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Projecting Textures On The Environment
Question submitted by (09 July 1999)
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I am trying to code a 3D engine in my spare time, and i got around to
building the lightmapping code for it. The standard lightmapping techniques
are too "standard", so i came up with something else.
Each lightsource is to have a volume, and 6 textures to represent light intensity destribution over it's bounding box(or 8mm slides, for that matter). The scene is then classified(ie clipped to 6 volumes) according to which b-box face goes on what poly. The next step is to project the appropriate texture onto the envirnoment. But, the question is, how do you project textures onto the envirnoment efficiently? There has to be some sort of trick to this, since it's very useful.
it sounds like you want to project, onto the environment, the
six faces of a box that surrounds a point lightsource. if this
is the case, then try the following:
let P be a point on a box face in world coordinates (WC). L is the location of your light source within this box, also in WC. the projection of P onto a surface is
if S is horizontal, where z = 0, then
and the coordinates of S in world coordinates are
the texel value at S(sx, sy, 0) is the same as the texel value at P.
in many instances you want to project a lightmap onto surfaces that are neither horizontal nor axis-aligned on a grid. hacking around with some matrix operations yields the following solution. the projection of P onto S with lightsource at L is
P and L are row vectors and G, the normal of the target surface S, is a column vector. I is an identity matrix. note that the matrix product GL is a 4x4 matrix, and the dot product (L . G) is a scalar.
if you want a full derivation of the following formulation, send e-mail to me at email@example.com
in both solutions, the box faces are *perspectively* projected. as a result, you should not simply project the four corners of a box face and linearly interpolate to yield all texel values for the interior of the box face.
because of this perspective projection, you may need to play around with the location of the lightsource to arrive at the results you want.
Response provided by Hin Jang
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