Hi! I''m wondering... what''s the name for object represented by mathematical formulas? Like spheres, bezier-lines, etc. (Not cubes, triangles.. they''re "point represented") I''d like to know where I can find the correct names for different objects. Like in the animal kingdom, there''s a species name and subspecies and even names above that. Like wolfsomething -> dogs -> doberman hope you understod me :D "No lies of sugar can sweeten the sournes of reality" }+TITANIUM+{ A.K.A. DXnewbie[onMIRC]

really? no one here knows the name for it?... damn...

"No lies of sugar can sweeten the sournes of reality"

}+TITANIUM+{ A.K.A. DXnewbie[onMIRC]

Parametric?

And it''s "canines" for dogs...

ToohrVyk
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kewl, canines

Isn''t parametric like... representing a line in
x = x0 + (x1-x0)*t
y = y0 + (y1-y0)*t

? parametric form?..


I''ve heard the word Quadric, but that seems to be for a phew objects (spheres, etc). Is there a higher level word?

"No lies of sugar can sweeten the sournes of reality"

}+TITANIUM+{ A.K.A. DXnewbie[onMIRC]

i dunno why but the words implicit and explicit spring to mind. could be completely wrong mind you.

I don't think there is really a word describing non mesh-based objects. I would just say "represented by an equation." Parametric is used for many objects, such as splines (1D and 2D). Parametric is not limited to lines, nor is it limited to 2 dimensions. You wrote

x = f1(t)
y = f2(t)

These equations could describe a curve in two dimensions. Also pretty common is this:

x = f1(u,v)
y = f2(u,v)
z = f3(u,v)

These equations would describe a surface in three dimensions.

Ray tracing programs take a more direct approach, without using approximations. They usually use implicit relations, usually in the form

F(x,y,z) = 0

or sometimes

F(x,y,z,t)=0

Then the program will solve to determine whether a certain point in time and/or space fits the equation. Quadric surfaces are usually in this form, and they are used frequently because they are relatively easy to solve. A quadric surface is one where the maximum degree of either x,y or z is 2. They are usually in the form

Ax^2 + By^2 + Cz^2 + Dx + Ey + Fz + Gxy + Hxz + Iyz + J = 0

Or something similar. Then you would have a function that takes A,B,C... as it's arguments, and it would return some value. Spheres, ellipsoids, cones and paraboloids, among other surfaces, are of this form, and cylinders are of a similar form.

I guess that doesn't really answer your question, but I'm going to post it anyway, because it took me like five minutes to type it all up.

You could check out mathworld.com. That's probably the best and biggest math site on the web.

[edited by - I WILL MURDER YOU IN YOUR on February 19, 2003 9:58:07 PM]

Its an interesting question! I too do not think that there is a single proper word, but there are some descriptive phrases that are accurate. Others suggested the word parametric, as in "parametric curve/surface." That is certainly one accurate description of the things you mention. Other descriptions are:

"algorithmic curve/surface"
"continuous curve/surface"

In computer graphics terms, things like bezier surfaces and B-spline surfaces, and NURBS are often called "patches."



Graham Rhodes
Senior Scientist
Applied Research Associates, Inc.