4D bezier surface - explanation needed

4D bezier surface - explanation needed

Post by Rudolf Potuc » Tue, 30 Mar 1999 04:00:00



Hi!

I've just been playing around wit hgeomview and I think I understand the
bezier-splines for 2D and 3D. But what is the meaning of the fourth
coordinate in 4D bezier splines? Do I see some kind of 3D section? Does
anyone know a good reference to expain 4D bezier surfaces?

Thx,

  Rudolf

--

 
 
 

4D bezier surface - explanation needed

Post by Nicholas Yu » Fri, 02 Apr 1999 04:00:00


I believe the fourth coordinate is present in homogenous coordinate
system.

        e.g. [x y z w]

        to obtain the actual 3D coordinate

        if (fabs(w)>EPSILON) {
          actualX = x/w;
          actualY = y/w;
          actualZ = z/w;
        }

You may find more detail explaination and mathematics in

        Computer Graphics : Principles and Pratice

        Foley, vanDam, Feiner, Hughes ISBN 0-201-1210-7 (Addison Wesley)


> Hi!

> I've just been playing around wit hgeomview and I think I understand the
> bezier-splines for 2D and 3D. But what is the meaning of the fourth
> coordinate in 4D bezier splines? Do I see some kind of 3D section? Does
> anyone know a good reference to expain 4D bezier surfaces?

> Thx,

>   Rudolf

> --

--
Nicholas Yue                    | RenderMan.

(C)
http://www.cwr.uwa.edu.au/~yue  | +61 8 9380-1897 (Office)
The Centre for Water Research   | +61 8 9380-1015 (Fax)

 
 
 

4D bezier surface - explanation needed

Post by Richard Hil » Wed, 07 Apr 1999 04:00:00


Oh I wondered whether taking Beziers into the 4th Dimension meant
introducing time in to their
definition/.. but I am just guessing.. .

just a thought

rich

 
 
 

1. 4D bezier surface - explanation needed

Hi!

I've just been playing around wit hgeomview and I think I understand the
bezier-splines for 2D and 3D. But what is the meaning of the fourth
coordinate in 4D bezier splines? Do I see some kind of 3D section? Does
anyone know a good reference to expain 4D bezier surfaces?

Thx,

  Rudolf

--

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