0, -9.8) = vector2(0, -0.00882)
But that is the formula :S
2. Since gravity is low, velocity is too strong.
Here is the video:
http://tinypic.com/player.php?v=1z50w3m&s=5
Trajectory formula form:
http://www.iforce2d.net/b2dtut/projected-trajectory
What should I do?
I found that if I set
StepGravity to something stronger like (0, -0.1)
and devide startVel by 8
I get nearly right trajectory, but i don't want that, I need true trajectory path.
Users from answer.unity3d.com said I should ask here, because here is a bigger group of mathematical coders.
And I searched a lot about this problem (that how I found that formula).

Answer 1

you're only calculating the effect of gravity over 1/30th of a second for each step - you need to do it cumulatively. Step 1 should end with a velocity of 0.09G, Step 2 with .18G, step3 with .27G etc.
Here's a very simple example that draws the ballistic trajectory based on start velocity and a supplied time:
using UnityEngine;
using System.Collections;
public class grav : MonoBehaviour {
public Vector3 StartVelocity;
public float PredictionTime;
private Vector3 G;
void OnDrawGizmos()
{
if (G == Vector3.zero)
{
// a hacky way of making sure this gets initialized in editor too...
// this assumes 60 samples / sec
G = new Vector3(0,-9.8f,0) / 360f;
}
Vector3 momentum = StartVelocity;
Vector3 pos = gameObject.transform.position;
Vector3 last = gameObject.transform.position;
for (int i = 0; i < (int) (PredictionTime * 60); i++)
{
momentum += G;
pos += momentum;
Gizmos.DrawLine(last, pos);
last = pos;
}
}
}
In you version you'd want draw your dots where I'm drawing the Gizmo, but it's the same idea unless I'm misunderstanding your problem.