Question

I am new to unity3d I want to make a path for animated object.
The path must be # elliptical circle # or # spring shape path #
I think there is a way to draw this path based on mathematics equation is it true?
or should I draw it using 3dmax.
Any help or related tutorial for this problem?

thanks

Answer 1

This is a helpful link for drawing a path w/ the mouse in game.

If you want to draw a spring programmatically you can use a Catmullrom or Bezier spline:

double bezier(double t, double p0,double p1,double p2,double p3){
    double t2 = t*t;
    double t3 = t2 * t;
    return (0.16667 *(  t3  *   (-p0 +  3 * p1 + -3 * p2 + p3) +    \
                    t2  *   (3 * p0 + -6 * p1 + 3 * p2) +       \
                    t   *   (-3*p0 + 3*p2) +                    \
                    1   *   (p0 + 4*p1 + p2)));
}
double catmullrom(double t, double p0,double p1,double p2,double p3){
    double t2 = t*t;
    double t3 = t2 * t;
    return (0.5 *(      (2 * p1) + (-p0 + p2) * t +(2*p0 - 5*p1 + 4*p2 - p3) * t2 +(-p0 + 3*p1- 3*p2 + p3) * t3));
}

The inputs p0,p1,p2,p3 are the 4 control points for a particular segment. To see a spiral building example, the rest of this code can be found on my Github page. Look at BuildPath() in particular to see how to use those functions to build a continuous path. I dislike linking to external accounts but my usage example is a little too big for an SO answer.

If you want to draw an ellipse, the simplest way I can think is to solve the basic equation and build a ring of points:

List<Vector3> pts = new List<Vector3>();
for(float x=-2.0f; x<2.0f;x+=0.1){
    y = sqrt( (1-x^2/a^2) * b^2 );//from eq. x^2/a^2 + y^2/b^2=1; 
    pts.Add(new Vector3(x,y,0));
}

That code assumes you have a horizontal major axis where ‘a’ is the radius of the horizontal major axis, ‘b’ is the radius of the vertical minor axis. Build the ellipse first along the X/Y axes and then apply whatever transform you wish to orient the ellipse.

Alternatively, and I don’t have code for this, you can use the general parametric equations to generate a rotated ellipse already off origin.