Moving between coordinate frames of camera and world space. I found that I was doing way too much when trying to find a single vector, V (of UVN space) from the full transformation matrix. The simplification comes from the substitution of zeroes for the algebra of matrix-vec multiply: Let v' be the vector in world space, v = [0 1 0 0], M a 4x4 transformation matrix. Normally we require: v' = Mv 4 mults, 3 adds for each row column pair --> 16 mults, 12 adds, 4 assignment operations. substituting zeroes v' = | 0 * m0 + 1 * m1 + 0 * m2 + 0 * m3 | | 0 * m4 + 1 * m5 + 0 * m6 + 0 * m7 | | 0 * m8 + 1 * m9 + 0 * m10 + 0 * m11 | | 0 * m12 + 1 * m13 + 0 * m14 + 0 * m15 | = | m1 | | m5 | | m9 | | 0 | 3 assignment ops! Normalise this and the same result as previously obtained! Note that we can only do this since it is a vector, not a vertex. The full transformation, involving translation, is not necessary. I'm sure this speedup will save many trees/babies. Xcode crashing consistently everyday since last post. Am I using it wrong? (Apple says users with iPhone reception problems are using it wrong) :P |
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