## Sunday, February 13, 2011

### XNA Bezier Curve Editor Demo

Here is a quick look at the Bezier Curve editor I made in XNA that uses the function from my prior blog . Note there are circular Paths each withe 3 segments. Each segment is a 4 point Bezier calculation.

The basic tricks in getting this to be a smooth curve across the whole path is to:

1. p3 of the each segment is in common to p0 of next each segment.
2. To make the circular, p3 of last segment must be same as p0 of 1st segment.
3. p2 and p3 of each segment must be on a strait line with p0 and p1 or the next segment. So this means
• If a path point was moved by user, you must also move left and right control handler points by same deltas
• If left handler moved,  must also move corresponding path point so it intersects line to other handler at mid point
• If right handler moved, must also move corresponding path point so it intersects line to other handler at mid point

### Simple function for a Bezier Curve in C#

The Bezier Curve formula below can be used to define  smooth curves between points in space.

P(t) = (1-t)^3P0 + 3(1-t)^2tP1 + 3(1-t)t^2P2 + t^3P3

The function below is a C# implementation of the formula return the X and Y coordinates for Time (t) given the 4 points that define the Bezier Curve.  You can extend this to 3D very easily.  Include this function in your c# projects to create smooth curves and multi-segment paths.  In a future post I will show how to implement multi-segment paths and circular paths using Bezier Curves.   I used this function and technique in my XNA game projects that required smooth paths for my objects.  I was also able to create a multi-segment curve editor which I will try to cover later on.

C# Code Sample:

private Vector2 GetPoint(float t, Vector2 p0, Vector2 p1, Vector2 p2, Vector2 p3)
{
float cx = 3 * (p1.X - p0.X);
float cy = 3 * (p1.Y - p0.Y);

float bx = 3 * (p2.X - p1.X) - cx;
float by = 3 * (p2.Y - p1.Y) - cy;

float ax = p3.X - p0.X - cx - bx;
float ay = p3.Y - p0.Y - cy - by;

float Cube = t * t * t;
float Square = t * t;

float resX = (ax * Cube) + (bx * Square) + (cx * t) + p0.X;
float resY = (ay * Cube) + (by * Square) + (cy * t) + p0.Y;

return new Vector2(resX, resY);
}

To use the function, simply pass in the 4 point and a time (between 0 and 1).   At  t=0 you will be at p0, and at t=1 you will be at p3.      To draw the curve, try calling this function from a for loop that looks something like this: