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Biezer Curves

Started by April 26, 2002 04:23 PM
2 comments, last by VisualB4BigD 22 years, 9 months ago
How would I make them, Is there a formula for this. And how would I make something follow that line? Thanx I sure hope this world isn''t one big joke, because I don''t get it.
There''s an article here on this site. Also, I cover this in "Real Time Rendering Tricks and Techniques in DirectX". (See the DirectX books section of this site).

Basically, the article gives you the formula. It should also give you some ideas on how to move something along that line. Post more questions if you need more help.
Author, "Real Time Rendering Tricks and Techniques in DirectX", "Focus on Curves and Surfaces", A third book on advanced lighting and materials
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P(t)=P0*(1-t)^3+3*P1*(1-t)^2*t+3*P2*(1-t)*t^2+P3*t^3 as t varies from 0 to 1. P0, P1, P2 and P3 are control points with P(0)=P0 and P(1)=P1. The slope, more or less, is the slope of the line from P0 to P1 when t=0 and P2 to P3 when t=1. In between it is a little more complicated, but generally you use a bezier because you want a smooth curve with a certain slope at the end points. That is a vector equation so P(t)=(x(t),y(t),z(t)) where x(t)=P0.x*(1-t)^3+3*P1.x*(1-t)^2*t+3*P2.x*(1-t)*t^2+P3.x*t^3.
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I have a formula for generating Bezier Curve of any degree. If you need it ,ask it here or mail me.

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