Maths Reference

Last updated 3rd May 2004

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Quick reference
Reflection
Specular
where H=normalize(normalize(I)+L)





Euler to Polar (2D)
P is input point.		 Kw
ss
tt
angle
r
Q
 		= any scale value;
= Px - Cs;
= Py - Ct;
= atan(ss, tt) + PI;
= sqrt(ss*ss + tt*tt) * Kw;
= point(angle/(2*PI), r, zcomp(Qin));

Refraction Eta is src refraction index / dst refraction index
Air = 1.003, Aqueous Humor = 1.337 (liquid between cornea and iris)

vector refract( vector I, N; float eta )
{
      float IdotN = I.N;
      float k = 1 - eta*eta*(1 - IdotN*IdotN);
      return k < 0 ? (0,0,0) : eta*I - (eta*IdotN + sqrt(k))*N;
}

Determinant of 2d Matrix
|A| = |a b|
|c d|		 = ad - bc

Cofactor Signs + - + . .
- + - . .
+ - + . .
.
.
the sign of each minor entry is
defined to be the scalar;
(-1)i+j

Inverting 3D matrix 1) Transpose rows and columns of M
2) Replace Elements by their cofactors (the resulting matrix is also called the Adjoint or adjugate matrix M* )
3) Divide matrix (i.e. each element) by the determinant, |M|

Smoothstep float smoothstep( float x )
{
      return (x < 0.f) ? 0.f :
      ((x > 1.f) ? 1.f : x * x * (3.f - 2.f * x));
}
float smoothstep( float x0, float x1, float x )
{
      return (x0 == x1) ?
      (float) (x > x0) : smoothstep ((x - x0) / (x1 - x0));
}

External Links

Matrices & Vectors

Matrix FAQ
Matrix Reference
Matrix Algebra
Matrix Playground MEL script
Quaternions

Calculus

When searching Google about calculus, use "Calculus integration techniques" or "Elementary Integration Methods". These will usually produce a whole bunch of excellent sites.
Calculus review (list of formulae)
sos math : calculus

Miscellaneous

sos math : fourier
york: short list of formulae
Right way to calculate things