Bezier Curves ( Path ) - More less constant speed when traversing through T

Question

Strict facts:

• Unfortunately i am not a math-guru
• I generate a bezier path by drawing it with my finger on the screen
• I have an object that follows this path
• I traverse this path when engine calls Tick(float fDelta) on the object in this manner:

if( m_fBezierTime < 1.0 ) {

m_fBezierTime += 0.1f * fDelta;

m_vPosition = m_Bezier.CalculatePosition(m_fBezierTime);

}

• This kind of approach gives 'huge' acceleration between points that have a higher distance than those being close to each other.

• I have heard this is normal behavior of the Bezier

Now the question :

• How can i make this speed at least 'close' or '~' to constant ?

Thanks for any comments on this.

Answer 1

Simple and fast solution: Get a bunch of regularly distributed points on your Bezier curve (for example 10 points per curve) like you are doing now and measure the Euclidian distance between those points (meaning: sqrt((x_1 - x_2)² + (y_1 - y_2)² … )). This should be a good measure for the length of the full curve, which you can use than to traverse with nearly constant speed.

There is more nifty stuff going on around here: http://steve.hollasch.net/cgindex/curves/cbezarclen.html but that might be overkill.