How should I specify rectangles in a 3D scene?

When rendering 3D rectangles (i.e. rectang开发者_运维百科les in 3D space), of course, they are specified as a list of vertexes for two triangles. However, that representation contains a lot of extraneous information that gets tiresome to code multiple times. I'd like to create a "Rectangle" object that will allow me to specify its texture, size, position, and orientation in space and export the list of vertexes (and indexes), but I'm not sure of the best way to do it. Should I specify the position of the lower left corner (pre-rotation), or the center of the rectangle? How should I specify the orientation, as a vector containing rotation angles? This is such a simple and standard requirement that I'm sure people have thought about it before, but I can't find anything on this site or elsewhere on the subject. I plan to use these objects a lot, so my primary goal (apart from performance) is ease of use rather than anything to do with the internal representation. It wouldn't be hard for me to simply code the first thing I can think of, but I don't want to miss anything and make it unnecessarily difficult.

So, how should I represent a Rectangle object? Opinions are welcome, but sources would be especially helpful.

Edit: if it helps, I believe I'd primarily be using the rectangles on the faces of cubes, though not necessarily as the entire faces of those cubes.

It would probably be simplest to store the homogeneous matrix that transforms a standard, axis-aligned square into the desired location, along with a separate matrix that determines how to map the texture onto it.

For the location matrix, you can store the 4x3 matrix that doesn't affect the w-coordinate. This is only a bit redundant: it uses 12 values where a general rectangle needs 8, but on the other hand, it will be much easier to convert it back to a form usable for rendering.

Alternately, you can store a point location (edge or center depending on whatever is most convenient), and two direction vectors, describing the direction and length of each edge; you are relying on your rectangle generator to make sure the edge vectors are orthogonal. This will take 9 values, which is almost the best you can do.

For the texture mapping, you can store a 3x2 matrix that defines an affine mapping of the (u,v) coordinates onto the coordinates defined by the edges of the rectangle. You can choose a zero-based (0,1)x(0,1) mapping, or a symmetric (-1,1)x(-1,1) mapping, based on whatever is convenient for your application. In any case, this will require 6 values.

As a rectangle is just a bounded plane, what about storing it as an extension of that: a point and a normal vector (defining the centre---or perhaps one of the corners---and orientation); but add in two more components for the width and height bounds?

I think it really depends on how you intend to use the rectangle.

For example: If you have lots of rectangles, storing the three points of one of the two triangles might be best, because it you only have to calculate one more point.

If you typically center your rectangles on something the center point, width, height and rotation angles might be more appropriate.

I'd say: start with what ever seems naturally for you. Make sure your class is able to do all the necessary calculations and hide them behind accessors. Have a good suite of tests for that.

That way you can change the implementation any time. Or you can even have different rectangle implementations for different needs