I have a set of equation that set up a volume. For example:

z < 3
z > 0
x^2 + y^2 < 1

which defines 3 planes of a cylinder (bottom plane, top plane and the mantle). Or

x^2 + y^2 + z^2 = 1

which defines a sphere.

I like to model volumes that are defined with these type of equations, but have no experience at all with openGL. Before I start diving into this topic, I'd like to know if it is possible to rendered volumes from a set of equations using delphi and openGL. If this is possible relatively easy, can someone tell me how to start?

Well... It is possible. Not in a direct way, but what you want is possible.

If you want to describe Volumes, you should use a Voxel engine. Today, even voxel graphis can be accelerated by OpenGL and with todays power in modern CPUs it should be possible.
This technique however is very complicated and I've mentioned here just for completeness

What you are aiming for is the calculation of volumes to extract polygonal informations. What I want to say is that you have to create Polygons - triangles - out from these volumes. A sphere i.e. can also be described not by volumes but by trigonometric functions. By using sin and cos you can create a sphere out of triangles. Alternatively you could use the glu Quadrics which provide an easy way for creating speheres an other orimitive objects in OpenGL.

OpenGL ist primary an graphics library. It is not designed for rendering volumes.

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I guess I'm looking for a simpler solution. The problem is, a computer program I will have to work with a lot, uses equations such as the ones I mentioned to set up volumes. There is no way of viewing those volumes, and so I thought that maybe I could write a simple Delphi program to do this, apparently I was over optimistic. I have never worked with openGL, and I sort of hoped you could define volumes, something like objectOpenGL.createSphere(x, y, z, radius) but from your words I take it you have to set up some sort of mesh.

Well... OpenGL is based on triangles and other primitives. What types of volumes are you aiming for? As I've already mentioned, the GLU has some helper routines to create spheres, toruses, discs, and some more.

You could, however, simulate volumes with point clouds. You move through a threedimensional array an check - let's say every cm - if this point is in the desired volume. If it is, you can draw a point there with something like this:

x, y and z are your vars in the for-constructs.

You could then adjust the pointsize or alternatively use textures and then you could view volumes This is in it's principles a basic voxel engine accelerated by OpenGL.

_________________
"Für kein Tier wird so viel gearbeitet wie für die Katz'."